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The present treatise assembles the theoretical foundations and experimental results on the generation and propagation of water waves generated by underwater explosions. After a brief overview of the physical processes and a presentation of order of magnitude of explosion generated water waves (EGWW) as function of explosion parameters, linear theories and experimental calibration are presented. Nonlinear wave theories and their calibration are necessary in shallow water when the water crater caused by the explosion is not small compared to water depth. The importance of dissipation processes due to wave-sea floor interactions is emphasized, particularly when an EGWW travels on long continental shelf. Methodologies for the propagation of transient waves over 3D bathymetries are developed. The simulation of EGWW in the laboratory is reviewed. Finally, a numerical method based on Boundary Integral Method is applied to investigate the dynamic of bubble formation and wave generation near the explosion. (MM)

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... The characteristics of a tsunami generated by a subaqueous volcanic explosion are shown in Figure 1c. For example, in the case of the 1716 eruption in Taal Lake, tsunamis are controlled by several physical parameters, such as water depth, size of the eruption vent, depth and energy of the explosion, and magma-water interaction, which are used to define the explosion itself (as explained in detail in Le Mehaute [10]; Kokelaar [11]; Wohletz [12]; Mirchina and Pelinovsky [13]; Duffy [14]; Le Mehaute and Wang [15]; Kedrinskii [16]; Egorov [17]; Morrissey et al. [18]; Paris and Ulvrova [3]). The explosion forms an initial crater, resulting in a similar cavity at the water surface with a cylindrical bore. ...

... The initial water displacement downward follows the upward displacement and forms a steep cone in the center of the bore. The cone collapses and generates a second bore, as reproduced by the experimental explosion and numerical models in previous studies [3,15,16,21,22]. ...

... The estimation of the maximum initial water level is related to the explosion energy and water depth of the explosion in the empirical function presented by Le Mehaute and Wang [15]: ...

A probabilistic hazard analysis of a tsunami generated by a subaqueous volcanic explosion was performed for Taal Lake in the Philippines. The Taal volcano at Taal Lake is an active volcano on Luzon Island in the Philippines, and its eruption would potentially generate tsunamis in the lake. This study aimed to analyze a probabilistic tsunami hazard of inundated buildings for tsunami mitigation in future scenarios. To determine the probabilistic tsunami hazard, different explosion diameters were used to generate tsunamis of different magnitudes in the TUNAMI-N2 model. The initial water level in the tsunami model was estimated based on the explosion energy. The tsunami-induced inundation from the TUNAMI-N2 model was overlaid on the distribution of buildings. The tsunami hazard analysis of inundated buildings was performed by using the maximum inundation depth in each explosion case. These products were used to calculate the probability of the inundated building given the occurrence of a subaqueous explosion. The results from this study can be used for future tsunami mitigation if a tsunami is generated by a subaqueous volcanic explosion.

... Generation of waves by underwater explosions is well documented (Le Méhauté, 1971;Duffy, 1992;Le Méhauté and Wang, 1996;Egorov, 2007). Immediately following the explosion, a water crater is formed at certain conditions depending on the water depth and the energy of explosion. ...

... Following the work of Torsvik et al. (2010) and Ulvrová et al. (2014), we adopt a semi-analytical approach where the dynamics of the underwater explosion is neglected by simply imposing an initial water disturbance whose propagation is modelled numerically. Initial surface displacement can be estimated as a function of explosion energy at a given depth, using the empirical formula of Le Méhaute and Wang (1996): ...

... where ƞ 0 is the vertical initial surface displacement in metres, E the energy of explosion in joules and c a constant. According to the explosion yield and water depth, two cases are distinguished (Le Méhaute and Wang, 1996): (1) c = 0.014 for smaller explosions for which holds 0.076 b d/W 1/3 b 2.286 (d: the depth of explosion in metres; W: the explosion yield in pounds of TNT); (2) c = 0.029 for larger explosions where 0 b d/W 1/3 b 0.076. A shallower explosion thus causes a deeper water crater for the same yield. ...

The 1650 AD explosive eruption of Kolumbo submarine volcano (Aegean Sea, Greece) generated a destructive tsunami. In this paper we propose a source mechanism of this poorly documented tsunami using both geological investigations and numerical simulations. Sedimentary evidence of the 1650 AD tsunami was found along the coast of Santorini Island at maximum altitudes ranging between 3.5 m a.s.l. (Perissa, southern coast) and 20 m a.s.l. (Monolithos, eastern coast), corresponding to a minimum inundation of 360 and 630 m respectively. Tsunami deposits consist of an irregular 5 to 30 cm thick layer of dark grey sand that overlies pumiceous deposits erupted during the Minoan eruption and are found at depths of 30–50 cm below the surface. Composition of the tsunami sand is similar to the composition of the present-day beach sand but differs from the pumiceous gravelly deposits on which it rests. The spatial distribution of the tsunami deposits was compared to available historical records and to the results of numerical simulations of tsunami inundation. Different source mechanisms were tested: earthquakes, underwater explosions, caldera collapse, and pyroclastic flows. The most probable source of the 1650 AD Kolumbo tsunami is a 250 m high water surface displacement generated by underwater explosion with an energy of ~ 2 × 1016 J at water depths between 20 and 150 m. The tsunamigenic explosion(s) occurred on September 29, 1650 during the transition between submarine and subaerial phases of the eruption. Caldera subsidence is not an efficient tsunami source mechanism as short (and probably unrealistic) collapse durations (< 5 min) are needed. Pyroclastic flows cannot be discarded, but the required flux (106 to 107 m3 · s− 1) is exceptionally high compared to the magnitude of the eruption.

... However, the present report studied the underwater explosions primarily because the converted energy to water waves is significantly larger for air explosions. It is well established that the use of a surface deformation as an initial condition results in a wave train which is qualitatively similar to those measured in explosions, (LeMéhauté and Wang [48]). ...

... Most types of free surface deformations were studied and applied for simulation and prediction of primary water wave generation due to the underwater explosion (see Figs. 4, 5, and 6). The most applied initial functions are presented by Whalin [18,49] and LeMehaute [12,48] as follows: The law of conservation of mass is ignored in the quadratic deformation without the lip (see Fig. 4), but other formulas tried to observe the law. In the second form, an uncommon discontinuity is produced in the geometry of water surface by the outer face of lip area in the vicinity of water-free surface line. ...

... 1. 40% in the pulsating motion of bubble, 2. 30% wasted irreversibly in water heating, and 3. 30% is radiated as a nonreturning pressure pulse. It is also found that the kinetic energy applied to bubble pulsation phenomenon causes water wave generation (Whalin, [49]; LeMehaute, [12,48]), and then 40% of total released explosion energy can be equated with water wave energy. ...

The current paper discusses the physical impacts of the various initial boundary conditions of the free surface of a waterbody on the initiation and propagation characteristics of water waves due to the underwater perturbations. Differences between traditional point of view and applied numerical method in this paper for exertion the initial conditions of the generated waves by surface deformation were surveyed in the Lagrangian domain vs. Eulerian. In this article, the smoothed-particle hydrodynamics (SPH) technique was applied for simulating of wave generation process using initial boundary condition of water surface deformation through utilizing DualSPHysics numerical code and comparing the modeling results with recorded data. As a distinct approach, we studied the effects of discrete water particles on properties of produced surface waves by using the Lagrangian analytical capability of SPH model. Illustrative compatibility on simulation results with experimental data proves that meshless techniques such as applied in DualSPHysics software can reproduce physical properties of the event very well, and this is a suitable alternative to existing classical approaches for prediction of shock occurrences with nonlinear behavior such as generated surface water waves by underwater disturbance. Besides, the waveforms and their characteristics behave more realistic by considering the thrown upward water mass which was not directly considered in old formula and theories. The results of numerical modeling indicated rational agreement between numerical and empirical data proving that a complicated nonlinear phenomenon could be predicted by an SPH model which modified initial boundary conditions were supposed into the model with actual assumptions.

... As a result, significant research efforts have usually been focused on non-linear fluid-structure interactions such as pressure loading from shock waves rather than any wave generation relationships. Still, some tests were conducted on this matter during the nucleartesting age and led to the development of theoretical models describing explosion-surface interaction and dynamics of the resultant wave field (Le Méhauté and Wang, 1996). Physical experimentation since the end of nuclear testing has been rare 50 due to cost, practicalities, environmental concerns and the challenges of scale experienced by previous tests. ...

... The current theoretical models summarised by Le Méhauté and Wang (1996) have been used in recent years to simulate the wavefield generated from events that produce analogous water surface cavitation such as submarine volcanic explosions 55 (Torsvik et al., 2010;Ulvrová et al., 2014; and asteroids impacting in ocean 2 https://doi.org/10.5194/nhess-2021-109 Preprint. ...

... (Le Méhauté, 1971;Le Méhauté and Wang, 1996) Bubble dynamics is a very active area of research in computational fluid dynamics (CFD), though, in the explosive realm, 85 the focus is usually on pressure waves and solid interactions . These studies are usually short in temporal range and are very computationally expensive as modelling the full problem requires accounting for compressibility and multiphase flow; thus, this has spawned specialist codes for their solution (Hallquist, 1994;Li et al., 2018). ...

Theoretical source models of underwater explosions are often applied in studying tsunami hazards associated with submarine volcanism; however, their use in numerical codes based on the shallow water equations can neglect the significant dispersion of the generated wavefield. A non-hydrostatic multilayer method is validated against a laboratory-scale experiment of wave generation from instantaneous disturbances and at field-scale submarine explosions at Mono Lake, California, utilising the relevant theoretical models. The numerical method accurately reproduces the range of observed wave characteristics for positive disturbances and suggests a previously unreported relationship of extended initial troughs for negative disturbances at low dispersivity and high nonlinearity parameters. Satisfactory amplitudes and phase velocities within the initial wave group are found using underwater explosion models at Mono Lake. The scheme is then applied to modelling tsunamis generated by volcanic explosions at Lake Taupō, New Zealand, for a magnitude range representing ejecta volumes between 0.04–0.4 km3. Waves reach all shores within 15 minutes with maximum incident crest amplitudes around 4 m at shores near the source. This work shows that the multilayer scheme used is computationally efficient and able to capture a wide range of wave characteristics, including dispersive effects, which is necessary when investigating submarine explosions. This research therefore provides the foundation for future studies involving a rigorous probabilistic hazard assessment to quantify the risks and relative significance of this tsunami source mechanism.

... On the contrary, the theory of waves generated by subaqueous explosions is well documented (Le Méhauté 1971;Mirchina and Pelinovsky 1988;Duffy 1992;Le Méhauté and Wang 1996;Egorov 2007). This particular type of tsunami consists of two main waves followed by smaller undulations propagating radially from the source, as demonstrated by experiments and numerical simulations (e.g., Le Méhauté and Wang 1996;Kedrinskii 2005;Torsvik et al. 2010;Ulvrova et al. 2014Ulvrova et al. , 2016. ...

... On the contrary, the theory of waves generated by subaqueous explosions is well documented (Le Méhauté 1971;Mirchina and Pelinovsky 1988;Duffy 1992;Le Méhauté and Wang 1996;Egorov 2007). This particular type of tsunami consists of two main waves followed by smaller undulations propagating radially from the source, as demonstrated by experiments and numerical simulations (e.g., Le Méhauté and Wang 1996;Kedrinskii 2005;Torsvik et al. 2010;Ulvrova et al. 2014Ulvrova et al. , 2016. The water is initially pushed upward (Fig. 2), forming a crater with a cylindrical bore that expands radially to form the leading wave, followed by a wave trough. ...

... The water crater collapses as in a dam break model, generating a steep cone of water in the centre that turns to a second cylindrical bore (Le Méhauté and Wang 1996). Subaqueous explosions typically generate short-period waves compared to earthquakes, and most of the time, the impact in the far field is limited (Latter 1981;Begét 2000;Paris 2015). ...

Volcanic subaqueous explosions can generate hazardous tsunamis, especially in lakes. In this paper, we simulate different scenarios of subaqueous explosions and related tsunamis in Taal Caldera Lake (Luzon, Philippines). Taal volcano is one of the most active volcanoes in Southeast Asia, and eruptive processes are mostly explosive. We test different energies of explosions at eight different explosion sites in the lake. The initial water surface displacement (ƞ0) generated by the explosion is estimated as a function of explosion energy at a given depth. We estimate the tsunami travel times, maximum wave heights, and wave periods at the shoreline. This type of hazard is typically neglected and our work has important implications for hazard assessment around Taal Lake. Due to fast propagation of tsunamis in the lake (waves typically crossing the lake in less than 10 min), there is only a short time available for issuing a warning. For ƞ0 ≤ 50 m, wave heights at the shoreline are less than 2 m with a non-dispersive numerical model, and less than 0.5 m with a dispersive model, whatever the explosion depth and location. Powerful explosions with ƞ0 > > 100 m generate wave heights greater than 2 m all around the lake and local peaks higher than 10 m.

... As a result, significant research efforts have usually been focused on non-linear fluid-structure interactions such as pressure loading from shock waves rather than any wave generation relationships. Still, some tests were conducted on this matter during the nuclear-testing age and led to the development of theoretical models describing explosion-surface interaction and dynamics of the resultant wave field (Le Méhauté and Wang, 1996). Physical experimentation since the end of nuclear testing has been rare due to cost, practicalities, environmental concerns, and the challenges of scale experienced by previous tests. ...

... The current theoretical models summarised by Le Méhauté and Wang (1996) have been used in recent years to simulate the wavefield generated from events that produce analogous water surface cavitation such as subaqueous volcanic explosions (Torsvik et al., 2010;Ulvrová et al., 2014; and asteroids impacting in ocean basins (Ward and Asphaug, 2000). However, numerical solutions often either utilise the empirically derived relations without validating their use in a numerical scheme against a suitable explosive physical experiment or test a generation mechanism in the local spatial range only at the cost of neglecting investigation of the generated wave field. ...

... This free-surface interaction is strongly linked with the depth of explosion relative to its energy; small-yield or deep detonations lead the explosive bubble to transfer a large portion of its energy to the surrounding water through rapid oscillations, which significantly reduces wave-making efficiency. (Le Méhauté, 1971;Le Méhauté and Wang, 1996) Bubble dynamics is a very active area of research in computational fluid dynamics (CFD), although, in the explosive realm, the focus is usually on pressure waves and solid interactions . These studies are usually short in temporal range and are very computationally expensive as modelling the full problem requires accounting for compressibility and multi-phase flow; thus, researchers have generated specialised codes as a solution (Hallquist, 1994;Li et al., 2018). ...

Theoretical source models of underwater explosions are often applied in studying tsunami hazards associated with subaqueous volcanism; however, their use in numerical codes based on the shallow water equations can neglect the significant dispersion of the generated wavefield. A non-hydrostatic multilayer method is validated against a laboratory-scale experiment of wave generation from instantaneous disturbances and at field-scale subaqueous explosions at Mono Lake, California, utilising the relevant theoretical models. The numerical method accurately reproduces the range of observed wave characteristics for positive disturbances and suggests a relationship of extended initial troughs for negative disturbances at low-dispersivity and high-non-linearity parameters. Satisfactory amplitudes and phase velocities within the initial wave group are found using underwater explosion models at Mono Lake. The scheme is then applied to modelling tsunamis generated by volcanic explosions at Lake Taupō, New Zealand, for a magnitude representing an ejecta volume of 0.1 km3. Waves reach all shores within 15 min with maximum incident crest amplitudes around 0.2 m at shores near the source. This work shows that the multilayer scheme used is computationally efficient and able to capture a wide range of wave characteristics, including dispersive effects, which is necessary when investigating subaqueous explosions. This research therefore provides the foundation for future studies involving a rigorous probabilistic hazard assessment to quantify the risks and relative significance of this tsunami source mechanism.

... A certain insight into the hydrodynamics of underwater explosions brings laboratory experiments by studying nuclear and chemical explosions (e.g. Le Méhauté and Wang, 1996;Kedrinskii, 2005). It has been observed that just after detonation, a cavity consisting predominantly of water vapour is formed. ...

... In this case, an underwater eruption is approximated by imposing a specific initial water disturbance whose propagation is modelled numerically. Although this strategy might seem too simplistic, Le Méhauté and Wang (1996) show that it reproduces satisfactorily characteristics of the wave field over a uniform depth bottom at a far distance using nonlinear and linear wave theory in comparison with artificially generated underwater explosions. The "far distance" is generally the distance where leading wave characteristics are formed but the non-linear behaviour can be ignored (i.e. three to four characteristic radii far from the detonation centre). ...

... Le Méhauté and Wang (1996) propose several uniformly valid mathematical models for the initial water displacement (η). Combining inverse transformation together with experimental wave records and theoretical solutions for simplified cases leads to the initial water disturbance that approximate the explosion source being a parabolic crater with a vertical steep water rim that also physically corresponds to water surface displacement observed in near-surface explosion experiments (Van Dorn et al., 1968). ...

Increasing human activities along the coasts of the world provoke the
necessity to assess tsunami hazard from different sources (earthquakes,
landslides, volcanic activity). In this paper, we simulate tsunamis generated
by underwater volcanic explosions from (1) a submerged vent in a shallow
water lake (Karymskoye Lake, Kamchatka), and (2) from Kolumbo submarine
volcano (7 km NE of Santorini, Aegean Sea, Greece). The 1996 tsunami in
Karymskoye lake is a well-documented example and thus serves as a case study
for validating the calculations. The numerical model reproduces realistically
the tsunami run-ups measured onshore. Systematic numerical study of tsunamis
generated by explosions of the Kolumbo volcano is then conducted for a wide
range of energies. Results show that in case of reawakening, the Kolumbo
volcano might represent a significant tsunami hazard for the northern,
eastern and southern coasts of Santorini, even for small-power explosions.

... Le Méhauté and Wang 1996. ...

... Le Méhauté and Wang 1996. 29 Cole 1965; Geers and Hunter 2002. ...

Underwater explosive devices, such as improvised explosive devices (IED), offer a high-risk threat within the maritime domain. An attack on ships in harbours, coastal infrastructure, such as locks and quays, by underwater explosives could have a detrimental effect on infrastructure functionality and national economy. Here, the physical effects of underwater explosives are reviewed and compared to surface firings. Next, a few examples in the maritime domain are treated in more detail: ships, divers and swimmers, tourist beaches, dikes, infrastructural assets and near-shore sea-bed communication. Moreover, possible detection methods and counter-strategies are discussed. A methodology for risk analysis of underwater explosion threats is outlined. Finally, conclusions and challenges for the future, focused on scientific research and preventive approaches are given.

... Specific source mechanisms of volcanic tsunamis include underwater explosions, pyroclastic flows, lava, and lahars entering the water, slope failures, volcanic earthquakes, shock waves from large explosions, and caldera subsidence (Begét, 2000;Day, 2015;Latter, 1981;Kienle et al., 1987;Paris, 2015). Volcanic tsunamis are generally characterized by short-period waves, greater dispersion, and limited far-field effects compared to earthquake-generated tsunamis, but the diversity of source mechanisms imply different types of waves (e.g., Choi et al., 2003;Le Méhauté & Wang, 1996;Nomanbhoy & Satake, 1995;Maeno & Imamura, 2011;Watts & Waythomas, 2003;Yokoyama, 1987). Owing to the diversity of complexity of these sources, inclusion of volcanic tsunamis into PTHA developed slowly. ...

... In the case of underwater eruptions, the expansion, rise, and gravitational collapse of the water crater produced by the explosion itself can produce tsunamis, depending on the water depth and energy of explosion (e.g., Le Méhauté & Wang, 1996). The best documented example is the 1996 tsunami in Karymsky Lake (Belousov et al., 2000;Torsvik et al., 2010;Ulvrova et al., 2014). ...

... It is interesting to note that tsunamis generated by underwater explosions consist of two main waves followed by smaller undulations, as demonstrated by experiments and numerical simulations (e.g. Le Méhauté & Wang, 1996;Kedrinskii, 2005;Torsvik et al., 2010;Ulvrová et al., 2014). The water is initially pushed upward and radially, forming a crater and a cylindrical bore expanding radially to form the leading wave, followed by a wave trough. ...

... The water is initially pushed upward and radially, forming a crater and a cylindrical bore expanding radially to form the leading wave, followed by a wave trough. The water crater then collapses as in a dam break model, thus generating a peak of water in the centre and a second cylindrical bore that progressively turns to a non-dissipative wave (Le Méhauté & Wang, 1996). However, a reflected wave or an uprushbackwash succession could also explain the structure and two-peak distribution of heavy minerals. ...

The concentration and distribution of heavy minerals in tsunami deposits is not random and mostly source-dependent. Heavy minerals may thus be good indicators of sediment provenance and tsunami flow dynamics. The tsunamis generated by the 1996 phreato-magmatic eruption in Karymskoye Lake represent a relevant case-study because the provenance of the abundant heavy minerals found in the tsunami deposits is well constrained (the on-going basaltic eruption itself). X-ray computed tomography (X-CT) of cores of tsunami sediments is used to identify heavy minerals and characterise their source and spatial distribution in the tsunami deposit, and to propose a scenario of the coupled eruption and tsunamis. An original combination of methods including X-CT, SEM and XRF core scanner allows distinguishing subunits corresponding to pulses of sediments deposition and associated inputs of heavy minerals, together with erosive contacts, laminations, and rip-up clasts of the substratum. The structure of the tsunami deposits suggests that a major tsunami consisting of two main waves inundated the coastal terrace up to 100 m inland on the eastern shore of the lake; a scenario that is consistent with waves generated by experimental explosions. This largest tsunami might have occurred when underwater explosions were at a critical water depth of 40 m (corresponding to a two-third submerged explosion in the 60 m deep lake). However, more investigations are needed to better understand the critical conditions leading to a tsunami during underwater eruptions.

... An active sonar system emits a short duration acoustic pulse that is propagated in the wa ter towards the desired target. There are two broad classes of pulses: coherent and incoherent sources (Le Méhauté & Wang, 1996;Urick, 1983). The choice o f pulse type is ap plication specific (Horton, 1957;Le Méhauté & Wang, 1996;Waite, 2002). ...

... There are two broad classes of pulses: coherent and incoherent sources (Le Méhauté & Wang, 1996;Urick, 1983). The choice o f pulse type is ap plication specific (Horton, 1957;Le Méhauté & Wang, 1996;Waite, 2002). The returned signal from the pulse received at the hydrophone array contains one or more echoes. ...

Sustained attention or operator vigilance is required in the detection of critical signals that occur infrequently and at irregular intervals over a prolonged period. In this paper, we review some methods for mitigating the vigilance decrement for an auditory sonar monitoring task. These methods pertain to enhancing the saliency of sonar targets for situations when the operator may be required to monitor multiple displays, listen to competing sound sources, attend to distractions, and cope with ambient noise. Enhanced target saliency is expected to assist in maintaining operator efficiency via increasing detection rate and decreasing detection latency of auditory sonar targets. This should lead to tactical superiority of sonar operators in the continuing threat of underwater warfare.

... However, nonlinear convective and dissipative effects are difficult to resolve or even formulate mathematically, although these effects are often too important to be neglected. Therefore, it would seem that there is little hope that such complex phenomenology can lead to well defined input boundary conditions to determine the wave field [1]. Physical models that include all main stages and features of the processes occurring in liquids must remain a key element in research [2]. ...

... First conclusion. This overview is based chiefly on the analysis of two monographs devoted to underwater explosions [1,2]. It is the authors' opinion that the little progress in the understanding of a shock-loaded liquid is connected mainly with the effort of the researchers to put such complex phenomenon as underwater explosion to Procrustean bed of the hydrodynamic phenomenology of wave generation and wave propagation. ...

In this contribution we report on modeling underwater explosion in the framework of molecular dynamics. We have developed a computer program which allows studying the underwater explosion in two dimensional Lennard – Jones liquid. Calculations of the dynamical structure of underwater explosion displayed the striking resemblance of the underwater-explosion evolution obtained and the real process; namely, generation of a shock wave and its expanding; formation of a cavity; disintegrating the shock wave, when reaching a surface, into two parts which begin to move in opposite direction parallel to the surface; transforming the cavity into a water crater of an arising water volcano; its activity and decay.

... Another main effect of the depth parameter is connected to the preloading of the structure due to the initial hydrostatic pressure. To better quantify this effect, a scaled depth parameter is implemented as follows [31]: ...

Incremental explosive analysis (IEA) is addressed as an applicable method for performance-based assessment of stiffened and unstiffened cylindrical shells subjected to underwater explosion (UNDEX) loading. In fact, this method is inspired by the incremental dynamic analysis (IDA) which is a known parametric analysis method in the field of earthquake engineering. This paper aims to introduce the application of IEA approach in UNDEX in order to estimate different limit states and deterministic assessment of cylindrical shells, considering the uncertainty of loading conditions. The local, bay, and general buckling modes are defined as limit states for performance calculation. Different standoff distances and depth parameters combining several loading conditions are considered. The explosive loading intensity is specified and scaled in several levels to force the structure through the entire range of its behavior. The results are plotted in terms of a damage measure (DM) versus selected intensity measure (IM). The statistical treatment of the obtained multi-IEA curves is performed to summarize the results in a predictive mode. Finally, the fragility curves as damage probability indicators of shells in UNDEX loading are extracted. Results show that the IEA is a promising method for performance-based assessment of cylindrical shells subjected to UNDEX loading.

... In the case of underwater eruptions, the expansion, rise, and gravitational collapse of the water crater produced by the explosion itself can produce tsunamis, depending on the water depth and energy of explosion (e.g., Le Méhauté & Wang, 1996). The best documented example is the 1996 tsunami in Karymsky Lake (Belousov et al., 2000;Torsvik et al., 2010;Ulvrova et al., 2014). ...

Applying probabilistic methods to infrequent but devastating natural events is intrinsically challenging. For tsunami analyses, a suite of geophysical assessments should be in principle evaluated because of the different causes generating tsunamis (earthquakes, landslides, volcanic activity, meteorological events, asteroid impacts) with varying mean recurrence rates. Probabilistic Tsunami Hazard Analyses (PTHAs) are conducted in different areas of the world at global, regional, and local scales with the aim of understanding tsunami hazard to inform tsunami risk reduction activities. PTHAs enhance knowledge of the potential tsunamigenic threat by estimating the probability of exceeding specific levels of tsunami intensity metrics (e.g., runup or maximum inundation heights) within a certain period of time (exposure time) at given locations (target sites); these estimates can be summarized in hazard maps or hazard curves. This discussion presents a broad overview of PTHA, including: (i) sources and mechanisms of tsunami generation, emphasizing the variety and complexity of the tsunami sources and their generation mechanisms; (ii) developments in modeling the propagation and impact of tsunami waves; (iii) statistical procedures for tsunami hazard estimates that include the associated epistemic and aleatoric uncertainties. Key elements in understanding the potential tsunami hazard are discussed, in light of the rapid development of PTHA methods during the last decade and the globally distributed applications, including the importance of considering multiple sources, their relative intensities, probabilities of occurrence and uncertainties in an integrated and consistent probabilistic framework.

... Close to formation, waves are highly nonlinear. But sufficiently far from the generation point the waves stabilize (Kamphuis & Bowering, 1970) and begin assuming a linear behaviour (Le Méhauté & Wang, 1996). The principles of equipartition, E w ≈ 2E w,pot , and conservation of the total energy E w are confirmed by the measurement done in the tank where: ...

ABSTRACTLandslides falling into water bodies can generate impulsive waves, which are a type of tsunamis. The propagating wave may be highly destructive for hydraulic structures, civil infrastructure and people living along the shorelines. A facility to study this phenomenon was set up in the laboratory of the Technical University of Catalonia. The set-up consists of a new device releasing granular material at high velocity into a wave basin. A system employing laser sheets, high-speed and high-definition cameras was designed to accurately measure the high velocity and geometry of the sliding mass as well as the produced water displacement in time and space. The analysis of experimental data helped to develop empirical relationships linking the landslide parameters with the produced wave amplitude, propagation features and energy, which are useful tools for the hazard assessment. The empirical relationships were successfully tested in the case of the 2007 event that occurred in Chehalis Lake (Canada).

... Oscillations of a liquid in a closed or semi-closed basin are phenomena of interest to various fields, including hydraulic, coastal, structural, and vehicle engineering, and can be generated by a number of causes, such as the oscillating motion of a partially filled tank [1] , the shear action of wind on the water surface [2,3] , a moving disturbance on the bottom [4][5][6] , the fall of a body, a landslide or snow avalanche into water (e.g., [7][8][9] ), an underwater explosion (e.g., [10] ), or seismic excitation. Earthquakes are natural events which may cause widespread devastation and extensive damage in terms of both casualties and economic losses. ...

In this paper time-dependent water motions generated by seismic-type horizontal excitation in shallow basins and channels are modelled by the two-dimensional depth-averaged shallow water equations in which a specific source term is added in order to include an earthquake-induced forcing effect. Sinusoidal excitation is considered as a first approximation, and the response of shallow basins and channels to this simple external forcing is characterized. The nondimensional form of the governing equations shows that the Strouhal number and a ratio representing the amplitude of the forcing acceleration are the influential dimensionless parameters. Novel exact solutions of sinusoidally-forced smooth waves in a prismatic tank, a rectangular open channel, and a parabolic basin are presented. In the first two cases, a sway motion occurs, and reflections take place at the side walls. In the last case, the water sloshes back and forth flowing up the sloping sides of the basin; the free surface remains planar and a moving circular shoreline is present. These analytical solutions provide useful standards for assessing the accuracy of the numerical models used to solve the two-dimensional shallow water equations with source terms.

... Unfortunately, it can be explosive, and in this case, the dynamics of the discharge are much more complex to represent within particular high temperature gases. The works of Le Méhauté and Wang [1996] and Kurkin and Pelinovsky [2004] (see Levin and Nosov [2009]) approach the real phenomena with the following estimation of the initial free surface deformation: ...

The impact of tsunamis on mankind is well known. During recent years, several events showed us the disasters they can trigger which reiterate the importance of understanding their dynamics. Due to the lack of in-situ data, the generation is the least known aspect of tsunamis. As a result, simplified models of the source are used for numerical tsunami modeling, as for seismic generation for which the traditional approach neglects several phenomena, among which is the kinematic deformation of the sea floor. This motion canbe characterized by two temporal parameters: the rupture velocity vp and a hydraulic rise time tr. The novelty here, is to investigate both parameters simultaneously and to extend the linear theoretical development to a non-linear numerical study. From these works, a resonance zone is identified for small tr and vp close to the long wave celerity. For these particular values, the waves are amplified beside the sea floor deformation and dispersive effects develop. To illustrate this theory, the 1947 New Zealand tsunami is simulatedwith the Non-Linear Shallow Water and Boussinesq models of Telemac2D. This seismic event corresponds to a tsunami earthquake with slow kinematics of deformation. Four generation models, with different values of vp and tr are compared. The impact of vp on the generated wave amplitudes is strong whereas the influence due to tr is significantly smaller. Additionally, it was found that the expected dispersive effects did not develop during the numerical modeling. Meanwhile, in the scope of the TANDEM project, the validation of the Telemac system is performed through test cases, covering: generation, propagation and run-up of tsunamis. Globally, the models from the Telemac system match the validation data, however we note a reliance on numerical parameters for sensitive cases as the propagation of a solitary wave. Finally, the Non-Linear Shallow Water model of Telemac2D is used to simulate the Tohoku-Oki tsunami that hit Japan in 2011. Thenumerical model succeeds in representing this real event incorporating all the stages of tsunami life, from generation to flooded areas. Some limitations in using the method were found, which one discussed in detail within the present manuscript

... The underwater explosion is another domain where the water gets compressed substantially and the associated density variation in the fluid is significant. Study on the water waves generated by underwater explosions in [3] considers the flow to be compressible in the initial phase before the shock wave separates from the bubble front. Water is treated to be inviscid and compressible in [4,5] and uses the Mie-Gruneisen EOS to determine the pressure of compressed and expanded water. ...

An equation of state (EOS) for compressible water is presented for the application over a wide range of pressure. The proposed EOS is a modified form of the Noble Abel Stiffened Gas equation (NASG) which is originally developed for the prediction of saturation properties of water. Three well-known EOS for water viz., the Tait EOS, the Stiffened Gas EOS, and the NASG EOS are used in the comparative study of the
proposed EOS. Accuracy of the density estimates of the modified EOS is quantified by comparing with the published NIST data. The evaluative study of the EOS is performed over the pressure range of 1 - 10^5 Pa to 1 - 10^9 Pa and temperature range of 280 K - 370 K. The analysis reveals the supremacy of the modified version of the NASG EOS over the original version for its improved accuracy and suggests its applicability over a wide range of pressure. The problem of water shock tube is selected in the study as an application of the EOS and to demonstrate the robustness of the modified EOS. The superiority of the modified NASG EOS over the Tait EOS in modelling non-isothermal flow problems with high accuracy is also revealed in the study.

... The problem of impulse-wave formation and propagation has attracted considerable attention in recent decades. Many of the physical insights into these phenomena have come from laboratory scale-down experiments (e.g., Kamphuis and Bowering 1970;Huber and Hager 1997;Fritz 2002;Evers and Hager 2017), and to a lesser extent from theoretical models (e.g., Kranzer and Keller 1959;Le Méhauté and Wang 1996;Zitti et al. 2016) and numerical simulations (e.g., Watts 1997;Abadie et al. 2010; Yavari-Ramshe and Ataie-Ashtiani 2018). ...

Experimental studies of impulse-wave formation have mostly used rigid blocks or granular materials to mimic landslides at the laboratory scale. These studies have deduced that material deformability plays a key part in wave formation: the more rigid the sliding mass, the higher the impulse wave. It is, however, still unclear whether higher wave amplitudes arise solely from lower deformability. Indeed, blocks are not only rigid, but they are also cohesive, whereas granular media are deformable and cohesionless. To shed light on this issue, we ran experiments using two deformable materials of equal density, one exhibiting no cohesion (soft 15-mm-diameter balls) and the other exhibiting cohesion (a viscoplastic polymeric gel called Carbopol Ultrez 10). A finite volume of material was released at the top of a chute, penetrated a body of water, and generated impulse waves. We monitored how the mass slid and interacted with the water volume. Using high-speed cameras, we measured maximum wave heights, amplitudes, and lengths of the leading wave. We used dimensionless groups to reduce the dimension of the parameter space, making it possible to carry out a regression analysis. Viscoplastic slides generated larger wave amplitudes but shorter wave lengths than granular materials. Surprisingly, the wave features did not depend on the polymer concentration. In other terms, impulse-wave features were not found to be dependent on the cohesion of the deformable material landslides causing them, within the range of concentrations tested.
Graphic abstract
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Variations in the scaled maximum wave amplitude Am to dimensionless group Q a for carbopol (at concentrations of 3.0%, 2.5% and 2.0%), b for carbopol and water balls
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Variation in the waves maximum potential energy Ep relative to the slides kinetic energy EI

... 그리고 수중발파 현장에서 측정한 자료로부터 진동추정식을 제안하였다 (Park et al., 2006). 수중발파에 대한 어류 및 구조물의 영향평가 (Lee et al., 2001;Choi et al., 2015) 그리고 Le Méhauté and Wang(1996) Fig. 12에서 (a), (b), (c), (d)는 Scenario S1-S4 (c) Scenario S3 (d) Scenario S4 Fig. 12 Spatial distributions of maximum elevation of water wave by a single-charge blasting 를 나타내며, 발파수심은 -1m, -6m, -11m, -15m, 장약량은 124kg, 90kg, 58kg, 25kg이다. Fig. 12보다 Fig. 13 ...

... 1. basal friction of landslide in its sub-aerial and underwater motion 2. 3D landslide deformation due to its granular feature and its interaction between bedrock and water body 3. energy dissipation due to friction at landslide-water boundary 4. splash effects, due to the surface tension breaking 5. air entrainment at impact, where energy can be lost due to air compressibility 132 LeMehaute & Wang (1996) and Walder et al. (2003) refer to those dissipative processes as difficult to analyze and incorporate in numerical models. Thus, they are either disregarded or incorporated into other dissipative processes as a "black box". ...

... Depending upon depth of explosion source underwater explosion is classified as deep and shallow underwater explosion. The criteria for classifying underwater explosion as deep or shallow are given by Le Mehaute, Bernard and Wang Shen [1]. Generally in deep underwater explosion crater formed on the surface is trivial while in case of shallow underwater explosion crater is considerable. ...

Rapid growth in computational capacity facilitates structural mechanics specialist to facilitate numerical simulation of complex explicit dynamics of detonation shock dynamics and explosive analysis. An attempt is made depict shock wave propagation behaviour and variation of its mechanical properties along the radial line of spherical shaped high explosives in the water domain. JWL equation of state for expansion of detonating products after explosion has been studied for several high explosives and simplified approach with PVγ form has been suggested to reduce complexity of calculation and computational time for underwater explosion phenomenon. Near-field effects cause severe effects on the structures leading to the local deformation and hazard to structure while with the spatial distance away from the explosive centre explosion effects reduces due to expansion of detonating products. There is strong need to segregate such effects to find the vulnerability of structures depending upon target structure distance from explosive centre. Typical spherical high explosives have been studied with variation of charge radius employing homogeneous and heterogeneous explosive model to study such behaviour. Successful criteria to distinguish near-field and far-field effect are evolved after parametric study. All the results with consolidated comparison are presented in this paper.

... The bursting of large underwater explosion bubbles and the water waves generated may cause significant damages to marine vessels, offshore structures and harbours (Méhauté and Wang, 1995). With the validated computational model, we simulate the bursting of an underwater explosion bubble generated by a charge with a large TNT equivalent of 1000 tons at various depths. ...

This paper is concerned with the bursting of a large bubble at a free surface. The numerical modelling is based on the boundary integral method. To validate the numerical model, experiments are carried out for the bursting of a spark generated bubble at a free surface in a low pressure tank, captured by using a high speed camera. Our numerical results agree qualitatively with the experiments. We further carry out numerical analysis for the bursting of an underwater explosion bubble at a free surface. We have considered the bursting of singly connected bubbles as well as toroidal bubbles. When a bubble is initiated very close to a free surface, the bursting occurs during the expansion phase, thus, resulting in a cone shaped spike at the free surface. However, when the bubble is initiated away from the free surface, it expands and collapses below the free surface and rises to the free surface due to buoyancy. An upward liquid jet forms during the later stage of collapse, which subsequently penetrates through the bubble. The toroidal bubble rises and bursts at the free surface, which results in a much higher water column due to the high speed bubble jet.

... If an explosive is detonated in water, several typical phenomena can be observed. Typical phenomena are the shock wave, gas bubble, cavitations etc. Figure 1 shows the underwater explosion phenomena [2]. ...

... The underwater explosion is another domain where the water gets compressed substantially and the associated density variation in the fluid is significant. Study on the water waves generated by underwater explosions in Ref. [3] considers the flow to be compressible in the initial phase before the shock wave separates from the bubble front. Water is treated to be inviscid and compressible in Refs. ...

The ammonia used for NOx reduction in urea SCR is formed from the decomposition of urea in the mixing chamber. The main challenges in urea SCR are the incomplete decomposition of urea to NH3 and their subsequent non-uniform distribution at the inlet of SCR. A uniform profile at the SCR inlet without accounting for the non-uniformities from the mixing chamber may lead to an error in the system design. For symmetrical injection of urea inside the mixing chamber, the insufficient exhaust gas temperature and lower residence time of urea are two important factors that lead to the incomplete conversion of urea and the non-uniform distribution of ammonia at the SCR inlet. A CFD analysis of the mixing chamber with a symmetrical injection of urea is carried out to study these factors. The analysis showed that by simultaneously lowering the flow rate of urea and reducing the velocity of the exhaust gas, which is at a sufficiently high temperature, improves the NH3 generation considerably. The CFD analysis was further extended to model the SCR with different inlet conditions. This analysis revealed that for SCR with non-uniform inlet conditions arising from the mixing chamber, the NOx reduction achieved is lower compared to the case of a uniform inlet profile to the SCR. The analysis shows that the radial variation in NOx reduction arising from the non-uniformities in the mixing chamber diminishes with a rise in the exhaust gas temperature. As compared to uniform inlet profiles, the NOx conversion in SCR with non-uniform inlet profiles exhibit a sharp rise with the increase in NO2 concentration.

... This requires more investigation and should be associated with underwater measurements such as in other similar experimental setup (e.g.: Mulligan and Take 2017;McFall et al. 2018). Regarding water surface tension breaking and air entrainment/detrainment, Le Méhauté and Wang (1996) and Walder et al. (2003) refer to those dissipative processes as difficult to analyze and incorporate in numerical models. Thus, they are either disregarded or, as in our method, incorporated into other dissipative processes as a "black box." ...

Landslides falling into water can trigger tsunamis, which are particularly destructive in the proximity of the landslide impact and in narrow water bodies. The energy transfer mechanism between landslide and water wave is complex, but its understanding is of fundamental importance for the numerical modelling which aims to predict the induced wave hazard. In order to study the involved physical processes, we set up an experimental facility consisting of a landslide generator releasing gravel at high-speed in a wave basin. With the aim of estimate the landslide-wave energy transfer, we implemented a simplified 1D conceptual model of landslide motion, including the 3D landslide deformations. We optimized the model with the experimental results. The model results explain that the deformable landslide has an average drag coefficient of 1.26 and a relatively inefficient energy transfer from landslide to wave. Of the landslide energy at impact, the 52% is dissipated by Coulomb basal friction between the slide and the water basin bottom, 42% is dissipated by other processes, including turbulence, and only the remaining 6% is transferred to the wave thus formed.

... Many researchers have investigated different approachs for underwater explosion according to their depth and the great damage occurred to naval ship[1,2]. Explosion conversion has been studied in details in different reference[3][4][5]demonstrating the propagation process until the formation of underwater shock wave and bubble pulse[6,7]. Developing underwater explosives by adding different energetic materials especially aluminum have been investigated[8-12]. ...

... Several authors [21][22][23][24][25][26][27] have calculated the effects of ocean impacts by small asteroids (300-400 m diameter). These calculations were based largely on the calculations of Van Dorn [28,29] with respect to underwater explosions and concluded that they would generate comparatively small tsunami waves. Furthermore, due to the Van Dorn effect, their force would be dissipated before reaching shore. ...

Large blocks and boulders of banded iron formations and massive hematite up to 40 × 27 × 6 m³ and in excess of 10,000 metric tonnes were detached from an outcrop of the Wilgie Mia Formation during the ca 2.20 Ga marine transgression at the base of the Paleoproterozoic Windplain Group and deposited in a broad band on the wave-cut surface 900 to 1200 m to the east. At the same time, sand and shingle were scoured from the sea floor, leaving remnants only on the western side of the Wilgie Mia Formation and on the eastern sides of the boulders. Evidence suggesting that the blocks were detached and transported and the sea floor scoured by a tsunami bore with a height of at least 40 m is provided by the following: (1) the deposition of the blocks indicates transportation by a unidirectional sub-horizontal force, whereas the smaller boulders are randomly oriented; (2) 900–1200 m separates the banded iron formation (BIF) outcrop and the blocks (3) there is an absence of the basal conglomerate between the blocks; (4) the blocks and boulders rest directly on the wave-cut surface of deeply weathered amphibolites; (5) the blocks and boulders are surrounded and overlain by fine-grained sandstone of the Windplain Group.

... These waves propagate more efficiently, reaching transoceanic distances, and are, in first approximation, non dispersive. On the contrary, landslide and volcanic sources, even if they encompass a broad range of source size, mostly generate localized tsunamis dominated by short-period waves with greater dispersion and limited far-field effects compared to earthquake-generated tsunamis (e.g., [19,91,184,[222][223][224][225][226][227][228][229][230][231][232]). Large volcanic explosions (e.g., caldera forming eruptions) and oceanic impacts of large asteroids may produce huge waves for which non-linearity may play a significant role for hundreds or even thousand of kilometres [197], with significant dispersive behaviours [196]. ...

Destructive tsunamis are most often generated by large earthquakes occurring at subduction interfaces, but also other “atypical” sources—defined as crustal earthquakes and non-seismic sources altogether—may cause significant tsunami threats. Tsunamis may indeed be generated by different sources, such as earthquakes, submarine or coastal landslides, volcano-related phenomena, and atmospheric perturbations. The consideration of atypical sources is important worldwide, but it is especially prominent in complex tectonic settings such as the Mediterranean, the Caribbean, or the Indonesian archipelago. The recent disasters in Indonesia in 2018, caused by the Palu-Sulawesi magnitude Mw 7.5 crustal earthquake and by the collapse of the Anak-Krakatau volcano, recall the importance of such sources. Dealing with atypical sources represents a scientific, technical, and computational challenge, which depends on the capability of quantifying and managing uncertainty efficiently and of reducing it with accurate physical modelling. Here, we first introduce the general framework in which tsunami threats are treated, and then we review the current status and the expected future development of tsunami hazard quantifications and of the tsunami warning systems in Italy, with a specific focus on the treatment of atypical sources. In Italy, where the memory of historical atypical events like the 1908 Messina earthquake or the relatively recent 2002 Stromboli tsunami is still vivid, specific attention has been indeed dedicated to the progressive development of innovative strategies to deal with such atypical sources. More specifically, we review the (national) hazard analyses and their application for coastal planning, as well as the two operating tsunami warning systems: the national warning system for seismically generated tsunamis (SiAM), whose upstream component—the CAT-INGV—is also a Tsunami Service Provider of the North-eastern Atlantic, the Mediterranean and connected seas Tsunami Warning System (NEAMTWS) coordinated by the Intergovernmental Coordination Group established by the Intergovernmental Oceanographic Commission (IOC) of UNESCO, and the local warning system for tsunamis generated by volcanic slides along the Sciara del Fuoco of Stromboli volcano. Finally, we review the state of knowledge about other potential tsunami sources that may generate significant tsunamis for the Italian coasts, but that are not presently considered in existing tsunami warning systems. This may be considered the first step towards their inclusion in the national tsunami hazard and warning programs.

... Subaqueous explosive eruptions are complicated phenomena that are challenging to replicate in physical experiments. Previously they have been conceptualized as phenomena within a spectrum ranging from explosions (Bernard & Shen, 1996;Stepanov & Navagin, 1966) to water jets (Chojnicki et al., 2015;Maurel et al., 1997), with gas jets as an intermediate case (Bie et al., 2016;Verolino et al., 2018). ...

A submarine volcanic eruption has the potential to generate a dangerous local tsunami. To better understand the free surface disturbance generated by an underwater volcanic eruption, which will form the initial condition for any subsequent wave generation, we conducted a series of laboratory experiments. In these experiments, compressed air was injected into a tank filled with water to simulate an underwater eruption. The experiments were repeated over a range of different pressures and water depths. Each eruption can be divided into three phases: A momentum‐driven jet, a buoyancy‐driven plume, and a fountain‐generation regime. Our experiments exhibit two fountain regimes (a dome regime and a finger regime), with a transition between them. These fountain regimes have been observed in several real submarine volcanic eruptions. This paper proposes a Froude number criterion to combine the water depths and source conditions together with the aspect ratios of fountains to quantify different fountain regimes. This quantitative relationship holds for two real subaqueous volcanic eruption cases (Myojin‐Sho eruption in 1952 and 1996 eruption in Karymskoye Lake). The fountain of the Myojin‐Sho shallow submarine eruption on September 23,1952 appears to have been in the dome regime, which means it was a relatively weak eruption. Unlike other eruptions from this volcano, which did generate tsunamis, no tsunami waves were detected on September 23 . This study contributes to an enhanced understanding of the usually unseen mechanism of free surface disturbances by volcanic gas injection during submarine eruptions.

... Although some investigations for bubble growth in underwater explosions exist [22][23][24][25][26], few models exist for bubble growth in offshore pipelines where axial cracks propagate. In the present study, we simplify bubble growth as a onedimensional gas flow, as shown in Fig. 12. ...

We developed the first model to evaluate unstable ductile crack arrestability in offshore pipelines. The proposed model is an integrated one-dimensional model with four sub-models to calculate (a) pipe deformation, (b) gas flow inside pipe, (c) bubble growth, and (d) crack propagation. We validated the proposed model by applying it to two types of tests: laboratory scale underwater rupture tests and existing data of a full-scale burst test of an offshore pipeline. In addition, the calculation results of the proposed model showed that a deep water depth results in increased unstable crack arrestability of the pipeline.

The experimental studies presented in this paper attempt to supply a reasonable comprehensive explanation for the key feature of the collapse bubble and the complex nature of the raised free surface. Six distinctive patterns of free surface motion were identified for bubbles initiated at different γf (the non-dimensional bubble-freesurface distance scaled with the maximum bubble radius). Special features such as “breaking wrinkles,” “spraying water film,” and other unstable phenomena were observed with free surface motions, which were hardly captured by a boundary integral scheme. Parameters defining the shape of the free surface, such as the spike height Hspike, the spike width Wbase, and the skirt height Hspray, are measured and analyzed against γf. Different voltages were used to generatebubbles with varies sizes, while the bubble and free surface motion patterns appeared to be largely independent of the bubble size. Finally, collapsing bubble shape, centroid migration, period of bubble oscillation, and jet tip velocity at different γf are investigated and noticeable variation trends are found.

Underwater explosion through complex medias is one of the research topics related to strong impulsive force in structure(oil plat form, offshore platform and ship) for disaster prevention from industrial accident explosions

The physics is described of tsunami formation by sources of nonseismic origin: landslides, volcanic eruptions, meteorological causes, and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

The results of modeling the cosmogenic tsunami on the basis of two models of its generation are presented. In the first model a parametrized source is given by an analytical expression, while in the second model it is obtained by numerically solving the system of Navier-Stokes equations. The results of the calculations of wave propagation in a constant-depth reservoir are presented and the wave parameters are compared.

The global tsunami and atmospheric waves that followed the eruption of the Tongan volcano Hunga Tonga–Hunga Ha’apai were observed around the world. Analysing the data could reshape our understanding of such events. Volcanic eruption caused a meteotsunami.

The physics is described of tsunami formation by sources of nonseis-mic origin: landslides, volcanic eruptions, meteorological causes and cosmic bodies falling into the ocean. Short descriptions are given of certain remarkable historical events (with the exception of cosmogenic tsunamis). Approaches to the mathematical description of tsunami generation by these sources are expounded. Basic regularities, relating parameters of a source and of the tsunami wave generated by it are presented.

Underwater Explosion (UNDEX) due to terrorism or accidental incident affects the people and structures causing irreparable loss of life and damage to survivability of the structure. This blast loading due to the explosion is challenging both the civilian and military structures. In order to minimize the effect on the structure, we need to understand the mechanics and the response of the structure submitted to blast loading. After a review of existing methods to simulate the response of a steel and composite structure submitted to dynamic pressure waves, the focus will be on the analysis of naval steel and composite structures when they are submitted to the primary shock wave generated from the underwater explosions. Finite element numerical simulations will be carried out to simulate the dynamic response of a non-stiffened immersed cylindrical shell submitted to such pressure loading. The pressure loading on the structure as a kinetic energy, which is transmitted by the shock wave is calculated from the explosion parameters by using analytical formulation. The assessment of the dynamic response and the fluid structure interaction was performed with explicit finite element solver LS-DYNA. Sensitivity analyses of the response to different parameters like shock factor, treatment of the fluid domain, Anisotropy of material will also be performed.
Keywords
LS-DYNA, Steel Cylinder, Composite Structure, Finite Element Analysis, Fluid Structure Interaction, UNDEX.

The low frequency load of an underwater explosion bubble and the generated waves can cause significant rigid motion of a ship that threaten its stability. In order to study the fluid-structure interaction qualitatively, a two-dimensional underwater explosion bubble dynamics model, based on the potential flow theory, is established with a double-vortex model for the doubly connected bubble dynamics simulation, and the bubble shows similar dynamics to that in 3-dimensional domain. A fully nonlinear fluid-structure interaction model is established considering the rigid motion of the floating body using the mode-decomposition method. Convergence test of the model is implemented by simulating the free rolling motion of a floating body in still water. Through the simulation of the interaction of the underwater explosion bubble, the generated waves and the floating body based on the presented model, the influences of the buoyancy parameter and the distance parameter are discussed. It is found that the impact loads on floating body caused by underwater explosion bubble near the free surface can be divided into 3 components: bubble pulsation, jet impact, and slamming load of the generated waves, and the intensity of each component changes nonlinearly with the buoyance parameter. The bubble pulsation load decays with the increase in the horizontal distance. However, the impact load from the generated waves is not monotonous to distance. It increases with the distance within a particular distance threshold, but decays thereafter.

This book explains the physical principles of high-resolution optical imagery of the ocean surface, discusses for the first time the capabilities of observing hydrodynamic processes and events, and emphasizes the integration of optical measurements and enhanced data analysis. It also covers both the assessment and the interpretation of dynamic multispectral optical databases and includes applications for advanced studies and nonacoustic detection.

Interaction between complex structure with underwater explosion (UNDEX) is related to extensive damage of structures and ship at sea or undersea from explosion hazards. This study is predicting for the pressure and momentum attenuation of UNDEX environment. Porous compressible material will be able to disperse the inertia and momentum of shock loading, bubble pulse, and bubble jet of UNDEX. Results show that semicircle wall in low-porosity foam shows good performance with attenuation of UNDEX environment.

A probabilistic hazard analysis of tsunami generated by subaqueous volcanic explosion is applied to the Campi Flegrei caldera (Campania, Italy). An event tree is developed to quantify the tsunami hazard due to the submarine explosions by: i) defining potential size classes of explosion magnitude on the basis of past volcanic activity in the Campi Flegrei caldera and sites in the underwater part of the caldera; ii) simulating the generation and propagation of the consequent tsunami waves able to reach the coasts of the Campania region for all combinations of tsunami-generating vents and sizes; and iii) quantifying the tsunami probability and relative uncertainty, conditional upon the occurrence of an underwater eruption at Campi Flegrei. Tsunami hazard generated by subaqueous volcanic explosions is considered crucial because of its potential high impact on the densely populated coastal areas of the Pozzuoli Bay and Gulf of Naples even if the probability for eruptions in the submarine part of the caldera is certainly low. The tsunami hazard analysis is presented using conditional hazard curves and maps, that is calculating the probability (and relative uncertainties) of exceeding given tsunami intensity thresholds (wave amplitudes at the coast), given the occurrence of a subaqueous eruption. The results indicate that a significant tsunami hazard exists in many areas of the Bay of Naples.

Investigation of the waves generated by underwater disturbances gives precious insight into the effect of man-made underwater explosions as well as natural phenomena, such as underwater volcanoes or oceanic meteor impact. On the other hand, prediction of the effects of such waves on the coastal installations and structures is required for preparation worthwhile criteria for coastal engineers to prepare a reliable design. This study aimed to investigate the interactional effects of water waves generated by underwater disturbances on sea walls through numerical modeling using the Smoothed Particle Hydrodynamics (SPH) method. The simulation was performed using the Dual-SPHysics numerical code. Comparison of the numerical results with the experimental data extracted from case studies demonstrated the good capability of the SPH algorithm used in the numerical code in the simulation of initial wave generation by the underwater disturbance and its propagation over the body of water. To examine the wave force exerted on the walls, the results of laboratory experiences on the effect of tsunami waves on coastal structures were used to verify the numerical model. The study found that the phenomena with such nonlinear behavior can be very well simulated with a calibrated SPH model. We also explored the effects of this type of wave and temporal changes of its resultant force on the wall. In this article, the explosion-generated water wave produced much stronger fluctuations in the vicinity of the wall than did the solitary wave, thus naturally, it can be more destructive.

The 1888 Ritter Island volcanic sector collapse triggered a regionally damaging tsunami. Historic eyewitness accounts allow the reconstruction of the arrival time, phase and height of the tsunami wave at multiple locations around the coast of New Guinea and New Britain. 3D seismic interpretations and sedimentological analyses indicate that the catastrophic collapse of Ritter Island was preceded by a phase of deep-seated gradual spreading within the volcanic edifice and accompanied by a submarine explosive eruption, as the volcanic conduit was cut beneath sea level. However, the potential impact of the deep-seated deformation and the explosive eruption on tsunami genesis is unclear. For the first time, it is possible to parameterise the different components of the Ritter Island collapse with 3D seismic data, and thereby test their relative contributions to the tsunami. The modelled tsunami arrival times and heights are in good agreement with the historic eyewitness accounts. Our simulations reveal that the tsunami was primarily controlled by the displacement of the water column by the collapsing cone at the subaerial-submarine boundary and that the submerged fraction of the slide mass and its mobility had only a minor effect on tsunami genesis. This indicates that the total slide volume, when incorporating the deep-seated deforming mass, is not directly scalable for the resulting tsunami height. Furthermore, the simulations show that the tsunamigenic impact of the explosive eruption energy during the Ritter Island collapse was only minor. However, this relationship may be different for other volcanogenic tsunami events with smaller slide volumes or larger magnitude eruptions, and should not be neglected in tsunami simulations and hazard assessment.

A probabilistic hazard analysis of a tsunami generated by a subaqueous volcanic explosion is performed for Taal Lake in the Philippines. The Taal volcano in Taal Lake is an active volcano on Luzon Island in the Philippines, and its eruption would have a strong impact on humans around the coastal area of the lake. This study aims to develop a probabilistic tsunami hazard model of inundated buildings for tsunami mitigation in future scenarios. To develop the probabilistic tsunami hazard model, different explosion diameters were used to generate tsunamis of different magnitudes in the TUNAMI-N2 model. The initial water level in the tsunami model was estimated based on the explosion energy as a function of the explosion diameter. The tsunami-induced inundation from the TUNAMI-N2 model was overlaid on the distribution of buildings. The statistical distribution of inundated buildings can be modeled with the lognormal distribution, which exhibits the best fit among nine candidate statistical distributions. The tsunami hazard analysis is explained by using the conditional hazard curve and map. These products were used to calculate the probability of building inundation given the occurrence of a subaqueous explosion. The results from this study can be used for future tsunami mitigation in the case of a tsunami generated by a subaqueous volcanic explosion.

Large blocks and boulders of banded iron formation and massive hematite up to 40 x 27 x 6 m and in excess of 10,000 metric tonnes were detached from outcrop of the Wilgie Mia Formation during the ca 2.20 Ga marine transgression at the base of the Paleoproterozoic Windplain Group, and deposited in a broad band on the wave-cut surface 900 to 1200 m to the east. At the same time sand and shingle was scoured from the sea floor, leaving remnants only on the western side of the Wilgie Mia Formation and on the eastern sides of the boulders. Evidence suggesting that the blocks were detached and transported and the sea floor scoured by a tsunami bore with a height of at least 40 m is provided by (1) the deposition of the blocks indicates transportation by a unidirectional sub-horizontal force, whereas the smaller boulders are randomly oriented (2) 900 -1200m separating the BIF outcrop and the blocks (3) the absence of the basal conglomerate between the blocks (4) the blocks and boulders rest directly on the wave-cut surface of deeply weathered amphibolites (5) the blocks and boulders are surrounded and overlain by fine-grained sandstone of the Windplain Group.

Submarine volcanic eruptions have the potential to generate tsunamis, which can cause destruction well beyond the range of the eruption itself. Here, we present a series of underwater eruption experiments in which a non‐condensing gas was injected into a water tank with a range of water depths and applied pressures. This study proposes an effective scaled water depth and categorizes underwater eruptions into three types: deep‐water eruptions, intermediate‐water eruptions, and shallow‐water eruptions. In deep‐water eruptions, most of the energy is dissipated within the water column before the plume reaches the surface, and negligible waves are generated. In intermediate‐water eruptions, reductions in water depth reduce the loss of energy to the water column, leaving more energy available for wave generation. This causes an increase in wave heights as water shallows, up to a point. In sufficiently shallow‐water cases, the water depth is so small that almost all of the energy from the eruptive jet or plume passes through the water and is dissipated into the air, so there is only small wave‐making potential, even with relatively intense source strength. Therefore, there exists a critical water depth at which an eruption with a given source intensity will generate the largest waves. That depth lies at the boundary between the intermediate‐ and shallow‐depth regimes, where the energy available for wave generation is at a maximum. This research reveals fundamental wave generation mechanisms related to underwater gas eruptions, thereby extending our understanding of submarine volcanic tsunami generation and providing a foundation for future hazard assessment.

This paper discusses the development of an analytical solution to a pure liquid shock tube problem with water as the working fluid. The solution procedure associated with classical gas shock tube problem has been extended for the case of a compressible liquid. The analytical model employed accounts for the compressibility effects in liquid water using the high-accuracy Modified NASG equation of state. The solution methodology presented in this work is unique in that it provides comprehensive modeling of the complete physics of the water shock tube problem. The work also demonstrates the applicability of analytical solution over a wide range of pressures and temperatures. The solution profiles of the water shock tube problem and the air shock tube problem for the same thermodynamic conditions and shock tube geometry were compared and salient features were discussed. The water shock tube problem is also solved numerically in this study, with a more elaborate PDE-based mathematical model, using the AUSM+-up numerical algorithm. The in-depth comparative analysis shows the close agreement of the numerical results with the analytical solution developed. The analytical solution to the liquid shock tube offers multiple flow features, such as shock wave, expansion fan, and contact discontinuity in the solution. These features make the proposed analytical solution a powerful benchmarking tool that could test the various computational capabilities of codes developed for simulation of compressible liquid flow transients. The solution procedure presented in this work is also flexible enough for application to any liquids provided that the relevant equations of state are available.

Modeling of the formation of an ocean wave system based on a space image taken from the International Space Station (ISS) as part of the “Uragan” (Hurricane) space experiment was performed. Due to the fact that the area of the ocean was known approximately, the simulation of wave excitation and propagation was performed for two cases: in the framework of the theory of long waves and for the ocean of infinite depth. Numerous calculations made it possible to achieve a similarity between the modeled wave system and the original one shown on the photo. This allowed us to confirm the hypothesis about the impulse nature of the initial disturbance necessary for the formation of such a phenomenon and determine its physical parameters. The model allows us to predict the development of such phenomena. Unfortunately, one static image does not allow us to judge the dynamics of the recorded phenomenon.

The giant tsunami that occurred in the Indian Ocean on 26th December 2004 draws attention to this natural phenomenon. The given course of lectures deals with the physics of the tsunami wave propagation from the source to the coast. Briefly, the geographical distribution of the tsunamis is described and physical mechanisms of their origin are discussed. Simplified robust formulas for the source parameters (dimension and height) are given for tsunamis of different origin. It is shown that the shallow-water theory is an adequate model to describe the tsunamis of the seismic origin; meanwhile for the tsunamis of the landslide or explosion origin (volcanoes, asteroid impact) various theories (from linear dispersive to nonlinear shallow-water equations) can be applied. The applicability of the existing theories to describe the tsunami wave propagation, refraction, transformation and climbing on the coast is demonstrated. Nonlinear-dispersive effects including the role of the solitons are discussed. The practical usage of the tsunami modeling for the tsunami forecasting and tsunami risk evaluation is described. We also give the results of the numerical simulations of the two global tsunamis in the Indian Ocean induced by the catastrophic Krakatau eruption in 1883 and the strongest North Sumatra earthquake in 2004.

Centrifuge experimental techniques provide possibilities for laboratory simulation of ground motion and cratering effects due to explosive loadings. The results of a similarity analysis for the thermomechanical response of a continuum show that increased gravity is a necessary condition for subscale testing when identical materials for both model and prototype are being used. The general similarity requirements for this type of subscale testing are examined both theoretically and experimentally. The similarity analysis is used to derive the necessary and sufficient requirements due to the general balance and jump equations and gives relations among all the scale factors for size, density, stress, body forces, internal energy, heat supply, heat conduction, heat of detonation, and time. Additional constraints due to specific choices of material constitutive equations are evaluated separately. A series of centrifuge experiments was performed to validate the derived similarity requirements and to determine the practicality of applying the technique to dry granular soils having little or no cohesion.

Experiments on the radial propagation of axisymmetric free-surface solitary waves are reported and compared with theoretical and numerical solutions of the cylinderical Korteweg–de Vries (CKdV) equation. A new experimental technique to obtain a continuous amplitude signature on photographic paper is reported. These measurements show that an isolated disturbance evolves into a slowly varying solitary wave with amplitude decaying as $r^{-\frac{2}{3}}$, where r is the radius measured from the centre of the disturbance. A numerical study of the CKdV equation is made to interpret the transient development of these waves into the nonlinear asymptotic regime. It is further pointed out that the CKdV equation also describes weakly nonlinear axisymmetric internal waves, and a comparison of theory for this case with internal-wave trajectory measurements reported by Maxworthy (1980) exhibit good agreement.

Some recent development on the analysis of surface water waves generated by locally impulsive disturbances is presented in this paper While the classical Cauchy-Poisson approach to the problem has various practical applications, the theoretical analysis has been limited to either leading wave or the trailing wave solution in the farfield. Direct numerical integration except for very simple form of disturbance has difficulties due to the highly oscillatory kernel function of the Cauchy-Poisson integral. The new development shows that the method of Fourier transform may remove all the difficulties which have been faced either analytically or numerically and the solution is uniformly valid for both leading and trailing waves, deep and shallow water and for either near or far field within the linear definition. An inverse application of this method may also determine the infield initial disturbances at the origin. Nonlinear approximate solution to the same problem in the nearfield
where linear solutions are not exactly valid is presented. Appropriate KdV equation in radial coordinate system are solved linearly using Fourier transform techniques but nonlinear corrections are added using implicit finite difference scheme. Wave data from experiments of TNT explosion and plate dropping in shallow water are presented. Substantiation of the theory is demonstrated by comparing the theoretical calculation with the experimental results.

The damping of small-amplitude surface waves on a viscous fluid over a permeable fixed bed is studied. Conservation arguments and consideration of the rate of doing work at the fluid-bed interface are applied in a careful analysis of the boundary conditions at the interface. It is shown that stresses are not continuous at the interface. A general dispersion relationship, which gives the damping characteristics for given wave parameters, is found together with the stream functions for the flow in the two regimes. The wave damping characteristics are different from those given in previous studies of waves over a permeable fixed bed and are a consequence of the new boundary conditions derived below. The damping effects due to percolation in the fixed bed are not always small in comparison with the viscous effects. Some numerical examples of typical situations are given.

The solution of Kranzer and Keller for explosively generated water waves has been evaluated for regions near the explosion and examples of results are presented. The integration method developed is valid throughout the entire fluid domain, as opposed to the method of stationary phase, which, as specified, is an asymptotic solution valid only at large distances, r, from the source of disturbance (of radius R). The integration process consists of a fourth-degree polynomial fit to each half-oscillation of the integrand, and the error can be bounded to almost any desired degree of accuracy, which in this case was ±0.02 meters. Evaluation of the integral by the method of stationary phase is noticeably inaccurate for r < 10R in the case of a parabolic impulse, and, for this region, it is recommended that the integral be evaluated by some other approximate method, such as that presented in this paper. At large distances from the source, r ≥ 10R, the usual Kelvin approximation is an excellent method of evaluating the wave amplitude and should be used for savings in computation time.

A mathematical model is presented for the prediction of the flood wave resulting from the instantaneous break of a dam in a prismatic, dry channel of general parabolic cross section. It consists of the numerical integration of the characteristic equations over the irregular grid formed by the characteristic lines using a predictor-corrector scheme. The solution is advanced towards the wave front by a gradual refinement of the characteristics net for reasons of accuracy and economy.

The dynamics of an underwater explosion bubble, including its collapse and interaction with a free or hard surface, are analyzed using incompressible flow theory and a boundary integral formulation. The formulation of the solution method and the crux of the numerical treatment are presented in detail. A computer program for axisymmetrical problems has been successfully developed. Numerical results, including bubble periods, maximum radii, and velocities of the reentrant jet tip, are compared to available experimental data and to computational results obtained using the PISCES finite difference code... . Boundary integral technique, Bubble jetting, Explosion bubble collapse, PISCES Code, Explosion bubbles, Cavitation, Finite element analysis

Theoretical and experimental studies were conducted to determine the run-up on a plane beach produced by systems of impulsive generation. The facility used for the studies consists of a wave basin which simulates the run-up of actual ocean waves on beaches. Wave trains were generated by bobbing the plunger up and down pneumatically in a single stroke or in arbitrary sequences chosen to produce wave trains simulating these produced by underwater or surface explosions. The para boloidal shape of the plunger was chosen because it resembles the crater produced by an underwater explosion. The wave trains were recorded at several distances from the center of plunger, and the corresponding run-up on test beach units of 1:15 slope was recorded. Theoretical results were derived and compared with the observed results. The extent of agreement between theory and experiment is discussed, and preliminary conclusions are that an adequate theory exists to predict wave generation due to underwater highexplosive blasts. (Author)

Surface Phenomena Measurements and Experimental Procedures in 4000 lb HBX-1 Shallow Underwater Explosion Tests (Project Heat)

- U Willey
- R L Phillips

59th Symposium on Shock and Vibrations, Albuquerque, New Mexico, pp. 209-236. (U) Willey, R. L. and Phillips, D.E. (1968). Surface Phenomena Measurements and Experimental Procedures in 4000 lb HBX-1 Shallow Underwater Explosion Tests (Project Heat). U.S

Experimental Investigations of Cavitation Bubble Collapse in the Neighbourhood of a Solid Boundary The Principle of Superposition Applied to the Theory of Cauchy-Poisson II-V, 1-28, DAASA No. DA-49-146-XZ-151 Explosion Generated Water Waves, Eighth Symposium of Naval Hydrodynamics

- U Lauterborn
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(U) Lauterborn, W. and H. Bolle (1975). Experimental Investigations of Cavitation Bubble Collapse in the Neighbourhood of a Solid Boundary. J. Fluid Mech. 72, 391-399. (U) Le Mehaute, B. (1963). The Principle of Superposition Applied to the Theory of Cauchy-Poisson, Vol.. II-V, 1-28, DAASA No. DA-49-146-XZ-151. (U) Le Mehaute, B. (1970). Explosion Generated Water Waves, Eighth Symposium of Naval Hydrodynamics, Pasadena, CA., ONR, pp. 71-91. (U) Le Mehaute, B. (1971). Explosion-Generated Water Waves, Advances in Hydrosciences, Academic Press, New York. (U) Le Mehaute, B. (1976). An Introduction to Hydrodynamics and Water Waves, Springer-Verlag

On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper I. Oceanographical Magazine (Japan On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper II On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper III

- U Unoki
- M Nakanou
- S Unoki
- M Nakano

(C5) pp 7989-7997. (U) Unoki, S. and M. Nakano (1953a). On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper I. Oceanographical Magazine (Japan), 4(4), pp. 119-141. (U) Unoki, S. and M. Nakano (1953b). On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper II. Oceanographical Magazine (Japan), Vol. 5(1), pp. 1-13. (U) Unoki, S. and M. Nakano (1953c). On the Cauchy-Poisson Waves Caused by the Eruption of a Submarine Volcano, Paper III. Met. Res. Inst. Papers in Met. and Geophys., Vol. 4(3-4), pp

Bureau of Standards Circular, 521 Transient Axisymmetric Motion of a Floating Cylinder

- Nat

Nat. Bureau of Standards Circular, 521. pp. 95-108. (U) Newman, J.N. (1985). Transient Axisymmetric Motion of a Floating Cylinder. J. Fluid Mech

Techn. Univ. of Denmark, paper No B-3 Surface Waves Resulting from Explosions in Deep Water Army Engineers Waterways Experiment Station Long Waves on Beach

- U Pace
- R W Whalin
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Symposium on Description and Modelling of Directional Seas. June 18-20. Techn. Univ. of Denmark, paper No B-3. (U) Pace, C.E., R. W. Whalin and J.N. Strange, (1970). Surface Waves Resulting from Explosions in Deep Water. Tech. report No. 647, Report 5, U.S. Army Engineers Waterways Experiment Station, Vicksburg, MS. (U) Peregrine, D.H. (1967). Long Waves on Beach. J. Fluid Mech. 27, 815-827. (U) Pinkston, J.M. Jr. (1964). Surface Waves Resulting from Explosions in Deep Water; Summary of Experimental Procedures and Results of Tests at WES Underwater Explosion Test Site

Oscillations Near the Water Surface Las Alamos Scientific Lab. Report, LA-4958 Numerical Modelling of Water Waves

- U Rmader
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5 38:351. (U) 366 rMader, C.L. (1972). Oscillations Near the Water Surface. Las Alamos Scientific Lab. Report, LA-4958. (U) Mader, C.L. (1988). Numerical Modelling of Water Waves. Univ. of Calif. Press, Berkely. (U) Madsen O.S., and W.D. Grant, (1976). Sediment Transport in the Coastal Environment, Tech

Also Shore Protection Manual CERC, US Army Corps of Engineers) A Finite Depth Wind Wave Model

- Pt

2, Pt. 2, (Also Shore Protection Manual, 1977, CERC, US Army Corps of Engineers). (U) Graber, H.C. and O.S. Madsen, (1988). A Finite Depth Wind Wave Model. J. ofPhys. Ocean