V. Yu. Liapidevskii

Russian Academy of Sciences | RAS · Lavrentyev Institute of Hydrodynamics

Two-layer flow of a density-stratified fluid with mass transfer between the layers is considered. In the Boussinesq approximation, the equations of motion are reduced to a homogeneous quasilinear system of partial differential equations of mixed type. The flow parameters in the intermediate mixed layer are determined from the equilibrium conditions...

This paper presents a discussion on observations of nonlinear internal waves (NLIWs) in the coastal zone of the Sea of Japan, based on the mooring of thermostring clusters in different seasons of 2022. For statistical evaluation of the frequency of event occurrence and determination of NLIW movement direction, we use our observations of the past 12...

The propagation and disintegration of nonlinear internal waves at the hydrophysical test site of the Pacific Oceanological Institute FEB RAS on the shelf of the Sea of Japan have been studied in the summer-autumn period for a number of years. The mechanisms of generation and propagation of nonlinear internal wave trains due to internal tide decay h...

We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispers...

We propose a mathematical model describing the mixing and propagation of nonlinear long waves in a shear three-layer flow of a stratified fluid under a lid. The shallow water equations describe the fluid flow in the outer almost potential homogeneous layers. In the intermediate mixing layer, the fluid is inhomogeneous and its flow is turbulent. Kin...

A one-dimensional long-wave model of an unsteady three-layer flow of a stratified fluid under a lid is proposed, taking into account turbulent mixing in the intermediate layer. In the Boussinesq approximation, the equations of motion are reduced to an evolutionary system of balance laws, which is hyperbolic for a small difference in velocities in t...

One of the main problems of managed pressure drilling (MPD) is detection and monitoring of gas kicks from the formation to the annulus. The model is proposed to estimate the parameters of the gas kick and gas-liquid flow in a well during MPD process based on measurements performed only at the surface. A gas-liquid flow is described by the kinematic...

We propose a hyperbolic system of first-order equations that approximates the 1D Nwogu model of the shallow water theory for non-hydrostatic unsteady flows. Solitary waves in the framework of these models are constructed and studied. The evolution of solitary waves on a mildly sloping beach is considered. We show that the solution of the hyperbolic...

Within the framework of the second approximation of the shallow water theory, the flow of a multilayer fluid stratified in density is under study. A mathematical model for the propagation of near-bottom and near-surface large-amplitude internal waves is constructed, taking into account the influence of the fine structure of thermocline (pycnocline)...

We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional instantaneous variables. This allows one to reduce the dispersive multi-layer Green–Naghdi model to a first-order system...

A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the non-linear stage of the Kelvin–Helmholtz instability development and by turbulent friction. In the framework of the shallow water th...

We derive a new hyperbolic model describing the propagation of internal waves in a stratified shallow water with a non-hydrostatic pressure distribution. The construction of the hyperbolic model is based on the use of additional `instantaneous' variables. This allows one to reduce the dispersive multi-layer Green--Naghdi model to a first-order syst...

A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the nonlinear stage of the Kelvin--Helmholtz instability development and by turbulent friction. In the framework of the shallow water th...

A model and a method of dynamic analysis of a drilling system with a Positive Displacement Motor (PDM) have been proposed. The relevance of the work is related to the need to consider the interaction of the models of the drillstring oscillations, well hydrodynamics, PDM, bit-rock interaction, and a drawworks. The drilling with PDM distinguishes fro...

Analysis of results of field experiments in the near-shore region of the Peter the Great Bay (the Sea pf Japan) is made from the point of view of internal waves (IW) influence on biological and geomorphologic processes in the shelf zone of sea. The main measured parameters were fluctuations of temperature, pressure and current velocity in the near-...

The problem of internal wave propagation in the coastal zone is considered. The solutions describing the evolution of nonlinear waves above the shelf are constructed on the basis of the mathematical three-layer shallow water model. An analysis of the solutions obtained makes it possible to establish the basic laws of transformation of solitary wave...

Some mathematical model is proposed of a flow in a long channel with compliant walls. This model allows us to describe both stationary and nonstationary (self-oscillatory) regimes of motion. The model is based on a two-layer representation of the flow with mass exchange between the layers. Stationary solutions are constructed and their structure is...

Horizontal shear motion of a homogeneous fluid in an open channel is considered in the approximation of the shallow water theory. The main attention is paid to studying the mixing process induced by the development of the Kelvin–Helmholtz instability and by the action of bottom friction. Based on a three-layer flow pattern, an averaged one-dimensio...

In this paper we develop a mathematical model of a wave packet formation due to rapid shut-in of water injector connected with fluid-filled reservoir. A numerical solution of this model have been found and a comparison between the experiments and a numerical simulations have been perfomed. Also we are focused on the optimal parameters choice to pro...

The paper presents an Averaged Drift-Flux Model (ADFM) facilitating consideration of the internal structure of the gas-liquid slug flow in a vertical pipe. Modulation equations are used for flow parameter averaging. The allowable domain of the ADFM has been determined and its difference from the conventional model has been demonstrated. The specifi...

The propagation of finite amplitude internal waves over an uneven bottom is considered. One of the specific features of the large amplitude internal waves is the ability of the waves to carry fluid in the “trapped core” for a long distance. The velocity of particles in the “trapped core” is very close and, even, exceeds the wave speed. Such waves a...

In the present article we consider the problem of underwater avalanches propagating over moderate slopes. The main goal of our work is to investigate the avalanche front velocity selection mechanism when it propagates downwards. We derive from the first principles a depth-averaged model. Then, we assume that sediments are uniformly distributed alon...

In the present article we consider the problem of underwater avalanches propagating over moderate slopes. The main goal of our work is to investigate the avalanche front velocity selection mechanism when it propagates downwards. We derive from the first principles a depth-averaged model. Then, we assume that sediments are uniformly distributed alon...

A Couette flow of a viscoelastic medium is considered that is described by the Johnson–Segalman–Oldroyd model with two relaxation times. The development of singularities related to the appearance of internal discontinuities is studied both analytically and numerically within one-dimensional nonstationary hyperbolic models of viscoelastic Maxwell-ty...

We consider a flow of a fluid in a long vertical tube with elastic walls and show that, for certain parameters of the flow, small perturbations of the flow at the inlet section of the tube give rise to roll waves. Depending on the properties of the closing relation, either regular or anomalous roll waves are formed. In the latter case, a roll wave...

In the present paper, results of an experimental and numerical study of gas flows in radial micro-nozzles are reported. The radial micro-nozzle consists of two disks spaced apart by a less than one millimeter distance. To the inlet of the radial nozzle, a gas under high pressure is supplied; through the nozzle, the pressurized gas is ejected into a...

A new one-dimensional kinematic model of viscous fingers growth is proposed. This model is based on the assumption of an intermediate layer formation. The shear instability of the flow is developed in this layer due to intensive mixing of liquids of different viscosities. The thickness of the intermediate layer between outer ones is determined by t...

This paper presents the observation results for the internal wave bore in the coastal region of the Sea of Japan with the use of vertical thermistor chains. The data obtained is interpreted by the mathematical models of shallow water in which the effect of nonlinearity and dispersion on the propagation of internal wave trains is taken into account....

A two-layer model describing the interaction of a shear bubble layer formed by breaking waves and an underlying potential layer is derived in shallow water approximation. A non-hydrostatic formulation taking into account the entrainment effects in shear flows is proposed. Time and space periodic solutions are found, and some basic problems (the for...

The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provi...

In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the other hand, the turbulent nature of the flow is also taken into account through the energy dissipation mechan...

A gas−liquid flow in a long vertical pipe is considered. A new mathematical model of the flow generalizing the known drift-flux model is constructed. The gas velocity and the average flow velocity in this model are connected by the Zuber−Findlay relation. The model is obtained by averaging the quasi-periodic slug flow regime. Contrary to the drift-...

A two-layer long-wave approximation of the homogeneous Euler equations for a free-surface flow evolving over mild slopes is derived. The upper layer is turbulent and is described by depth-averaged equations for the layer thickness, average fluid velocity and fluid turbulent energy. The lower layer is almost potential and can be described by Serre–S...

Horizontal-shear thin-layer homogeneous fluid flow in the open channel is considered. A one-dimensional mathematical model of the development and evolution of the horizontal mixing layer is derived within the framework of the three-layer scheme. The steady-state solutions of the equations of motion are constructed and investigated. In particular, s...

The purpose of this paper is to develop a numerical method of solving the problem of evolution of the finite gas volume that entered in a liquid flow at a set flow rate. The drift- flux model is used as gas-liquid mixture equations. The velocities of both phases, mixture and gas, are related by the Zuber-Findlay equation which coefficients depend o...

In this paper we study the emergence and development of roll waves in two-layer fluid flow in a Hele-Shaw cell. We propose the mathematical model of such flow and define the conditions of transition from stable state to instability in the form of the roll waves. We find out the physical parameters of flows at which the roll waves exist. A linear st...

Propagation of nonlinear waves in a two-layer fluid in the shallow water approximation is considered. In a horizontal channel with a free surface and under lid, the large amplitude subsurface solitary waves describing the wave with “trapped core” are investigated. The flow regime diagram for solitary waves is constructed in the plane of governing p...

A mathematical unsteady pseudoshock model describing the continuous transition from supersonic to subsonic flow is constructed for a barotropic gas flow in a long flat channel or a nozzle. The model is based on a two-layer scheme of flow with mass transfer including a potential supersonic core and a turbulent boundary layer.

A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and maintains self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets o...

A hierarchy of mathematical models describing viscosity-stratified flow in a Hele-Shaw cell is constructed. Numerical modelling of jet flow and development of viscous fingers with the influence of the forces of inertia and friction is carried out. One-dimensional multi-layer flows are studied. In the framework of three-layer flow scheme the interpr...

In the long-wave approximation, the flow of a homogeneous fluid with a free surface in the gravity field is considered. Mathematical models of the surface turbulent layer in shear flows are derived. Steady solutions of the problem of evolution of the mixing layer under the free surface and formation of a surface turbulent jet are constructed. In pa...

A two-dimensional motion of an incompressible viscoelastic Maxwell continuum is considered. The system of quasilinear equations describing this motion has both real and complex characteristics. A class of effectively one-dimensionalmotions is analyzed for which the original system of equations is decomposed into a hyperbolic subsystem and a quadrat...

Observations and numeric modeling of internal wave generation and transformation in the shelf zone of sea show that the main part of tidal energy is transported to shores in form of internal gravitational waves. Long-term measurements of temperature and current velocity fluctuations at many levels in the near-bottom thermocline were carried out dur...

In the natural environment most large-scale flows in rivers and coastal areas can be considered as shallow, i.e., the horizontal length scales of the flow domain are much larger than the depth. In shallow waters the flows are considered as two-dimensional, they are highly affected by bottom friction and are subjected to lateral shear like in mixing...

The evolution of large amplitude internal waves propagating towards the shore and more specifically the run up phase over the "swash" zone is considered. The mathematical model describing the generation, interaction, and decaying of solitary internal waves of the second mode in the interlayer is proposed. The exact solution specifying the shape of...

Modulation equations for wave flows of a fluid film along a vertical wall are presented. At the fixed average flow rate of a fluid, the free parameter determining the periodic solutions is the wavelength, which can vary from zero to infinity. One of the unsolved problems of the theory of roll waves consists in determining the boundaries of nonlinea...

In this paper we study two-dimensional flows of incompressible viscoelastic Maxwell media with Jaumann corotational derivative in the rheological constitutive law. In the general case, due to the incompressibility condition, the equations of motion have both real and complex characteristics. Group properties of this system are studied. On this basi...

Open channel flows of ideal incompressible fluid with velocity shear are considered in the long wave approximation. Nonlinear integro-differential models of shallow flow with continuous vertical or horizontal velocity distribution are derived. It is shown that mathematically the models are equivalent and, consequently, the obtained early results fo...

Dynamics of large amplitude internal waves in two-layers of shallow water is considered. It is demonstrated that in laboratory experiments the subsurface waves of depression over a shelf may be simulated by internal symmetric solitary waves of the mode 2 ("lump-like" waves). The mathematical model describing the propagation and decaying of large in...

Second-mode nonlinear internal waves at a thin interface between homogeneous layers of immiscible fluids of different densities have been studied theoretically and experimentally. A mathematical model is proposed to describe the generation, interaction, and decay of solitary internal waves which arise during intrusion of a fluid with intermediate d...

The evolution of large amplitude internal solitary waves propagating towards the shore as the subsurface waves of depression is studied. It is shown that in laboratory experiments such flows could be simulated by internal symmetric solitary waves of mode 2 ("lump-like" waves). The mathematical model describing solitary waves propagating, interactio...

Breaking internal waves (IW) in seasonal thermocline are a common phenomenon in coastal ocean. The thermocline can shoal over a sloping bottom or deepen during the cold periods. In the both cases highly nonlinear IW can have the same amplitudes as near-bottom thermocline thickness or even higher. Complex experiments were conducted in the shelf zone...

The concepts of sub- and supercritical flows are introduced for the longwave approximation model describing the steady-state horizontal-shear motions of an ideal incompressible fluid with a free boundary in a channel of variable cross-section. Fluid layer flows developed in a local channel contraction or expansion are analyzed. Continuous and disco...

A study was conducted to carry out the theoretical and experimental investigation of second-mode nonlinear internal waves on a thin interface between homogeneous layers of mixing fluids of different densities. It proposed a mathematical model describing the generation, interaction, and decay of the solitary internal waves arising during the intrusi...

This paper considers a nonlinear integrodifferential model constructed for the motion of an ideal incompressible fluid in an open channel of variable section using the long-wave approximation. A characteristic equation for describing the perturbation propagation velocity in the fluid is derived. Necessary and sufficient conditions of generalized hy...

In the shallow-water approximation, nonlinear long waves are considered with account for small-scale waves on the free surface. The undular-bore structure, which within the framework of this model is represented as a discontinuous solution with a relaxation zone adjacent to the discontinuity, is investigated. The wave-packet damping rate is found....

A set of dispersive and hyperbolic depth-averaged equations is obtained using a hyperbolic approximation of a chosen set of fully nonlinear and weakly dispersive Boussinesq-type equations. These equations provide, at a reasonably reduced cost, both a physically sound description of the nearshore dynamics and a complete representation of dispersive...

The problem of a homogeneous heavy liquid flow over a local obstacle is considered in the long-wave approximation. The steady and unsteady waves in the vicinity of the obstacle are described by second-order models of the shallow-water theory and their hyperbolic approximations. The flow in the vicinity of the leading and trailing edges of bluff bod...

A generalized solution in the large is constructed for a mixed problem for a system of equations describing the one-dimensional motions of an ideal isothermal gas with cylindrical and spherical waves. Bibliography: 9 titles.

Brief information of the INTAS funded project is given. The project focuses on the mathematical description of the breaking-wave-induced mixing of coastal wa-ters. The analysis involves both tackling a number of theoretical issues (characteri-zation/modeling of breaking waves, of the generation/evolution of large-scale vertical structures, of the i...

The evolution of breaking waves propagating towards the shore and more specifically the run-up phase over the swash-zone for surface as well as for internal waves is considered. The study is based on a) laboratory run up experiments for surface waves ; b) laboratory stratified flow experiments and c) on field data describing the internal wave run u...

Nonequilibrium flows of an inhomogeneous liquid in channels and pipes are considered in the long-wave approximation. Nonlinear dispersion hyperbolic flow models are derived allowing taking into account the influence of internal inertia during the relative motion of phases upon the structure of nonlinear wave fronts. The asymptotic derivation of dis...

Homogeneous heavy fluid flows over an uneven bottom are studied in a long-wave approximation. A mathematical model is proposed that takes into account both the dispersion effects and the formation of a turbulent upper layer due to the breaking of surface gravity waves. The asymptotic behavior of nonlinear perturbations at the wave front is studied,...

Breaking waves in a free-surface homogeneous fluid flow in the neighborhood of a local variation in the channel depth are studied experimentally and theoretically. The structure of both a steady-state hydraulic jump generated by a local obstacle in the channel and an unsteady wave configuration consisting of two turbulent bores in the problem of lo...

Stability of periodic travelling waves of finite amplitude is investigated for the inhomogeneous hyperbolic equations of the gas dynamic type. A criterion for stability is formulated in terms of the hyperbolicity of the modulation equations for the periodic wave packets (roll waves). Asymptotic formulae for nonlinear stability in the cases of infin...

The special class of periodic travelling waves which is known as roll waves is investigated for nonhomogeneous hyperbolic equations of gas dynamics type. In this Note these equations are applied to shallow water flows in inclined open channels, but the results obtained are more general and far-reaching. The necessary conditions for the existence of...

For nonlinear hyperbolic equations of a gas dynamic type with flow acceleration and friction terms, the classification of a special class of periodic travelling waves, which are known as roll waves, is given. As an illustration, the shallow water equations for the inclined channels of an arbitrary cross-section are considered. The analysis shows th...

Twolayer miscible flow above an uneven bottom is considered. A mathematical model in the shallowwater approximation is constructed for the development of a turbulent layer between homogeneous layers of different density in a twolayer channel flow over a local obstacle. The influence of the mixing process on the formation of an initial segment of th...

Steady free-surface flows over an elongated obstacle located on the channel bottom are studied theoretically and experimentally. For determining the free-surface shape and the main flow parameters, the first and second shallow-water approximations are used. In the second approximation, a solution describing a smooth transition from the subcritical...

The stability of finite amplitude roll waves that may develop at a liquid free surface in inclined open channels of arbitrary cross-section is studied. In the framework of shallow water theory with turbulent friction the modulation equations for wave series are derived and a nonlinear stability criterion is obtained. To cite this article: A. Boudla...

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with contin...

The formation dynamics and structural features of the two-dimensional reaction zone of a detonation wave propagating in a two-layer bubbly medium is numerically studied within the framework of the Iordanskii–Kogarko one-velocity model.

A mathematical model for the evolution of a mixing layer in shear flows is constructed. The problem of a mixing layer with pressure gradient is solved: in particular, the distributions of the velocity and basic characteristics of turbulent flow in the mixing layer are obtained.

The structure of non-linear waves in a two-layer Row of an incompressible fluid in extended channels is investigated. Periodic discontinuous solutions, describing roll waves of finite amplitude, are constructed for the equations of two-laver shallow water. "Anomalous" waves of limited amplitude are found which correspond to the transition from stra...