# Gerassimos A. AthanassoulisNational Technical University of Athens | NTUA · School of Naval Architecture and Marine Engineering

Gerassimos A. Athanassoulis

Professor Dr.

I currently continue my research work in Stochastic Dynamics and Nonlinear Water Waves. I am open to collaboration.

## About

160

Publications

24,210

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2,022

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Citations since 2016

Introduction

Gerassimos A. Athanassoulis currently works at the School of Naval Architecture and Marine Engineering, National Technical University of Athens. Gerassimos does research in Ocean and Mechanical Engineering, Naval Architecture and Applied Mathematics. His work focuses on mathematical modelling and numerical solution of nonlinear problems in the fields of water waves, dynamical systems and wave-body interactions.
He applies and develops both deterministic and stochastic methods, aiming at a realistic (removing unjustified simplifications) modelling of complex phenomena.
His main current projects are:
1. Fully nonlinear water waves over arbitrary bathymetry,
2. Stochastic responses of nonlinear oscillators under colored noise excitation.

Additional affiliations

April 2014 - December 2017

## Publications

Publications (160)

Hamiltonian variational principles have provided, since the 1960s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that almost all flows in the sea are not irrotational, raises the question of extending Hamilton’s princ...

Abstract: Hamiltonian variational principles provided, since 60s, the means of developing very successful wave theories for nonlinear free-surface flows, under the assumption of irrotationality. This success, in conjunction with the recognition that almost all flows in the sea are not irrotational, raises the question of extending Hamilton’s Princi...

American Institute of Mathematical Sciences. The Alber equation is a moment equation for the nonlinear Schrodinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first well-posedness theory for the Alber equation with the...

Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a ran-dom functional with a Gaussian argument multiplied by the argument itself. In this work, the NF theorem is extended for mappings (function-functionals) of two arguments...

The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The problem we focus on is the transformation of an incoming solitary wave by the tr...

The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally formed or man-made, trenches. The problem we focus on is the transformation of an incoming solitary wave by the tr...

Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present wo...

The Hamiltonian coupled-mode theory (HCMT), recently derived by Athanassoulis and Papoutsellis [1], provides an efficient new approach for solving fully nonlinear water-wave problems over arbitrary bathymetry. In HCMT, heavy use is made of the roots of a local, water-wave dispersion relation with varying parameter, which have to be calculated at ev...

Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present wo...

Novikov-Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. In this work, the NF theorem is extended for mappings (function-functionals) of two arguments,...

Solving a nonlinear random differential equation (RDE) excited by Gaussian colored noise is an important problem arising in both physics and engineering, whose difficulty lies in the non-Markovian nature of its response. In the present work, approximate generalized Fokker-Planck-Kolmogorov (genFPK) equations that govern the evolution of the probabi...

The Alber equation has been proposed as a model for stochastic ocean waves, and it is associated with a nonlinear "eigenvalue relation" which controls the possible linear instability of given wave spectra. We call this condition the "Penrose condition" after a similar one appearing in plasma physics, and we show that it can be easily understood by...

The solution of systems of nonlinear random differential equations (RDEs) excited by Gaussian colored noise is an important
question in physics and engineering. An established way of work, which is revisited in the present paper, is to formulate
approximate equations governing the probability density function of the RDE system response, called the...

In this paper, we model Rogue Waves as localized instabilities emerging from homogeneous and stationary background wavefields, under NLS dynamics. This is achieved in two steps: given any background Fourier spectrum P(k), we use the Wigner transform and Penrose’s method to recover spatially periodic unstable modes, which we call unstable Penrose mo...

A novel, exact, Hamiltonian system of two nonlinear evolution equations, coupled with a time-independent system of horizontal differential equations providing the Dirichlet-to-Neumann operator for any bathymetry, is applied to the study of the evolution of wave trains in finite depth, aiming at the identification of nonlinear high waves in finite d...

This paper deals with the implementation of a new, efficient, non-perturbative, Hamiltonian coupled-mode theory (HCMT) for the fully nonlinear, potential flow (NLPF) model of water waves over arbitrary bathymetry, Papoutsellis and Athanassoulis (2017) (arXiv:1704.03276). Applications considered herein concern the interaction of solitary waves with...

Series expansions of unknown fields $\Phi=\sum\varphi_n Z_n$ in elongated waveguides are commonly used in acoustics, optics, geophysics, water waves and other applications, in the context of coupled-mode theories (CMTs). The transverse functions $Z_n$ are determined by solving local Sturm-Liouville problems (reference waveguides). In most cases, th...

A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The obtained Euler-Lagrange equations contain infinite series and can rederive various existing model equations upon trun...

Short-term educational events having the duration from several days to several weeks bring together participants from different educational institutions with diverse backgrounds and provide a unique opportunity to foster their collaborative competencies beyond a familiar environment. In this paper, we consider a short-term event as a basis for depl...

This paper addresses the effects of estimated climate change on the sea-surface dynamics of the Aegean and Ionian Seas (AIS). The main aim is the identification of climate change impacts on the severity and frequency of extreme storm surges and waves in areas of the AIS prone to flooding. An attempt is made to define design levels for future resear...

The analytic determination of the long-time, stationary response probability density
functions (pdfs) for stochastic oscillators is significant, both as a theoretical result and as a result
that could be useful in applications. In a recent work (Mamis & Athanassoulis 2016), the authors
presented a new methodology of finding exact, analytic, station...

The analytic determination of exact stationary response probability density functions (pdf) to nonlinear oscillators under additive and/or multiplicative white-noise excitation is an interesting problem for both theoretical stochastic dynamics and applications. A few analytic solutions are known, with a prominent example being the Dimentberg oscill...

The coupled-mode model developed by Belibassakis & Athanassoulis (2005) is extended and applied to the hydroelastic analysis of three-dimensional large floating bodies of shallow draft or ice sheets of small thickness, lying over variable bathymetry regions. A general bathymetry is assumed, characterised by a continuous depth function, joining two...

Equations for the evolution of the Response-Excitation
(RE) pdf of non-Markovian responses of non-linear random
differential equations (RDEs) under colored excitation
are non-closed in general or exhibit limitations due to
high-dimensionality. We present a closure scheme for the
generalized RE Liouville equation (Athanassoulis, Tsantili,
Kapelonis,...

Finding exact stationary probabilistic solutions to nonlinear oscillators under additive and/or multiplicative white-noise excitation has been an interesting and difficult problem arising in theoretical and applied stochastic dynamics. As a rule, such results are obtained by solving the corresponding stationary or reduced, as it is commonly called,...

A dynamical downscaling approach is used for the projection of the Mediterranean wave climate under greenhouse gas emission scenario A1B (SRES). Two classical approaches of extreme value analysis, that is the Block Maxima and the Peaks-Over-Threshold (POT) methods, are implemented for the estimation of the return values of significant wave heights...

The development of numerical solution schemes for stochastic oscillators under additive and/or parametric white noise excitation also calls for the determination of benchmark cases, i.e. oscillators with known characteristics and response probability density functions (pdfs). In the present paper, the stationary response pdfs for a new class of osc...

We present an annual international Young Scientists Conference (YSC) on computational science http://ysc.escience.ifmo.ru/, which brings together renowned experts and young researchers working in high-performance computing, data-driven modeling, and simulation of large-scale complex systems. The first YSC event was organized in 2012 by the Universi...

Uncertainty quantification for dynamical systems under non-white excitation is a difficult problem encountered across many scientific and engineering disciplines. Difficulties originate from the lack of Markovian character of system responses. The response-excitation (RE) theory, recently introduced by Sapsis & Athanassoulis (Sapsis & Athanassoulis...

We present a new Hamiltonian formulation for the non-linear evolution of surface gravity waves over a variable impermeable bottom. The derivation is based on Luke's variational principle and the use of an exact (convergent up to the boundaries) infinite-series representation of the unknown wave potential , in terms of a system of prescribed vertica...

A new Hamiltonian formulation for the non-linear water-wave problem over variable bathymetry is presented. It consists of two evolution equations closed by a time-independent, coupled-mode system of horizontal 2nd order linear partial differential equations. The numerical solution of the latter system shows very good accuracy and convergence proper...

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction s...

A new model is presented for harmonic wave propagation and scattering problems in non-uniform, stratified waveguides, governed by the Helmholtz equation. The method is based on a modal expansion, obtained by utilizing cross-section basis defined through the solution of vertical eigenvalue problems along the waveguide. The latter local basis is enha...

A variety of engineering applications, including interaction of waves with coastal fixed or floating structures, coastal morphodynamics and harbour maintenance, requires detailed information about nearshore and onshore wave conditions. Since information concerning sea states is usually available offshore, there is need for developing appropriate mo...

In this paper a new method is introduced for the formulation and solution of moment equations corresponding to a nonlinear differential equation with additive and multiplicative random excitations, of arbitrary correlation structure. Response moment equations are directly formulated by using the differential equation. These equations are not closed...

We consider the problem of acoustic propagation and scattering in inhomogeneous waveguide governed by the Helmholtz equation. We focus on an ideal, cylindrically symmetric ocean waveguide, limited above by an acoustically soft boundary modelling the free surface, and below by a hard boundary modelling the impenetrable seabed with general bottom top...

The fully dispersive, coupled-mode model introduced by Athanassoulis & Belibassakis (1999), and further extended to 3D by Belibassakis et al (2001), Gerostathis et al (2008) and modified to include effects of ambient currents by Belibassakis et al (2011), is exploited in order to transform wave conditions from offshore to nearshore and coastal area...

In this paper a new method is presented for the formulation and solution of
two-time, response-excitation moment equations for a nonlinear dynamical system
excited by colored, Gaussian or non-Gaussian processes. Starting from equations
for the two-time moments (e.g. for Cxy(t,s), Cxx(t,s)), the method uses an
exact time-closure condition, in additi...

New form of the Hamiltonian equations for the nonlinear water-wave problem, based to a new representation of DtN operator, are derived. As a first application of the new exact water-wave equations, we present a unified numerical treatment of nonlinear steady traveling waves, corresponding to a wide range of amplitudes and water depths.
REMARK: Th...

Sea waves induce significant pressures on coastal surfaces, especially on rocky vertical cliffs or breakwater structures (Peregrine 2003). In the present work, this hydrodynamic pressure is considered as the excitation acting on a piezoelectric material sheet, installed on a vertical cliff, and connected to an external electric circuit (on land). T...

The fully dispersive, coupled-mode model introduced by Athanassoulis & Belibassakis (1999), and further extended to 3D by Belibassakis et al. (2001), Gerostathis et al. (2008) and modified to include effects of ambient currents by Belibassakis et al. (2011), is exploited in order to transform wave conditions from offshore to nearshore and coastal a...

In this work the problem of the approximate numerical determination of a semi-infinite supported, continuous probability density function (pdf) from a finite number of its moments is addressed. The target space is carefully defined and an approximation theorem is proved, establishing that the set of all convex superpositions of appropriate Kernel D...

In the present work the probabilistic characteristics of the long-time (when dynamic statistical equilibrium has been reached), steady-state response of a half oscillator, subject to a colored, asymptotically stationary, Gaussian or non Gaussian (cubic Gaussian) excitation, are derived by means of the Response-Excitation (RE) theory, first introduc...

In the present work the probabilistic characteristics of the long-time (when dynamic statistical equilibrium has been reached), steady-state response of a half oscillator, subject to a colored, asymptotically stationary, Gaussian or non Gaussian (cubic Gaussian) excitation, are derived by means of the Response-Excitation (RE) theory, first introduc...

Sea waves induce significant pressures on coastal surfaces, especially on rocky vertical cliffs or breakwater structures (Peregrine, 2003). In the present work, this hydrodynamic pressure is considered as the excitation acting on a piezoelectric material sheet, installed on a vertical cliff, and connected to an external electric circuit (on land)....

The interaction of a random incident wave field with a floating structure in variable bathymetry regions is studied, considering the free surface displacement process in the context of first-order potential theory. The hybrid (BEM - coupled mode) model developed by Belibassakis (2008) is employed to obtain the hydrodynamic analysis of the system. T...

The response excitation theory, introduced in Athanassoulis & Sapsis (2006) and Sapsis & Athanassoulis (2008), is a new powerful method that can be used for treating nonlinear systems with arbitrary polynomial non-linearities excited by colored, Gaussian or non Gaussian, stochastic processes. Since the assumption of delta-correlated excitation is o...

We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the...

A coupled-mode model is developed for treating the wave-current-seabed interaction problem, with application to wave scattering by non-homogeneous, steady current over general bottom topography. The vertical distribution of the scattered wave potential is represented by a series of local vertical modes containing the propagating mode and all evanes...

A non-linear coupled-mode system of horizontal equations is presented, modelling the evolution of nonlinear water waves in finite depth over a general bottom topography. The vertical structure of the wave field is represented by means of a local-mode series expansion of the wave potential. This series contains the usual propagating and evanescent m...

The transformation of the directional wave spectrum over an inhomogeneous sea/coastal environment is considered. Inhomogeneities include intermediate-water depth, strongly varying 3D bottom topography and ambient currents. The consistent coupled-mode model, developed by Athanassoulis and Belibassakis (1999), extended to three dimensions by Belibass...

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this,...

A solution based on coupled mode expansions is presented for the 3D problem of acoustic scattering from a radially layered penetrable cylindrical obstacle in a shallow-water plane-horizontal waveguide. Each cylindrical ring is characterized by a general, vertical sound speed and density profile (ssdp), the ocean environment around the obstacle can...

A non-linear coupled-mode system of horizontal equations has been derived with the aid of Luke's (1967) variational principle, modelling the evolution of nonlinear water waves in intermediate depth and over a general bathymetry Athanassoulis & Belibassakis (2002, 2008). Following previous work by the authors in the case of linearised water waves (A...

A weakly dissipative free-surface flow model is presented, based on the potential flow approach previously developed by the authors (Athanassoulis & Belibassakis 2002, 2006). The potential flow model is derived with the aid of Luke's (1967) variational principle, in conjunction with a complete vertical expansion, leading to a non-linear coupled-mod...

A weakly nonlinear, coupled-mode model is developed for the wave-current-seabed interaction problem, with application to wave scattering by steady currents over general bottom topography. Based on previous work by the authors (Athanassoulis & Belibassakis 1999, Belibassakis et al 2001), the vertical distribution of the scattered wave potential is r...

In the present work the problem of determining the probabilistic structure of the dynamical response of nonlinear systems subjected to general, external, stochastic excitation is considered. The starting point of our approach is a Hopf-type equation, governing the evolution of the joint, response–excitation, characteristic functional. Exploiting th...

We compare the results of a coupled mode method (CCMM) with those of a finite ele- ment method (FENL) and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between th...

The problem of transformation of the directional spectrum of an incident wave system over an intermediate-depth region of strongly varying 3D bottom topography is studied in the context of linear theory. The consistent coupled-mode model, developed by Athanassoulis and Belibassakis (J. Fluid Mech. 389, pp. 275–301 (1999)) and extended to three dime...