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Nonlinear Wave Hydrodynamics, Volume II
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Nonlinear Wave Hydrodynamics, Volume II

A special issue of Fluids (ISSN 2311-5521). This special issue belongs to the section "Geophysical and Environmental Fluid Mechanics".

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 28220

Special Issue Editors

Prof. Michel Benoit

E-Mail Website1 Website2
Guest Editor
1. EDF R&D Laboratoire National d’Hydraulique et Environnement (LNHE), 78400 Chatou, France
2. Saint-Venant Hydraulics Laboratory (LHSV), Ecole des Ponts, EDF R&D, 78400 Chatou, France
Interests: nonlinear waves; ocean waves; coastal waves; rogue waves; wave hydrodynamics; environmental fluid mechanics; wave–bottom interaction; coastal engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Amin Chabchoub

E-Mail Website1 Website2
Guest Editor
1. School of Civil Engineering, University of Sydney, Sydney 2006, Australia
2. Hakubi Center for Advanced Research, Kyoto University, Kyoto 615-8540, Japan
3. Disaster Prevention Research Institute, Kyoto University, Kyoto 611-0011, Japan
Interests: nonlinear waves; rogue waves; wave hydrodynamics; environmental fluid mechanics; water waves
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Takuji Waseda

E-Mail Website1 Website2
Guest Editor
Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan
Interests: nonlinear waves; rogue waves; ocean waves; extreme waves; wave-ice interaction; marine renewable energy; remote sensing; metocean support
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The rigorous framework of nonlinear wave hydrodynamics has its origins in the 18th century. Since then, significant theoretical, numerical, and experimental progress has been made that has set the foundations for several applications in ocean engineering, coastal hydrodynamics, and physical oceanography. Recently, this research topic also motivated ground-breaking studies investigating rogue waves and dispersive shock waves in other nonlinear physical media, for instance, in optics. The interaction of waves with an ambient flow field or variable seabed topography may also result in extreme waves and possibly lead to wave breaking.

In all these situations, nonlinearity plays a central role in the dynamics of the wave trains. Nonlinearity may also be important for waves under surface and lateral boundary constraints, such as waves under ice sheet, waves in an enclosed basin, and more generally wave–structure interactions. Strong nonlinearity may occur as a result of weakly nonlinear evolution or a forced wave motion.

This Special Issue aims to present recent advances in the interdisciplinary field of nonlinear wave hydrodynamics including solitons, surface gravity waves in the ocean, nearshore and coastal zones, internal waves, and wave turbulence in applied mathematics, physics, and engineering. Papers are also invited to discuss recent progress in the knowledge of physical mechanisms and modern developments and trends in the accurate modeling and prediction of hydrodynamic wave processes.

Prof. Michel Benoit
Prof. Dr. Amin Chabchoub
Prof. Dr. Takuji Waseda
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Nonlinear wave modeling
  • Ocean waves
  • Coastal waves
  • Wave–wave interaction
  • Wave–structure interaction
  • Extreme wave events
  • Freak waves
  • Flexural–gravity waves
  • Wave breaking

Published Papers (16 papers)

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Research

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13 pages, 1764 KiB  
Article
Phase Resolved Simulation of the Landau–Alber Stability Bifurcation
by Agissilaos G. Athanassoulis
Fluids 2023, 8(1), 13; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids8010013 - 30 Dec 2022
Cited by 1 | Viewed by 1182
Abstract
It has long been known that plane wave solutions of the cubic nonlinear Schrödinger Equation (NLS) are linearly unstable. This fact is widely known as modulation instability (MI), and sometimes referred to as Benjamin–Feir instability in the context of water waves. In 1978, [...] Read more.
It has long been known that plane wave solutions of the cubic nonlinear Schrödinger Equation (NLS) are linearly unstable. This fact is widely known as modulation instability (MI), and sometimes referred to as Benjamin–Feir instability in the context of water waves. In 1978, I.E. Alber introduced a methodology to perform an analogous linear stability analysis around a sea state with a known power spectrum, instead of around a plane wave. This analysis applies to second moments, and yields a stability criterion for power spectra. Asymptotically, it predicts that sufficiently narrow and high-intensity spectra are unstable, while sufficiently broad and low-intensity spectra are stable, which is consistent with empirical observations. The bifurcation between unstable and stable behaviour has no counterpart in the classical MI (where all plane waves are unstable), and we call it Landau–Alber bifurcation because the stable regime has been shown to be a case of Landau damping. In this paper, we work with the realistic power spectra of ocean waves, and for the first time, we produce clear, direct evidence for an abrupt bifurcation as the spectrum becomes narrow/intense enough. A fundamental ingredient of this work was to look directly at the nonlinear evolution of small, localised inhomogeneities, and whether these can grow dramatically. Indeed, one of the issues affecting previous investigations of this bifurcation seem to have been that they mostly looked for the indirect evidence of instability, such as an increase in overall extreme events. It is also found that a sufficiently large computational domain is crucial for the bifurcation to manifest. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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31 pages, 1148 KiB  
Article
Hamiltonian Variational Formulation of Three-Dimensional, Rotational Free-Surface Flows, with a Moving Seabed, in the Eulerian Description
by Constantinos P. Mavroeidis and Gerassimos A. Athanassoulis
Fluids 2022, 7(10), 327; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7100327 - 14 Oct 2022
Cited by 1 | Viewed by 1554
Abstract
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 [...] Read more.
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 principle to rotational free-surface flows. The Euler equations governing the bulk fluid motion have been derived by means of Hamilton’s principle since the late 1950s. Nevertheless, a complete variational formulation of the rotational water-wave problem, including the derivation of the free-surface boundary conditions, seems to be lacking until now. The purpose of the present work is to construct such a missing variational formulation. The appropriate functional is the usual Hamilton’s action, constrained by the conservation of mass and the conservation of fluid parcels’ identity. The differential equations governing the bulk fluid motion are derived as usually, applying standard methods of the calculus of variations. However, the standard methodology does not provide enough structure to obtain the free-surface boundary conditions. To overcome this difficulty, differential-variational forms of the aforementioned constraints are introduced and applied to the boundary variations of the Eulerian fields. Under this transformation, both kinematic and dynamic free-surface conditions are naturally derived, ensuring the Hamiltonian variational formulation of the complete problem. An interesting feature, appearing in the present variational derivation, is a dual possibility concerning the tangential velocity on the boundary; it may be either the same as in irrotational flow (no condition) or zero, corresponding to the small-viscosity limit. The deeper meaning and the significance of these findings seem to deserve further analysis. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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12 pages, 3537 KiB  
Article
Detuned Resonances
by Greg Colyer, Yuuichi Asahi and Elena Tobisch
Fluids 2022, 7(9), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7090297 - 09 Sep 2022
Viewed by 917
Abstract
Detuned resonance, that is, resonance with some nonzero frequency mismatch, is a topic of widespread multidisciplinary interest describing many physical, mechanical, biological, and other evolutionary dispersive PDE systems. In this paper, we attempt to introduce some systematic terminology to the field, and we [...] Read more.
Detuned resonance, that is, resonance with some nonzero frequency mismatch, is a topic of widespread multidisciplinary interest describing many physical, mechanical, biological, and other evolutionary dispersive PDE systems. In this paper, we attempt to introduce some systematic terminology to the field, and we also point out some counter-intuitive features: for instance, that a resonant mismatch, if nonzero, cannot be arbitrarily small (in some well-defined sense); and that zero-frequency modes, which may be omitted by studying only exact resonances, should be considered. We illustrate these points with specific examples of nonlinear wave systems. Our main goal is to lay down the common language and foundations for a subsequent study of detuned resonances in various application areas. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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11 pages, 2960 KiB  
Article
Rational Solitons in the Gardner-Like Models
by Efim Pelinovsky, Tatiana Talipova and Ekaterina Didenkulova
Fluids 2022, 7(9), 294; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7090294 - 06 Sep 2022
Cited by 2 | Viewed by 1264
Abstract
Rational solutions of nonlinear evolution equations are considered in the literature as a mathematical image of rogue waves, which are anomalously large waves that occur for a short time. In this work, bounded rational solutions of Gardner-type equations (the extended Korteweg-de Vries equation), [...] Read more.
Rational solutions of nonlinear evolution equations are considered in the literature as a mathematical image of rogue waves, which are anomalously large waves that occur for a short time. In this work, bounded rational solutions of Gardner-type equations (the extended Korteweg-de Vries equation), when a nonlinear term can be represented as a sum of several terms with arbitrary powers (not necessarily integer ones), are found. It is shown that such solutions describe first-order algebraic solitons, kinks, and pyramidal and table-top solitons. Analytical solutions are obtained for the Gardner equation with two nonlinear terms, the powers of which differ by a factor of 2. In other cases, the solutions are obtained numerically. Gardner-type equations occur in the description of nonlinear wave dynamics in a fluid layer with continuous or multilayer stratification, as well as in multicomponent plasma, and their solutions are used for the interpretation of rogue waves. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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22 pages, 3035 KiB  
Article
Phase Convergence and Crest Enhancement of Modulated Wave Trains
by Hidetaka Houtani, Hiroshi Sawada and Takuji Waseda
Fluids 2022, 7(8), 275; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7080275 - 11 Aug 2022
Cited by 4 | Viewed by 1420
Abstract
The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully nonlinear numerical studies have indicated that the amplification [...] Read more.
The Akhmediev breather (AB) solution of the nonlinear Schrödinger equation (NLSE) shows that the maximum crest height of modulated wave trains reaches triple the initial amplitude as a consequence of nonlinear long-term evolution. Several fully nonlinear numerical studies have indicated that the amplification can exceed 3, but its physical mechanism has not been clarified. This study shows that spectral broadening, bound-wave production, and phase convergence are essential to crest enhancement beyond the AB solution. The free-wave spectrum of modulated wave trains broadens owing to nonlinear quasi-resonant interaction. This enhances bound-wave production at high wavenumbers. The phases of all the wave components nearly coincide at peak modulation and enhance amplification. This study found that the phase convergence observed in linear-focusing waves can also occur due to nonlinear wave evolution. These findings are obtained by numerically investigating the modulated wave trains using the higher-order spectral method (HOSM) up to the fifth order, which allows investigations of nonlinearity and spectral bandwidth beyond the NLSE framework. Moreover, the crest enhancement is confirmed through a tank experiment wherein waves are generated in the transition region from non-breaking to breaking. Owing to strong nonlinearity, the maximum crest height observed in the tank begins to exceed the HOSM prediction at an initial wave steepness of 0.10. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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13 pages, 432 KiB  
Article
Serre-Green-Naghdi Dynamics under the Action of the Jeffreys’ Wind-Wave Interaction
by Miguel Alberto Manna and Anouchah Latifi
Fluids 2022, 7(8), 266; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7080266 - 04 Aug 2022
Cited by 2 | Viewed by 1115
Abstract
We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in the context of nonlinear dynamics of surface water waves under wind forcing, in finite depth. The anti-dissipation occurs du to the continuos transfer of wind energy to water surface wave. We find the solitary [...] Read more.
We derive the anti dissipative Serre-Green-Naghdi (SGN) equations in the context of nonlinear dynamics of surface water waves under wind forcing, in finite depth. The anti-dissipation occurs du to the continuos transfer of wind energy to water surface wave. We find the solitary wave solution of the system, with an increasing amplitude under the wind action. This leads to the blow-up of surface wave in finite time for infinitely large asymptotic space. This dispersive, anti-dissipative and fully nonlinear phenomenon is equivalent to the linear instability at infinite time. The theoretical blow-up time is calculated based on real experimental data. Naturally, the wave breaking takes place before the blow-up time. However, the amplitude’s growth resulting in the blow-up could be observed. Our results show that, based on the particular type of wind-wave tank data used in this paper, for h=0.14m, the amplitude growth rate is of order 0.1 which experimentally, is at the measurability limit. But we think that by gradually increasing the wind speed U10, up to 10 m/s, it is possible to have the experimental confirmation of the present theory in existing experimental facilities. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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18 pages, 3009 KiB  
Article
The Influence of Characteristic Sea State Parameters on the Accuracy of Irregular Wave Field Simulations of Different Complexity
by Helene Lünser, Moritz Hartmann, Nicolas Desmars, Jasper Behrendt, Norbert Hoffmann and Marco Klein
Fluids 2022, 7(7), 243; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7070243 - 15 Jul 2022
Cited by 4 | Viewed by 1496
Abstract
The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is [...] Read more.
The accurate description of the complex genesis and evolution of ocean waves, as well as the associated kinematics and dynamics is indispensable for the design of offshore structures and the assessment of marine operations. In the majority of cases, the water-wave problem is reduced to potential flow theory on a somehow simplified level. However, the nonlinear terms in the surface boundary conditions and the fact that they must be fulfilled on the unknown water surface make the boundary value problem considerably complex. Hereby, the contrary objectives with respect to a very accurate representation of reality and numerical efficiency must be balanced wisely. This paper investigates the influence of characteristic sea state parameters on the accuracy of irregular wave field simulations of different complexity. For this purpose, the high-order spectral method was applied and the underlying Taylor series expansion was truncated at different orders so that numerical simulations of different complexity can be investigated. It is shown that, for specific characteristic sea state parameters, the boundary value problem can be significantly reduced while providing sufficient accuracy. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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15 pages, 736 KiB  
Article
Periodic and Solitary Wave Solutions of the Long Wave–Short Wave Yajima–Oikawa–Newell Model
by Marcos Caso-Huerta, Antonio Degasperis, Priscila Leal da Silva, Sara Lombardo and Matteo Sommacal
Fluids 2022, 7(7), 227; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7070227 - 04 Jul 2022
Cited by 3 | Viewed by 1596
Abstract
Models describing long wave–short wave resonant interactions have many physical applications, from fluid dynamics to plasma physics. We consider here the Yajima–Oikawa–Newell (YON) model, which was recently introduced, combining the interaction terms of two long wave–short wave, integrable models, one proposed by Yajima–Oikawa, [...] Read more.
Models describing long wave–short wave resonant interactions have many physical applications, from fluid dynamics to plasma physics. We consider here the Yajima–Oikawa–Newell (YON) model, which was recently introduced, combining the interaction terms of two long wave–short wave, integrable models, one proposed by Yajima–Oikawa, and the other one by Newell. The new YON model contains two arbitrary coupling constants and it is still integrable—in the sense of possessing a Lax pair—for any values of these coupling constants. It reduces to the Yajima–Oikawa or the Newell systems for special choices of these two parameters. We construct families of periodic and solitary wave solutions, which display the generation of very long waves. We also compute the explicit expression of a number of conservation laws. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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14 pages, 1401 KiB  
Article
Two Models for 2D Deep Water Waves
by Sergey Dremov, Dmitry Kachulin and Alexander Dyachenko
Fluids 2022, 7(6), 204; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7060204 - 15 Jun 2022
Viewed by 1423
Abstract
In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in [...] Read more.
In this paper we propose two Hamiltonian models to describe two-dimensional deep water waves propagating on the surface of an ideal incompressible three-dimensional fluid. The idea is based on taking advantage of the Zakharov equation for one-dimensional waves which can be written in the form of so-called compact equations. We generalize these equations to the case of two-dimensional waves. As a test of our models, we perform numerical simulations of the dynamics of standing waves in a channel with smooth vertical walls. The results obtained in the proposed models are comparable, indicating that the models are similar to the original Zakharov equation. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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30 pages, 1731 KiB  
Article
Statistical Dynamics of Mean Flows Interacting with Rossby Waves, Turbulence, and Topography
by Jorgen S. Frederiksen and Terence J. O’Kane
Fluids 2022, 7(6), 200; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7060200 - 09 Jun 2022
Cited by 1 | Viewed by 1417
Abstract
Abridged statistical dynamical closures, for the interaction of two-dimensional inhomogeneous turbulent flows with topography and Rossby waves on a beta–plane, are formulated from the Quasi-diagonal Direct Interaction Approximation (QDIA) theory, at various levels of simplification. An abridged QDIA is obtained by replacing the [...] Read more.
Abridged statistical dynamical closures, for the interaction of two-dimensional inhomogeneous turbulent flows with topography and Rossby waves on a beta–plane, are formulated from the Quasi-diagonal Direct Interaction Approximation (QDIA) theory, at various levels of simplification. An abridged QDIA is obtained by replacing the mean field trajectory, from initial-time to current-time, in the time history integrals of the non-Markovian closure by the current-time mean field. Three variants of Markovian Inhomogeneous Closures (MICs) are formulated from the abridged QDIA by using the current-time, prior-time, and correlation fluctuation dissipation theorems. The abridged MICs have auxiliary prognostic equations for relaxation functions that approximate the information in the time history integrals of the QDIA. The abridged MICs are more efficient than the QDIA for long integrations with just two relaxation functions required. The efficacy of the closures is studied in 10-day simulations with an easterly large-scale flow impinging on a conical mountain to generate rapidly growing Rossby waves in a turbulent environment. The abridged closures closely agree with the statistics of large ensembles of direct numerical simulations for the mean and transients. An Eddy Damped Markovian Inhomogeneous Closure (EDMIC), with analytical relaxation functions, which generalizes the Eddy Dampened Quasi Normal Markovian (EDQNM) to inhomogeneous flows, is formulated and shown to be realizable under the same circumstances as the homogeneous EDQNM. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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12 pages, 4537 KiB  
Article
A Hydrodynamic Analog of the Casimir Effect in Wave-Driven Turbulent Flows
by Mahdi Davoodianidalik, Hamid Kellay and Nicolas Francois
Fluids 2022, 7(5), 155; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7050155 - 27 Apr 2022
Viewed by 1918
Abstract
We present experimental results on a fluctuation-induced force observed in Faraday wave-driven turbulence. As recently reported, a long-range attraction force arises between two walls that confine the wave-driven turbulent flow. In the Faraday waves system, the turbulent fluid motion is coupled with the [...] Read more.
We present experimental results on a fluctuation-induced force observed in Faraday wave-driven turbulence. As recently reported, a long-range attraction force arises between two walls that confine the wave-driven turbulent flow. In the Faraday waves system, the turbulent fluid motion is coupled with the disordered wave motion. This study describes the emergence of the fluctuation-induced force from the viewpoint of the wave dynamics. The wave amplitude is unaffected by the confinement while the wave erratic motion is. As the wall spacing decreases, the wave motion becomes less energetic and more anisotropic in the cavity formed by the walls, giving rise to a stronger attraction. These results clarify why the modelling of the attraction force in this system cannot be based on the wave amplitude but has to be built upon the wave-fluid motion coupling. When the wall spacing is comparable to the wavelength, an intermittent wave resonance is observed, and it leads to a complex short-range interaction. These results contribute to the study of aggregation processes in the presence of turbulence and its related problems such as the accumulation of plastic debris in coastal marine ecosystems or the modelling of planetary formation. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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17 pages, 5693 KiB  
Article
A Numerical Study on Distant Tsunami Propagation Considering the Strong Nonlinearity and Strong Dispersion of Waves, or the Plate Elasticity and Mantle Fluidity of Earth
by Taro Kakinuma
Fluids 2022, 7(5), 150; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7050150 - 25 Apr 2022
Cited by 2 | Viewed by 2065
Abstract
Numerical simulations were generated to investigate the propagation processes of distant tsunamis, using a set of wave equations based on the variational principle considering both the strong nonlinearity and strong dispersion of waves. First, we proposed estimate formulae for the time variations of [...] Read more.
Numerical simulations were generated to investigate the propagation processes of distant tsunamis, using a set of wave equations based on the variational principle considering both the strong nonlinearity and strong dispersion of waves. First, we proposed estimate formulae for the time variations of the tsunami height and wavelength of the first distant tsunami, by assuming that the initial tsunami profile was a long crest in a uniform bathymetry. Second, we considered the plate elasticity and upper-mantle fluidity of Earth, to examine their effects on the distant tsunami propagation. When the plate and upper mantle meet certain conditions with both a large depth and moderately large density of the upper mantle, the internal-mode tsunamis with a significant tsunami height propagated slower than the tsunamis in the corresponding one-layer problems, leading to the delay of the arrival time observed in distant tsunamis from that evaluated by the one-layer calculation. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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23 pages, 2391 KiB  
Article
Nonlinear Waves Passing over Rectangular Obstacles: Multimodal Method and Experimental Validation
by Eduardo Monsalve, Agnès Maurel, Vincent Pagneux and Philippe Petitjeans
Fluids 2022, 7(5), 145; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7050145 - 23 Apr 2022
Cited by 2 | Viewed by 1891
Abstract
We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and [...] Read more.
We report a theoretical and experimental investigation of the propagation of nonlinear waves passing over a submerged rectangular step. A multimodal method allows calculating the first- and second-order reflected and transmitted waves. In particular, at the second order, the propagation of free and bound waves is theoretically presented. A detailed analysis of the convergence of the second-order problem shows that a finite truncation of the series of evanescent bound waves is necessary to obtain a smooth and convergent solution. The computed coefficients of the first and second harmonics are experimentally validated via a complete space-time-resolved measurements of the wave propagation, which permits us to verify the relative amplitude, phase and spatial interference (beating) of the free and bound waves at the second order. This result can be useful in future multimodal models since it not only keeps the accuracy of the model with the inclusion of the first part of the evanescent bound terms (being also the dominants) but also ensures the convergence of the multimodal computation with an error that decreases as a function of the number of modes. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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16 pages, 10101 KiB  
Article
The Hydrodynamic Behavior of Vortex Shedding behind Circular Cylinder in the Presence of Group Focused Waves
by Iskander Abroug, Nizar Abcha, Fahd Mejri, Emma Imen Turki and Elena Ojeda
Fluids 2022, 7(1), 4; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7010004 - 22 Dec 2021
Cited by 1 | Viewed by 2436
Abstract
Vortex shedding behind an elastically mounted circular cylinder in the presence of group focused waves propagating upstream was investigated using a classical approach (time series and FFT) and nonclassical approach (complex 2D Morlet wavelets). Wavelet analysis emerged as a novel solution in this [...] Read more.
Vortex shedding behind an elastically mounted circular cylinder in the presence of group focused waves propagating upstream was investigated using a classical approach (time series and FFT) and nonclassical approach (complex 2D Morlet wavelets). Wavelet analysis emerged as a novel solution in this regard. Our results include wave trains with different nonlinearities propagating in different water depths and derived from three types of spectra (Pierson–Moskowitz, JONSWAP (γ = 3.3 or γ = 7)). It was found that the generated wave trains could modify regimes of shedding behind the cylinder, and subharmonic frequency lock-in could arise in particular situations. The occurrence of a lock-in regime in the case of wave trains propagating in intermediate water locations was shown experimentally even for small nonlinearities. Moreover, the application of time-localized wavelet analysis was found to be a powerful approach. In fact, the frequency lock-in regime and its duration could be readily identified from the wavelet-based energy and its corresponding ridges. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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18 pages, 1835 KiB  
Article
Modulation Instability of Hydro-Elastic Waves Blown by a Wind with a Uniform Vertical Profile
by Susam Boral, Trilochan Sahoo and Yury Stepanyants
Fluids 2021, 6(12), 458; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids6120458 - 16 Dec 2021
Viewed by 1696
Abstract
An interesting physical phenomenon was recently observed when a fresh-water basin is covered by a thin ice film that has properties similar to the property of a rubber membrane. Surface waves can be generated under the action of wind on the air–water interface [...] Read more.
An interesting physical phenomenon was recently observed when a fresh-water basin is covered by a thin ice film that has properties similar to the property of a rubber membrane. Surface waves can be generated under the action of wind on the air–water interface that contains an ice film. The modulation property of hydro-elastic waves (HEWs) in deep water covered by thin ice film blown by the wind with a uniform vertical profile is studied here in terms of the airflow velocity versus wavenumber. The modulation instability of HEWs is studied through the analysis of coefficients of the nonlinear Schrödinger (NLS) equation with the help of the Lighthill criterion. The NLS equation is derived using the multiple scale method in the presence of airflow. It is demonstrated that the potentially unstable hydro-elastic waves with negative energy appear for relatively small wind speeds, whereas the Kelvin–Helmholtz instability arises when the wind speed becomes fairly strong. Estimates of parameters of modulated waves for the typical conditions are given. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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Review

Jump to: Research

39 pages, 5611 KiB  
Review
Impact of the Dissipation on the Nonlinear Interactions and Turbulence of Gravity-Capillary Waves
by Michael Berhanu
Fluids 2022, 7(4), 137; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids7040137 - 12 Apr 2022
Cited by 4 | Viewed by 2507
Abstract
Gravity-capillary waves at the water surface are an obvious example illustrating wave propagation in the laboratory, and also nonlinear wave phenomena such as wave interactions or wave turbulence. However, at high-enough frequencies or small scales (i.e., the frequencies typically above 4 Hz or [...] Read more.
Gravity-capillary waves at the water surface are an obvious example illustrating wave propagation in the laboratory, and also nonlinear wave phenomena such as wave interactions or wave turbulence. However, at high-enough frequencies or small scales (i.e., the frequencies typically above 4 Hz or wavelengths below 10 cm), the viscous dissipation cannot be neglected, which complicates experimental, theoretical, and numerical approaches. In this review, we first derive, from the fundamental principles, the features of the gravity-capillary waves. We then discuss the origin and the magnitude of the viscous wave. dissipation in the laboratory and under field conditions. We then show that the significant level of dissipation has important consequences on nonlinear effects involving waves. The nonlinearity level quantified by the wave steepness must be large enough to overcome the viscous dissipation. Specifically, using water as fluid in the field and in the laboratory, nonlinear wave interactions and wave turbulence occur most of the time in a non-weakly nonlinear regime, when the waves are in the capillary or gravity-capillary range. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics, Volume II)
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