Numerical simulation of interaction between wind and 2D freak waves

This paper presents a newly developed approach for the numerical modelling of wind effects on the generation and dynamics of freak waves. In this approach, the quasi arbitrary Lagrangian-Eulerian finite element method (QALE-FEM) developed by the authors of this paper is combined with a commercial software (StarCD). The former is based on the fully nonlinear potential model, in which the wind-excited pressure is modelled using a modified Jeffreys’ model (C. Kharif, et al. J. Fluid Mech. 594:209-247,2008). The latter has a volume of fluid (VOF) solver which can handle violent air-wave interaction problems. The combination can simulate the interaction between freak waves and winds with an improved computational efficiency. The numerical approach is validated by comparing its predictions with experimental data. Satisfactory agreements are achieved. Detailed numerical investigations of the interaction between winds and 2D freak waves are carried out, which not only explore different air flow states but also reveal the wind effects on the change of freak wave profiles. Both breaking and non-breaking freak waves are considered.

[1]  Nobuhito Mori,et al.  Analysis of freak wave measurements in the Sea of Japan , 2002 .

[2]  T. Baldock,et al.  NUMERICAL CALCULATIONS OF LARGE TRANSIENT WATER WAVES , 1994 .

[3]  John W. Miles,et al.  Surface-wave generation revisited , 1993, Journal of Fluid Mechanics.

[4]  Q. Ma,et al.  Numerical Simulation of Wind Effects On Breaking Solitary Waves , 2009 .

[5]  Qingwei Ma,et al.  Finite element simulations of fully non-linear interaction between vertical cylinders and steep waves. Part 2: Numerical results and validation , 2001 .

[6]  Qingwei Ma,et al.  QALE‐FEM for modelling 3D overturning waves , 2009 .

[7]  M. Banner.  The influence of wave breaking on the surface pressure distribution in wind—wave interactions , 1990, Journal of Fluid Mechanics.

[8]  C. Kharif,et al.  Experimental study of the wind effect on focusing of transient wave groups , 2006, physics/0607010.

[9]  James C. McWilliams,et al.  Simulation of turbulent flow over idealized water waves , 2000, Journal of Fluid Mechanics.

[10]  Stephan T. Grilli,et al.  A fully non‐linear model for three‐dimensional overturning waves over an arbitrary bottom , 2001 .

[11]  S. Douglass.  INFLUENCE OF WIND ON BREAKING WAVES , 1990 .

[12]  Philippe Fraunié,et al.  Solitary wave breaking on sloping beaches: 2-D two phase flow numerical simulation by SL-VOF method , 2001 .

[13]  Günther Clauss,et al.  Task-Related Rogue Waves Embedded in Extreme Seas , 2002 .

[14]  Stephan T. Grilli,et al.  Modeling of Freak Wave Generation In a 3D-NWT , 2001 .

[15]  Atle Jensen,et al.  Experimental velocities and accelerations in very steep wave events in deep water , 2006 .

[16]  T. Brooke Benjamin,et al.  Shearing flow over a wavy boundary , 1959, Journal of Fluid Mechanics.

[17]  Harold Jeffreys,et al.  On the Formation of Water Waves by Wind (Second Paper) , 1926 .

[18]  Ho-Hwan Chun,et al.  Fully nonlinear numerical wave tank (NWT) simulations and wave run-up prediction around 3-D structures , 2003 .

[19]  W. Easson,et al.  Experimental study of three-dimensional breaking wave kinematics , 1997 .

[20]  Tom E. Baldock,et al.  A laboratory study of nonlinear surface waves on water , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[21]  Qingwei Ma,et al.  QALE‐FEM for numerical modelling of non‐linear interaction between 3D moored floating bodies and steep waves , 2009 .

[22]  Phung Dang Hieu,et al.  Numerical simulation of breaking waves using a two-phase flow model , 2004 .

[23]  Q. W. Ma.  Numerical Generation of Freak Waves Using MLPG{\_}R and QALE-FEM Methods , 2007 .

[24]  Pierre Lubin,et al.  Fully three-dimensional direct numerical simulation of a plunging breaker , 2003 .

[25]  J. Miles.  On the generation of surface waves by shear flows , 1957, Journal of Fluid Mechanics.

[26]  O. Phillips.  On the generation of waves by turbulent wind , 1957, Journal of Fluid Mechanics.

[27]  Bertrand Alessandrini,et al.  A 2D+T VOF fully coupled formulation for the calculation of breaking free-surface flow , 2004 .

[28]  Alexey V. Porubov,et al.  Three reasons for freak wave generation in the non-uniform current , 2006 .

[29]  F. Veron,et al.  Wind Effects on Shoaling Wave Shape , 2005 .

[30]  V. Zakharov,et al.  Freak waves as nonlinear stage of Stokes wave modulation instability , 2006 .

[31]  S. Pells,et al.  Water wave attenuation due to opposing wind , 2003, Journal of Fluid Mechanics.

[32]  Masashi Kashiwagi,et al.  A CIP-based method for numerical simulations of violent free-surface flows , 2004 .

[33]  Stephan T. Grilli,et al.  Modeling of Breaking and Post-breaking Waves on Slopes by Coupling of BEM and VOF Methods , 2003 .

[34]  Harold Jeffreys,et al.  On the Formation of Water Waves by Wind , 1925 .

[35]  C. Swan,et al.  A laboratory study of the focusing of transient and directionally spread surface water waves , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[36]  Efim Pelinovsky,et al.  Physical Mechanisms of the Rogue Wave Phenomenon , 2003 .

[37]  Q. W. Ma,et al.  Numerical simulation of fully nonlinear interaction between steep waves and 2D floating bodies using the QALE-FEM method , 2007, J. Comput. Phys..

[38]  Efim Pelinovsky,et al.  Freak waves under the action of wind: experiments and simulations , 2006 .

[39]  Djamel Lakehal,et al.  Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface , 2003, Journal of Fluid Mechanics.

[40]  Q. W. Ma,et al.  Quasi ALE finite element method for nonlinear water waves , 2006, J. Comput. Phys..

[41]  Stephan T. Grilli,et al.  Numerical modeling of extreme rogue waves generated by directional energy focusing , 2007 .

[42]  Stéphane Zaleski,et al.  TWO-DIMENSIONAL NAVIER-STOKES SIMULATION OF BREAKING WAVES , 1996, comp-gas/9605002.

[43]  Qingwei Ma,et al.  Nonlinear Simulation of 3-D Freak Waves Using a Fast Numerical Method , 2008 .

[44]  J. Sethian,et al.  Wave breaking over sloping beaches using a coupled boundary integral-level set method , 2003 .

[45]  John W. Miles,et al.  Surface-wave generation: a viscoelastic model , 1996, Journal of Fluid Mechanics.

[46]  N. Reul,et al.  Air flow separation over unsteady breaking waves , 1999 .

[47]  V. De Angelis,et al.  Direct numerical simulation of turbulent flow over a wavy wall , 1997 .

[48]  C. Baker,et al.  Changes to wave parameters in the surf zone due to wind effects , 1996 .

[49]  J. McWilliams,et al.  Turbulent flow over water waves in the presence of stratification , 2002 .

[50]  Efim Pelinovsky,et al.  Influence of wind on extreme wave events: experimental and numerical approaches , 2007, Journal of Fluid Mechanics.

[51]  W. K. Melville,et al.  On the separation of air flow over water waves , 1976, Journal of Fluid Mechanics.