Experiments on wind-perturbed rogue wave hydrodynamics using the Peregrine breather model

Being considered as a prototype for description of oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrodinger equation has been recently observed and intensely investigated experimentally in particular within the context of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breather evolution dynamics even in the presence of strong wind and chaotic wave field generated by it. Furthermore, we have shown that characteristic spectrum of the Peregrine breather persists even at the highest values of the generated wind velocities thus making it a viable characteristic for prediction of rogue waves.

[1]  Y. Nakamura,et al.  Observation of Peregrine solitons in a multicomponent plasma with negative ions. , 2011, Physical review letters.

[2]  N. Hoffmann,et al.  Rogue wave observation in a water wave tank. , 2011, Physical review letters.

[3]  D. Chalikov,et al.  Influence of Wind Forcing on Modulation and Breaking of One-Dimensional Deep-Water Wave Groups , 2012 .

[4]  D. Chalikov,et al.  Predicting the breaking onset of surface water waves , 2007 .

[5]  John M. Dudley,et al.  Rogue wave early warning through spectral measurements , 2011 .

[6]  Günther Clauss,et al.  Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test , 2013, PloS one.

[7]  Wooyoung Choi,et al.  Nonlinear surface waves interacting with a linear shear current , 2009, Math. Comput. Simul..

[8]  N. Hoffmann,et al.  Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves , 2012 .

[9]  M. Donelan,et al.  Effects of Velocity Shear on the Stability of Surface Deep Water Wave Trains , 1988 .

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

[11]  J. Touboul,et al.  Under which conditions the Benjamin-Feir instability may spawn an extreme wave event: A fully nonlinear approach , 2010 .

[12]  T. Brooke Benjamin,et al.  The disintegration of wave trains on deep water Part 1. Theory , 1967, Journal of Fluid Mechanics.

[13]  M. Okamura,et al.  The Linear Stability of Finite Amplitude Surface Waves on a Linear Shearing Flow , 1989 .

[14]  Adrian Ankiewicz,et al.  Early detection of rogue waves in a chaotic wave field , 2011 .

[15]  Manuel A. Andrade,et al.  Physical mechanisms of the Rogue Wave phenomenon , 2022 .

[16]  A. Baumstein.  Modulation of Gravity Waves with Shear in Water , 1998 .

[17]  T. Hara,et al.  Frequency downshift in narrowbanded surface waves under the influence of wind , 1991, Journal of Fluid Mechanics.

[18]  Vladimir E. Zakharov,et al.  Stability of periodic waves of finite amplitude on the surface of a deep fluid , 1968 .

[19]  Henry C. Yuen,et al.  Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves , 1980 .

[20]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[21]  Christian Kharif,et al.  The modulational instability in deep water under the action of wind and dissipation , 2010, Journal of Fluid Mechanics.

[22]  M. Donelan,et al.  Wave-Follower Field Measurements of the Wind-Input Spectral Function. Part II: Parameterization of the Wind Input , 2006 .

[23]  C. Kharif,et al.  A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity , 2012, 1207.2246.

[24]  Umberto Bortolozzo,et al.  Rogue waves and their generating mechanisms in different physical contexts , 2013 .

[25]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[26]  Nonlinear evolution of the modulational instability under weak forcing and damping , 2010 .

[27]  J. Touboul,et al.  On the interaction of wind and extreme gravity waves due to modulational instability , 2006 .

[28]  T. Waseda,et al.  Experimental study of the stability of deep-water wave trains including wind effects , 1999, Journal of Fluid Mechanics.

[29]  N. Hoffmann,et al.  Spectral properties of the Peregrine soliton observed in a water wave tank , 2012 .

[30]  N. Huang,et al.  Experimental study of the influence of wind on Benjamin–Feir sideband instability , 1986, Journal of Fluid Mechanics.

[31]  K. Dysthe,et al.  Action of Windstress and Breaking on the Evolution of a Wavetrain , 1992 .

[32]  I. E. Alber,et al.  The effects of randomness on the stability of two-dimensional surface wavetrains , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[33]  A Iafrati,et al.  Modulational instability, wave breaking, and formation of large-scale dipoles in the atmosphere. , 2012, Physical review letters.

[34]  The propagation of nonlinear wave packets in a shear flow with a free surface , 1987 .

[35]  P. Mestayer,et al.  Wind‐water tunnel simulation of small‐scale ocean‐atmosphere interactions , 1981 .

[36]  Miguel Onorato,et al.  Approximate rogue wave solutions of the forced and damped nonlinear Schrödinger equation for water waves , 2012, 1203.4735.

[37]  N. Akhmediev,et al.  Exact first-order solutions of the nonlinear Schrödinger equation , 1987 .