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SUMMARY:Soliton fission and solitonic turbulence for shallow water waves: 
 a numerical study with different models - Michel Benoit (Electricté de Fr
 ance)
DTSTART:20220712T140000Z
DTEND:20220712T143000Z
UID:TALK175859@talks.cam.ac.uk
DESCRIPTION:This work deals with the mathematical modelling and numerical 
 simulation of the dynamics of water wave trains propagating in shallow wat
 er. In the case of uniform water depth and 2D waves in a vertical plane (x
 \, z)\, two physical situations are addressed:A. The fission of an initial
  free surface deformation into a set of solitons. The number of solitons t
 hat appear from a given initial condition\, the duration necessary for the
 ir emergence\, the occurrence of a possible recurrence (or quasi-recurrenc
 e) of the Fermi-Pasta-Ulam type\, etc. (Trillo et al.\, 2016) &nbsp\;is st
 udied.B. The solitonic turbulence regime corresponding to the evolution of
  a set of solitons interacting with each other through multiple collisions
  over a long distance/time (i.e. soliton gas dynamics).To carry out this w
 ork\, we use three numerical wave models of increasing complexity\, with r
 egard to dispersion and nonlinearity:1) the Korteweg-de Vries (KdV) model\
 , which is weakly dispersive and weakly nonlinear (and limited to waves pr
 opagating in only one direction)\,2) the Serre-Green-Naghdi (SGN) type mod
 els\, which is partially dispersive and fully nonlinear (at this order of 
 dispersion)\,3) a fully nonlinear and dispersive potential-flow model\, ba
 sed on Euler-Zakharov equations\, with the whispers3D code\, using the app
 roach presented and validated by Raoult et al. (2016).\nOne of the objecti
 ves of this work is to evaluate the effects associated with these differen
 t levels of consideration of nonlinear and dispersive effects on the dynam
 ics of the shallow wave trains\, and the consequences on the dynamics of t
 he wave trains\, the statistical (high-order moments\, statistical distrib
 ution of free surface elevation\, etc.) and spectral (frequency- and wave-
 number spectra\, etc.) descriptions of wave fields. The second objective i
 s to evaluate the capabilities (and limitations) of these different modell
 ing approaches to reproduce the physical effects observed in the above-men
 tioned experiments.\nRaoult C.\, Benoit M.\, Yates M.L. (2016) Validation 
 of a fully nonlinear and dispersive wave model with laboratory non-breakin
 g experiments. Coastal Engineering\, Vol. 114\, pp 194&ndash\;207.&nbsp\;\
 nTrillo S.\, Deng G.\, Biondini G.\, Klein M.\, Clauss G. F.\, Chabchoub A
 .\, Onorato M. (2016) Experimental observation and theoretical description
  of multisoliton fission in shallow water. Phys. Rev. Lett.\, 117(14)\, 14
 4102.
LOCATION:Seminar Room 1\, Newton Institute
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