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SUMMARY:Large mode-2 internal solitary waves in three-layer flows - Ricard
 o Barros (Loughborough University)
DTSTART:20220712T133000Z
DTEND:20220712T140000Z
UID:TALK175856@talks.cam.ac.uk
DESCRIPTION:Internal waves are commonly observed in the world&rsquo\;s oce
 ans and are of great importance in physical oceanography. It is estimated 
 that 90% of the kinetic energy associated with oceanic internal waves is c
 ontained within the first two baroclinic modes. While extensive experiment
 al and mathematical research into mode-1 waves exists\, there are very lim
 ited studies into mode-2 waves\, despite the increasing recognition of the
 ir importance. &nbsp\;In this talk we shall discuss mode-2 large amplitude
  internal solitary waves in a three-layer configuration\, bounded above an
 d below by a rigid wall. We will start by considering a strongly nonlinear
  model that extends the two-layer Miyata-Choi-Camassa (MCC) model. Its sol
 itary-wave solutions are governed by a Hamiltonian system with two degrees
  of freedom\, and revealed by Barros et al. (2020) to have several strongl
 y nonlinear characteristics that fail to be captured by the existing weakl
 y nonlinear theory. In addition to large amplitude mode-2 waves with singl
 e-hump profiles\, new classes of mode-2 solutions\, characterised by multi
 -humped wave profiles of large amplitude\, are also found. The rationale b
 ehind the existence of such waves is explained based on the asymptotic lim
 it when the density transition layer is thin. Our analytical predictions b
 ased on asymptotic theory are then corroborated by a numerical study of th
 e full dynamical system.Then\, we will move to the fully nonlinear theory 
 of Euler equations and compare the solutions obtained for the two models. 
 These share the same conjugate states corresponding to potential front sol
 utions and a good agreement of solutions is expected. Although\, as we wil
 l show\, regimes can be identified where even though the long-wave approxi
 mation appears valid\, certain features of solutions only match qualitativ
 ely. &nbsp\;&nbsp\;&nbsp\;References:&nbsp\;R.Barros\, W.Choi\, P.A.Milews
 ki (2020) Strongly non&shy\;linear effects on internal solitary waves in t
 hree-&shy\;layer flows. J. Fluid Mech. 883 A16.&nbsp\;A.Doak\, R.Barros\, 
 P.A.Milewski (2022) Large mode&shy\;-2 internal solitary waves in three-&s
 hy\;layer flows JFM\, Submit&shy\;ted\, https://doi.org/10.48550/arXiv.220
 5.00503&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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