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SUMMARY:Large mode-2 internal solitary waves in three-layer flows - Ricard
 o Barros (Loughborough University)
DTSTART:20220830T100000Z
DTEND:20220830T110000Z
UID:TALK177560@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.\nIn this talk we shall discuss mode-2 large amplitude inter
 nal solitary waves in a three-layer configuration\, bounded above and belo
 w by a rigid wall. We will start by considering a strongly nonlinear model
  that extends the two-layer Miyata-Choi-Camassa (MCC) model. Its solitary-
 wave solutions are governed by a Hamiltonian system with two degrees of fr
 eedom\, and revealed by Barros et al. (2020) to have several strongly nonl
 inear characteristics that fail to be captured by the existing weakly nonl
 inear theory. In addition to large amplitude mode-2 waves with single-hump
  profiles\, new classes of mode-2 solutions\, characterised by multi-humpe
 d wave profiles of large amplitude\, are also found. The rationale behind 
 the existence of such waves is explained based on the asymptotic limit whe
 n the density transition layer is thin. Our analytical predictions based o
 n asymptotic theory are then corroborated by a numerical study of the full
  dynamical system.\nThen\, we will move to the fully nonlinear theory of E
 uler equations and compare the solutions obtained for the two models. Thes
 e share the same conjugate states corresponding to potential front solutio
 ns and a good agreement of solutions is expected. Although\, as we will sh
 ow\, regimes can be identified where even though the long-wave approximati
 on appears valid\, certain features of solutions only match qualitatively.
LOCATION:Seminar Room 2\, Newton Institute
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