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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Large mode-2 internal solitary waves in three-laye
r flows - Ricardo Barros (Loughborough University)
DTSTART;TZID=Europe/London:20220712T143000
DTEND;TZID=Europe/London:20220712T150000
UID:TALK175856AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175856
DESCRIPTION:Internal waves are commonly observed in the world&
rsquo\;s oceans and are of great importance in phy
sical oceanography. It is estimated that 90% of th
e kinetic energy associated with oceanic internal
waves is contained within the first two baroclinic
modes. While extensive experimental and mathemati
cal research into mode-1 waves exists\, there are
very limited studies into mode-2 waves\, despite t
he increasing recognition of their importance. &nb
sp\;In this talk we shall discuss mode-2 large amp
litude internal solitary waves in a three-layer co
nfiguration\, bounded above and below by a rigid w
all. We will start by considering a strongly nonli
near model that extends the two-layer Miyata-Choi-
Camassa (MCC) model. Its solitary-wave solutions a
re governed by a Hamiltonian system with two degre
es of freedom\, and revealed by Barros et al. (202
0) to have several strongly nonlinear characterist
ics that fail to be captured by the existing weakl
y nonlinear theory. In addition to large amplitude
mode-2 waves with single-hump profiles\, new clas
ses of mode-2 solutions\, characterised by multi-h
umped wave profiles of large amplitude\, are also
found. The rationale behind the existence of such
waves is explained based on the asymptotic limit w
hen the density transition layer is thin. Our anal
ytical predictions based on asymptotic theory are
then corroborated by a numerical study of the full
dynamical system.Then\, we will move to the fully
nonlinear theory of Euler equations and compare t
he solutions obtained for the two models. These sh
are the same conjugate states corresponding to pot
ential front solutions and a good agreement of sol
utions is expected. Although\, as we will show\, r
egimes can be identified where even though the lon
g-wave approximation appears valid\, certain featu
res of solutions only match qualitatively. \;
\; \;References: \;R.Barros\, W.Choi\
, P.A.Milewski (2020) Strongly non\;linear eff
ects on internal solitary waves in three-\;lay
er flows. J. Fluid Mech. 883 A16. \;A.Doak\, R
.Barros\, P.A.Milewski (2022) Large mode\;-2 i
nternal solitary waves in three-\;layer flows
JFM\, Submit\;ted\, https://doi.org/10.48550/a
rXiv.2205.00503 \;
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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