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SUMMARY:Plenary Talk: Mode-2 solitary waves in 3-layer flows - Paul Milews
 ki (University of Bath)
DTSTART:20221208T090000Z
DTEND:20221208T100000Z
UID:TALK183821@talks.cam.ac.uk
DESCRIPTION:\n\n\nStratified fluids with narrow regions of rapid density v
 ariation with respect to depth (pycnoclines) are often modelled as layered
  flows. In this talk we shall examine horizontally propagating internal wa
 ves of the second baroclinic mode (mode-2)\, by computing travelling wave 
 solutions within three-layer fluid. We will be presenting numerical soluti
 ons to both the full Euler equations and to a reduced fully-nonlinear\, we
 akly dispersive model\, the three-layer Miyata-Choi-Camassa (MCC3) equatio
 ns. Mode-2 nonlinear waves (typically) occur within the linear spectrum of
  mode-1 waves\, and are hence generically associated with an infinite ener
 gy resonant mode-1 oscillatory tail. However\, in line with recent results
  for the MCC3 system by Barros\, Choi & Milewski (JFM\, 2020)\, we will pr
 esent numerical evidence that these oscillations can be found to have zero
  amplitude\, resulting in families of truly localised solutions (so called
  embedded solitary waves) in the Euler equations. We also discuss limiting
  solutions which are related to heteroclinic connections between the so ca
 lled conjugate states of the system (which are identical in Euler and MCC3
 ). This is joint work with Ricardo Barros and Alex Doak.\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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