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SUMMARY:On surface and internal ring waves on currents: dispersive hydrody
 namics in 3D - Karima Khusnutdinova (Loughborough University)
DTSTART:20220712T100000Z
DTEND:20220712T103000Z
UID:TALK175847@talks.cam.ac.uk
DESCRIPTION:Oceanic surface and internal waves often have curvilinear fron
 ts and propagate over various depth-dependent currents. We study long weak
 ly-nonlinear waves using a linear modal decomposition in the far-field set
  of Euler equations with the boundary conditions appropriate for oceanogra
 phic applications. The theoretical framework consists of a spectral proble
 m defining three-dimensional modal functions and dispersion relation (angu
 lar adjustment equation in the form of a nonlinear first-order ODE)\, as w
 ell as an amplitude equation (generally\, 2+1-dimensional) with coefficien
 ts dependent on solutions of the modal equations.&nbsp\; I will discuss re
 cent&nbsp\; analytical results for two- and three-layered fluids with basi
 c shear flows suitable for the modelling of wind-generated currents\, rive
 r inflows and exchange flows in straits.&nbsp\; I will also discuss numeri
 cal results&nbsp\; which reveal interesting features including the formati
 on of transient dispersive shock waves only in the upstream part of the ri
 ng wave. The structure of the wave field in strongly three-dimensional. Si
 ngularities of the swallowtail-type may arise near the onset of the long-w
 ave instability of the basic flow. Based on joint works with Curtis Hooper
 \, Roger Grimshaw\, Dmitri Tseluiko\, Noura Alharthi and Ricardo Barros.
LOCATION:Seminar Room 1\, Newton Institute
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