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SUMMARY:Dispersive effects of bathymetry on water waves - David Ketcheson 
 (King Abdullah University of Science and Technology (KAUST))
DTSTART:20221209T103000Z
DTEND:20221209T110000Z
UID:TALK183824@talks.cam.ac.uk
DESCRIPTION:\n\n\n\nI will discuss the flow of water waves over bathymetry
  that varies periodically along one direction. Starting from the dispersio
 nless linearized shallow water model\, perturbation analysis shows that th
 e periodic bathymetry induces an effective dispersion\, distinct from the 
 dispersion inherently present in water waves. This dispersion can be relat
 ed to the effective dispersion introduced by changes in the bathymetry in 
 non-rectangular channels. Numerical simulations using the (nonlinear) shal
 low water equations reveal that a balance between this effective dispersio
 n and nonlinearity can create solitary waves. We derive a KdV-type equatio
 n that approximates the behavior of these waves in the weakly- nonlinear r
 egime. We show that\, depending on geometry\, dispersion due to bathymetry
  can be much stronger than traditional water wave dispersion and can preve
 nt wave breaking in strongly nonlinear regimes. Computational experiments 
 using depth-averaged water wave models as well as a full two-fluid Navier-
 Stokes model confirm the analysis and suggest that experimental observatio
 n of these solitary waves is possible.\n\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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