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Mathematics Colloquium: Numerical simulations of density-stratified Kelvin-Helmholtz instability in a channel
4:10 pm Neill 5W
Abstract: A system of two incompressible inviscid immiscible fluids of different densities shearing one past another in the inclined channel is considered. The approach uses a boundary integral representation in which the fluid interface is approximated by a free vortex sheet and the channel walls by bound vortex sheets. The behavior of the interface between the fluids is studied numerically using the vortex blob method. The goal is to simulate the flow in the inclined channel and compare the numerical results with the experimental results obtained by Thorpe [J. Fluid Mech. 46 (1971) 299--319]. Another problem of interest is the dynamics of large amplitude internal solitary wave solutions of Euler equations in a channel, which is also studied by using a vortex sheet model discretized by a point vortex method. The initial conditions are taken to be traveling solitary wave solutions of a strongly nonlinear long-wave model studied by Jo and Choi [Stud. Appl. Math. 109 (2002) 205--227]. We validate numerical results by considering the case when channel is flat and horizontal. The goal is to simulate the formation of Kelvin-Helmholtz billows and study the deformation of a solitary wave propagating over non-uniform topography.