HR: 16:10h
AN: OS44A-03 INVITED     [Abstracts]
TI: On the Existence of Solitary Wave Solutions for the Rotating Shallow Water Equations
AU: * Stastna, M
AF: University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1 Canada
AU: Poulin, F J
EM: fpoulin@math.uwaterloo.ca
AF: University of Waterloo, 200 University Ave. West, Waterloo, ON N2L 3G1 Canada
AB: It has been suggested in a recent paper (JPO, vol. 34, pg 856) that the inviscid shallow water equations allow zonally propagating solitary waves. A peculiar trait of these solutions is found at the crest of the wave and takes the form of a cusp for the surface elevation and zonal component of velocity and a discontinuity in the meridional velocity. The authors suggest (but do not demonstrate) that both the discontinuity and the cusp would be smoothed in the presence of eddy viscosity. In this talk we will employ dynamical systems techniques to demonstrate why, in the inviscid case, any zonally traveling waves must exhibit a singularity. We will subsequently demonstrate that when viscosity is nonzero the singularity is indeed smoothed, but the solution is no longer bounded, and hence no solitary waves can exist. The analytical results will be compared with numerical solutions of the geostrophic adjustment problem in a zonal channel. Finally we will contrast the f-plane case with a nonrotating stratified adjustment problem which is dominated by solitary wave trains.
DE: 3220 Nonlinear dynamics
DE: 4508 Coriolis effects
DE: 4544 Internal and inertial waves
DE: 4560 Surface waves and tides (1255)
SC: Ocean Sciences [OS]
MN: 2005 Joint Assembly