HR: 1340h
AN: A43B-1158    [Abstracts]
TI: Kelvin Waves in the Nonlinear Shallow Water Equations on the Sphere: Nonlinear Traveling Waves and the Corner Wave Bifurcation
AU: * Zhou, C
EM: zhouc@umich.edu
AF: Department of Atmospheric, Oceanic and Space Science, University of Michigan, Ann Arbor, MI 48109, United States
AU: Boyd, J P
EM: jpboyd@umich.edu
AF: Department of Atmospheric, Oceanic and Space Science, University of Michigan, Ann Arbor, MI 48109, United States
AB: The Kelvin wave is the lowest eigenmode of Laplace's Tidal Equation and is widely observed in both the ocean and the atmosphere. In this work, we neglect mean currents, but instead include the full effects of the earth's sphericity and the wave dispersion it induces. Through a mix of perturbation theory and numerical computations using a Fourier/Newton iteration/continuation method, we show that for sufficiently small amplitude, there are Kelvin traveling waves(cnoidal waves). As the amplitude increaes, the branch of traveling waves terminates in a so-called '' corner wave" with a discontinuous first derivative. All waves larger than the corner wave evolve to fronts and break. The singularity is a point singularity in which only the longitudinal derivative is discontinuous. As we solve the nonlinear shallow water equations on the sphere with increasing ε ('' Lamb's parameter"), dispersion weakens, the amplitude of the corner wave decreases rapidly, and the longitudinal profile of the corner wave narrows dramatically.
DE: 1620 Climate dynamics (0429, 3309)
DE: 3367 Theoretical modeling
DE: 3374 Tropical meteorology
DE: 3389 Tides and planetary waves
DE: 4231 Equatorial oceanography
SC: Atmospheric Sciences [A]
MN: 2007 Fall Meeting