Research in Nonlinear Water Waves
Quarterly letter progress rept. 1 Oct-31 Dec 1990
CALIFORNIA INST OF TECH PASADENA DEPT OF APPLIED MATHEMATICS
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Work has continued during the quarter on the dynamical effects of a thin shear layer on the structure and stability of finite amplitude water waves. One problem of interest is the possibility of an explosive instability which occurs when there is resonance between waves of opposite signature. The signature can be thought of as the energy of the wave, and the explosive instability is an interaction between waves with positive and negative energy. Work was started on the effect of a thin, vorticity containing shear layer in the water on the Kelvin-Helmholtz and Miles instabilities of the air flow over water. The team is in the process of formulating the equations and are now considering efficient methods of solution and deciding upon the relevant parts of parameter space to search. Preliminary calculations with a stick profile suggest that some rather interesting results may be obtained. In order to determine the effect of a thin vortical layer, it is necessary to study first the classical case of wind over water in the absence of vorticity in the water.
- Fluid Mechanics