Nonlinear Interactions in Rotating Stratified Flow.
MICHIGAN UNIV ANN ARBOR COLL OF ENGINEERING
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Nonlinear interactions in a rotating, stratified fluid with a free surface are considered. The field variables are expanded in terms of eigenfunctions of the linearized problem, with coefficients dependent on time. Orthogonality relations are developed to obtain evolution equations for the coefficients, and these are simplified through use of the method of averaging for weakly nonlinear motions. The geostrophic mode, which alone possesses potential vorticity, is tested with regard to the quasi-geostrophic equations when wave modes are presented. The phases of the wave modes are affected by the presence of the geostrophic mode, with ferequency splitting for steady geostrophic flow. Resonant interactions between waves are observed for a resonant triad consisting of two external waves and one interval wave. Author
- Fluid Mechanics