Nonlinear-Dispersive Shallow Water Equations on a Rotating Sphere and Conservation Laws
Z. I. Fedotova, G. S. Khakimzyanov
Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: shallow water equations on a sphere, surface waves, nonlinear dispersive equations, Boussinesq type equations, energy conservation law
Abstract
Nonlinear dispersive shallow water equations on a sphere are obtained without using the potential flow assumption. Boussinesq-type equations for weakly nonlinear waves over a moving bottom are derived. It is found that the total energy balance holds for all obtained nonlinear dispersive equations on a sphere.
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