Gravity Waves on the Surface of the Sphere
We propose a Hamiltonian model for gravity waves on the surface of a fluid layer surrounding a gravitating sphere. The general equations of motion are nonlocal and can be used as a starting point for simpler models, which can be derived systematically by expanding the Hamiltonian in dimensionless parameters. In this paper, we focus on the small wave amplitude regime. The first-order nonlinear terms can be eliminated by a formal canonical transformation. Similarly, many of the second order terms can be eliminated. The resulting model has the feature that it leaves invariant several finite-dimensional subspaces on which the motion is integrable.
KeywordsPeriodic Orbit Gravity Wave Poisson Bracket Water Wave Canonical Transformation
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