When we consider waves of large enough scale, the sphericity of the Earth can no longer be ignored. Rossby was the first to point out that the most significant effect of the Earth’s sphericity is that it rendered the Coriolis parameter f = 2Ω; sin θa function of latitude. Since the large scale motions in the ocean are nearly horizontal, the only component of the Coriolis acceleration that really matters is the one involving the horizontal velocities, and therefore only the local vertical component of the Coriolis parameter is dynamically significant. Otherwise, for scales that are large but still sub-planetary, a Cartesian coordinate system can be used to obtain at least a qualitatively correct view of the dynamics. Such an approximation in which the variation of the Coriolis parameter with latitude is treated but in which the geometry is otherwise Cartesian is called the beta-plane approximation, and we shall use it without a detailed justification. The student is referred to Pedlosky (1987) for a careful derivation. In this course, we will use the heuristic approach outlined above.
KeywordsGroup Velocity Gravity Wave Rossby Wave Potential Vorticity Phase Speed
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