On nonlinear planetary waves: A class of solutions missed by the traditional quasi-geostrophic approximation |
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Authors: | Toshio Yamagata |
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Institution: | (1) Research Institute for Applied Mechanics, Kyushu Univ., 6-10-1 Hakozaki, 812 Higashi-ku, Japan;(2) Present address: Geophysical Fluid Dynamics Program, Princeton University, P.O. Box 308, 08540 Princeton, N.J., USA |
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Abstract: | Weakly nonlinear quasi-geostrophic planetary waves on a beta-plane and topographic waves over a linearly inclined bottom are examined by use of shallow water equations for a small beta parameter. Long solitary wave solutions missed by the use of the traditional quasi-geostrophic approximation are found in a channel ocean with neither a sheared current nor a curved (non-linearly inclined) bottom topography. The solutions are missed in the traditional approach because the irrotational motion associated with the geostrophic divergence is neglected by the quasi-geostrophic approximation. Another example which calls attention to the limitation of the traditional quasi-geostrophic approximation is the nonlinear evolution of divergent planetary eddies whose scale is much larger than the Rossby's radius of deformation. Some aspects of a new evolution equation are briefly discussed. |
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