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An asymptotic solution of the tidal equations

Published online by Cambridge University Press:  28 March 2006

Stanley J. Jacobs
Stanley J. Jacobs
Affiliation:
Department of Meteorology and Oceanography, The University of Michigan, Ann Arbor, Michigan
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Abstract

The Cauchy problem for the β-plane form of the tidal equations is solved for both oscillatory and delta function initial data. The radius of deformation is assumed to be much less than the radius of the earth, and in accord with this assumption a ray approximation is employed.

It is shown that, owing to the rapid rate of propagation of inertio-gravity waves, the motion in its initial development tends towards geostrophic balance. However, the solution given by the ray approximation is singular on certain surfaces in space and time, the envelopes of the rays. A local boundary-layer theory is employed to correct this deficiency. The existence of these caustics implies that the process of geostrophic adjustment is more complicated than hitherto imagined.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 3 , 29 November 1967 , pp. 417 - 438
Copyright
© 1967 Cambridge University Press

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