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The evolution of cyclonic disturbances and lee waves over a topography in a rapidly rotating stratified flow

Published online by Cambridge University Press:  21 April 2006

Hamid T. Hefazi  and
H. K. Cheng
Hamid T. Hefazi
Affiliation:
Department of Mechanical Engineering, California State University, Long Beach, CA 90840, USA
H. K. Cheng
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089, USA
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Abstract

The temporal evolution of the flow patterns about a shallow bottom topography in a deep, rapidly rotating, stratified flow is studied on the basis of an inviscid Boussinesq model. The initial boundary-value problem, linearized for a thin three-dimensional obstacle, is solved for an impulsively started flow. The indicial response obtained reveals a window for the horizontal wavenumber spectra of the obstacle geometry. Only the portion of spectra within this window, which is shut at the start and widens linearly with increasing time, contributes to the solution. Thus, only the relatively large-scale, cyclonic feature associated with the wavenumber origin can dominate the flow in the early period, while the more familiar inertial wave system emerges much later.

Examples of solutions computed via an FFT algorithm confirm that, except in the two opposite limits for the zero and infinite stratification, the cyclonic disturbance and inertial waves coexist, but a solitary pressure hill associated with the cyclonic disturbance remains dominant throughout most evolution stages. For a sufficiently strong stratification, the solution to the linear pressure equation suggests the emergence of a secondary eddy in the lee; its significance and validity are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 195 , October 1988 , pp. 57 - 76
Copyright
© 1988 Cambridge University Press

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