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Evolution and decay of a rotating flow over random topography

Published online by Cambridge University Press:  04 December 2009

L. ZAVALA SANSÓN ,
A. GONZÁLEZ-VILLANUEVA  and
L. M. FLORES
L. ZAVALA SANSÓN*
Affiliation:
Department of Physical Oceanography, CICESE, Km 107 Carretera Tijuana-Ensenada, 22860 Ensenada, Baja California, México
A. GONZÁLEZ-VILLANUEVA
Affiliation:
Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, San Lorenzo Tezonco, 09790 Iztapalapa, México D.F.
L. M. FLORES
Affiliation:
Department of Physical Oceanography, CICESE, Km 107 Carretera Tijuana-Ensenada, 22860 Ensenada, Baja California, México
*
†Email address for correspondence: [email protected]
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Abstract

The evolution and decay of a homogeneous flow over random topography in a rotating system is studied by means of numerical simulations and theoretical considerations. The analysis is based on a quasi-two-dimensional shallow-water approximation, in which the horizontal divergence is explicitly different from zero, and topographic variations are not restricted to be much smaller than the mean depth, as in quasi-geostrophic dynamics. The results are examined by comparing the evolution of a turbulent flow over different random bottom topographies characterized by a specific horizontal scale, or equivalently, a given mean slope. As in two-dimensional turbulence, the energy of the flow is transferred towards larger scales of motion; after some rotation periods, however, the process is halted as the flow pattern becomes aligned along the topographic contours with shallow water to the right. The quasi-steady state reached by the flow is characterized by a nearly linear relationship between potential vorticity and transport function in most parts of the domain, which is justified in terms of minimum-enstrophy arguments. It is found that global energy decays faster for topographies with shorter horizontal length scales due to more effective viscous dissipation. In addition, some comparisons between simulations based on the shallow-water and quasi-geostrophic formulations are carried out. The role of solid boundaries is also examined: it is shown that vorticity production at no-slip walls contributes for a slight disorganization of the flow.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 159 - 180
Copyright
Copyright © Cambridge University Press 2009

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References

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