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On inertial flow over topography. Part 1. Semigeostrophic adjustment to an obstacle

Published online by Cambridge University Press:  20 April 2006

L. J. Pratt
L. J. Pratt
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543 Present address: Graduate School of Oceanography, University of Rhode Island, Kingston, RI 02881.
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Abstract

The nonlinear time-dependent adjustment of a homogeneous rotating-channel flow to the sudden obtrusion of an obstacle is studied. Solutions are obtained using a Lax–Wendroff numerical scheme which allows rotating breaking bores and jumps to form and be maintained. The flow upstream of the obstacle is found to be completely blocked, partially blocked (and hydraulically controlled), or unobstructed depending upon the height of the obstacle. Partial blockage is accomplished through the excitation of a combination of nonlinear Kelvin waves, some of which steepen into interfacial shocks. Riemann invariants for the Kelvin waves are found, and jump conditions on mass, momentum and potential vorticity for the shocks are discussed. The shocks are surrounded by dispersive regions of Rossby deformation scale, and the potential vorticity of passing fluid is altered at a rate proportional to the differential rate of energy dissipation along the line of breakage. For the special case of initially uniform potential vorticity the asymptotic state is found as a function of the initial conditions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 131 , June 1983 , pp. 195 - 218
Copyright
© 1983 Cambridge University Press

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