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Frontogenesis in a fluid with horizontal density gradients

Published online by Cambridge University Press:  26 April 2006

J. E. Simpson  and
P. F. Linden
J. E. Simpson
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
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Abstract

The adjustment under gravity of a fluid containing a horizontal density gradient is described.’ The fluid is initially at rest and the resulting motion is calculated as the flow accelerates, driven by the baroclinic density field. Two forms of the initial density distribution are considered. In the first the initial horizontal gradient is constant. A purely horizontal motion develops as the isopycnals rotate towards the horizontal. The vertical density gradient increases continually with time but the horizontal density gradient remains unchanged. The horizontal velocity has a uniform vertical shear, and the gradient Richardson number is constant in space and decreases monotonically with time to ½. The second density distribution consists of a piecewise constant gradient with a jump in the gradient along a vertical isopycnal. The density is continuous. In this case frontogenesis is predicted to occur on the isopycnal between the two constant-density-gradient regions, and the timescale for the formation of a front is determined. Laboratory experiments are reported which confirm the results of these calculations. In addition, lock exchange experiments have been carried out in which the horizontal mean gradient is represented by a series of step density differences separated by vertical gates.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 1 - 16
Copyright
© 1989 Cambridge University Press

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