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Two-layer spin-up and frontogenesis

Published online by Cambridge University Press:  20 April 2006

P. F. Linden  and
G. J. F. Van Heijst
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
G. J. F. Van Heijst
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW Present address: Institute of Meteorology and Oceanography. University of Utrecht, Princetonplein 5, Utrecht, The Netherlands.
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Abstract

The spin-up of a two-layer fluid in a cylinder with a free surface and with a thin lower layer is examined in the laboratory. It is found that when the increase in rotation rate of the cylinder is large enough the radial outflow in the viscous boundary layer on the tank bottom is sufficient to cause the interface to descend near the centre of the tank and to intersect the bottom. The intersection between the interface and the bottom produces a front between stratified (two-layer) fluid and a central region (called the bare spot) in which the upper layer is in direct contact with the bottom. It is observed that the radius of the circular bare spot increases until the lower layer is spun up. Observations of the maximum size of the bare spot are compared with a theoretical calculation in which it is assumed that the lower layer acquires the new angular velocity of the container and where viscous coupling between the layers is neglected. An expansion in F, the upper-layer Froude number, gives good agreement with the observations.

At larger times the circular front is observed to be unstable to frontal waves which appear to gain energy via baroclinic instability from the sloping density interface. At large amplitude these waves ‘break’, producing regions of closed streamlines in the upper layer. The shape of the bare spot is severely distorted by these waves and the associated motions. The effect of the bottom stress on the spin-up of the upper layer is found to be limited to the bare spot where it is in direct contact with the bottom. Some comments are made on the formation and decay of fronts in the benthic boundary layer of the ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 143 , June 1984 , pp. 69 - 94
Copyright
© 1984 Cambridge University Press

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