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Gravity currents moving along a lateral boundary in a rotating fluid

Published online by Cambridge University Press:  20 April 2006

R. W. Griffiths  and
E. J. Hopfinger
R. W. Griffiths
Affiliation:
Institut de Mécanique de Grenoble, B.P. 53 X, Centre de Tri, 38041 Grenoble, France Present address: Research School of Earth Sciences, The Australian National University, P.O. Box 4, Canberra 2600, Australia.
E. J. Hopfinger
Affiliation:
Institut de Mécanique de Grenoble, B.P. 53 X, Centre de Tri, 38041 Grenoble, France
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Abstract

Density currents in a rotating fluid are produced by releasing a volume of buoyant fluid from a lock at one end of a long rotating channel. Coriolis forces hold the current against one wall. It is observed that the velocity and depth of the nose decrease exponentially in time, implying that the nose can effectively come to a halt at a finite distance from the lock. In reality though, the flow regime eventually changes and a viscous wedge-shaped intrusion continues. The high-Reynolds-number currents contain three-dimensional turbulence a short distance behind the nose, but the influence of rotation causes this to become quasi-two-dimensional further upstream. The intrusion and turbulent motions represent a forcing to the lower layer that produces vortex and wave-like motions which penetrate deep into the lower-layer fluid. It is shown that the exponential decay can be attributed to radiation of momentum by these inertial waves.

The width l of the turbulent current varies with distance behind the nose, from 0.6 times the local time-dependent deformation radius at the ‘head’ to l ≈ R0 far upstream, where R0 is the initial deformation radius in the lock. The nose of the boundary current is unstable, with billows appearing near the tip of the intruding nose and leading to an intermittent breakup of the ‘head’ structure and oscillations of the nose velocity. These oscillations are rapid, often having frequencies much greater than f (where f = 2Ω is the Coriolis parameter), and, along with the production of the turbulence that is so characteristic of the currents, are attributed to a Kelvin–Helmholtz instability. Rotationally dominated baroclinic waves appear only a very large distance behind the nose.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 134 , September 1983 , pp. 357 - 399
Copyright
© 1983 Cambridge University Press

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