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A numerical study of rapidly rotating flow over surface-mounted obstacles

Published online by Cambridge University Press:  20 April 2006

P. J. Mason  and
R. I. Sykes
P. J. Mason
Affiliation:
Meteorological Office, Bracknell, Berkshire
R. I. Sykes
Affiliation:
Meteorological Office, Bracknell, Berkshire Aeronautical Research Associates of Princeton, 50 Washington Road, Princeton, N.J. 08540.
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Abstract

Three-dimensional numerical integrations of the Navier-Stokes equations have been made for parameters corresponding to some previous laboratory studies of transverse flow past obstacles in a rotating fluid. In the laboratory experiments the character of the flow was found to depend upon the parameter [Sscr ]L = L/DR, where R is the Rossby number U0/ΩL, L is the horizontal scale of the obstacle, D the depth of the fluid, U0 the flow speed and ω the angular rate of rotation. For [Sscr ]L [Gt ] 1 the flows appeared twodimensional and our results confirm the applicability of this assumption in previous asymptotic theories. For [Sscr ]L ∼ 1 a leaning disturbance is produced which can look columnar in character (‘leaning Taylor column’) and our results enable a detailed examination of this structure. To clarify the importance of nonlinear effects in the leaning Taylor column we compare them with the predictions of a linear inertial wave theory. This theory is valid only for small obstacle slopes but provided it includes the effects of viscosity it gives good predictions of the amplitude of the disturbances. The main difference between the viscous linear theory and the Navier-Stokes solution is a flow asymmetry of nonlinear origin. The role of viscosity is important but passive in the sense that it does not alter the flow structure near the obstacle but progressively dissipates the disturbance with increasing distance from the obstacle. This viscous confinement of the disturbance makes the lee wave flow structure look columnar and is important in allowing some laboratory flows to seem unbounded. The results also confirm the conjecture of Mason (1975, 1977) that the large drag forces occurring in these flows are due to inertial wave radiation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 175 - 195
Copyright
© 1981 Cambridge University Press

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