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The ‘sliced-cylinder’ laboratory model of the wind-driven ocean circulation. Part 2. Oscillatory forcing and Rossby wave resonance

Published online by Cambridge University Press:  29 March 2006

Robert C. Beardsley
Robert C. Beardsley
Affiliation:
Department of Meteorology, Massachusetts Institute of Technology, Cambridge
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Abstract

The response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is studied here in part 2 for the case of an oscillatory ‘wind’ stress. The model consists of a rapidly rotating right cylinder with a planar sloping bottom. This basin geometry contains no closed geostrophic contours, so that low frequency topographic Rossby wave modes possessing mean vorticity exist in the sliced-cylinder model by the physical analogy between topographic vortex stretching and the β effect for large-scale planetary flows. The interior flow in the laboratory model is driven by the time-dependent Ekman-layer suction produced by the periodic relative angular velocity of the upper lid. The frequency of the forcing is sufficiently small that the interior motion is quasi-geostrophic with the horizontal velocities being independent of depth. Simple two-dimensional analytic and numerical models are developed and compared very favourably with the laboratory results. The observed horizontal velocity field exhibits both (i) westward intensification and decreased horizontal scale when the forcing frequency is decreased, and (ii) a significant resonant magnification when the forcing frequency is tuned to the natural frequency of one of the lower inviscid topographic Rossby wave modes. The observed westward phase speed of the driven motion is accurately predicted and shows little dependence on the amplitude of the forcing. The instantaneous and mean Lagrangian fluid particle trajectories were measured in the laboratory model. The general derivation by Moore (1970) of the governing equations for the mean Lagrangian motion are extended to incorporate forcing and Ekman-layer dissipation. The results suggest that the mean Lagrangian flow should be significantly reduced near resonant frequencies, since the mean Eulerian motion is partially offset by the Stokes drift associated with the topographic Rossby wave modes. This result is consistent with the small observed amplitude of the mean Lagrangian motion. Also presented are the results for a laboratory experiment conducted using a combined steady and oscillatory ‘wind’ stress.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 69 , Issue 1 , 13 May 1975 , pp. 41 - 64
Copyright
© 1975 Cambridge University Press

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References

Beardsley, R. C. 1969 A laboratory model of the wind-driven ocean circulation J. fluid Mech. 38, 255.Google Scholar
Beardsley, R. C. 1973 A numerical investigation of a laboratory analogy of the wind-driven ocean circulation. Proc. 1972 NAS Symp. on Numerical Models of Ocean Circulation.Google Scholar
Beardsley, R. C. & Robbins, K. 1975 The ‘sliced cylinder’ laboratory model of the wind-driven ocean circulation. Part 1. Steady forcing and topographic Rossby wave breakdown. J. Fluid Mech. 69, 27–40.Google Scholar
Crease, J. 1962 Velocity measurements in the deep water of the western North Atlantic J. Geophys. Res. 67, 3173.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Greenspan, H. P. 1969 A note on the laboratory simulation of planetary flows Studies in Appl. Math. 48, 147.Google Scholar
Holton, J. 1971 An experimental study of forced barotropic Rossby waves J. Geophys. Fluid Dyn. 2, 323.Google Scholar
Ibbetson, A. & Phillips, N. 1967 Some laboratory experiments on Rossby waves in a rotating annulus Tellus, 19, 81.Google Scholar
Lamb, H. 1945 Hydrodynamics. Cambridge University Press.
LONGUET-HIGGINS, M. S. 1969 On the transport of mass by time-varying ocean currents Deep-Sea Res. 16, 431.Google Scholar
Moore, D. 1970 The mass transport velocity induced by free oscillations at a single frequency Geophys. Fluid Dyn. 1, 237.Google Scholar
Munk, W. H. & Moore, D. 1968 Is the Cromwell Current driven by equatorial Rossby waves? J. Fluid Mech. 33, 241.Google Scholar
Pedlosky, J. 1965 A study of the time dependent ocean circulation J. Atmos. Sci. 22, 267.Google Scholar
Pedlosky, J. & Greenspan, H. P. 1967 A simple laboratory model for the oceanic circulation J. Fluid Mech. 27, 291.Google Scholar
Phillips, N. 1965 Elementary Rossby waves Tellus, 17, 295.Google Scholar
Phillips, N. 1966 Large-scale eddy motion in the western Atlantic J. Geophys. Res. 71, 3883.Google Scholar
Robinson, A. R. 1965 Research Frontiers in Fluid Dynamics, chap. 17, pp. 504–533. Interscience.
Rossby, C. et al. 1939 Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action J. Mar. Res. 2, 38.CrossRefGoogle Scholar
Slater, J. & Frank, N. 1947 Mechanics. McGraw-Hill.
Swallow, M. 1961 Measuring deep currents in midocean New Scientist, 9, 740.Google Scholar
Veronis, G. 1970 Effect of fluctuating winds on ocean circulation Deep-Sea Res. 17, 421.Google Scholar