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Steady currents induced by oscillations round islands

Published online by Cambridge University Press:  29 March 2006

M. S. Longuet-Higgins
M. S. Longuet-Higgins
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge, and National Institute of Oceanography, Wormley, Surrey.
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Abstract

An oscillating current such as a tidal stream or an inertial oscillation may have a horizontal scale of the order of many times the local depth of water. Thus an island projecting from an otherwise uniform sea bed will give rise to a local, periodic disturbance near the island. It is shown that this disturbance may be resolved into two waves travelling in opposite senses round the island. If the particle orbits at large distances are circular, then only one of these waves has non-zero amplitude.

In addition to the oscillatory motion, however, there is a steady d.c. streaming, or mass-transport velocity, whose magnitude is of order u2/σa where u denotes the magnitude of the oscillatory velocity at large distances, σ denotes the radian frequency, and a is the radius of the island. In this paper the profile of the streaming velocity is calculated for circular islands, with or without shoaling regions offshore. It is shown that resonance with the free modes trapped by the shoaling regions may greatly increase the streaming velocity. Viscosity (or horizontal mixing) also tends to increase the streaming velocity close to the shoreline.

The conclusions are supported by some simple model experiments. It is suggested that such streaming may partly account for the observed pattern of currents near Bermuda.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 4 , 30 July 1970 , pp. 701 - 720
Copyright
© 1970 Cambridge University Press

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References

Allen, J. & Gibson, D. H. 1959 Experiments on the displacement of water by waves of various heights and frequencies. Min. Proc. Instn Civ. Engrs. 13, 363–386.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Hunt, J. N. & Johns, B. 1963 Currents induced by tides and gravity waves. Tellus, 15, 343–351.Google Scholar
Lamb, H. 1932 Hydrodynamics (6th end.). Cambridge University Press.
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1960 Mass transport in the boundary layer at a free oscillating surface. J. Fluid Mech. 8, 293–306.Google Scholar
Longuet-Higgins, M. S. 1969a On the trapping of long-period waves round islands. J. Fluid Mech. 37, 773–784.Google Scholar
Longuet-Higgins, M. S. 1969b On the transport of mass by time-varying ocean currents. Deep-Sea Res. 16, 431–477.Google Scholar
Moore, D. 1969 The mass transport velocity induced by free oscillations at a single frequency. Geophys. Fluid Dynam. (To be published.)Google Scholar
Munk, W. H. & Moore, D. 1968 Is the Cromwell Current driven by equatorial Rossby waves? J. Fluid Mech. 33, 241–259.Google Scholar
Mysak, L. A. 1967 On the theory of continental shelf waves. J. Mar. Res. 25, 205–227.Google Scholar
Pedlosky, J. 1965 A study of the time dependent ocean circulation. J. Atmos. Sci. 22, 267–272.Google Scholar
Phillips, N. A. 1965 Elementary Rossby waves. Tellus, 17, 295–301.Google Scholar
Rhines, P. B. 1967 The influence of bottom topography on long-period waves in the ocean. Ph.D. Thesis, Cambridge University.
Rhines, P. B. 1969 Slow oscillations in an ocean of varying depth. Part 2. Islands and seamounts. J. Fluid Mech. 37, 191–205.Google Scholar
Robinson, A. R. 1965 Research Frontiers in Fluid Dynamics. New York: Interscience.
Russell, R. C. H. & Osorio, J. D. C. 1958 An experimental investigation of drift profiles in a closed channel. Proc. 6th Conf. on Coastal Engng Miami 1957, pp. 171–193.Google Scholar
Schlichting, H. 1932 Berechnung ebener periodischer Grenzschchitstromungen. Phys. Z. 33, 327–335.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Stommel, H. 1954 Serial observations of drift currents in the central North Atlantic Ocean. Tellus, 6, 203–214.Google Scholar