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On mass transports generated by tides and long waves

Published online by Cambridge University Press:  20 April 2006

J. M. Huthnance
J. M. Huthnance
Affiliation:
Institute of Oceanographic Sciences, Bidston Observatory, Merseyside L43 7RA
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Abstract

For small-amplitude barotropic wave motion in a shallow fluid, Moore (1970) found that the associated mean mass transport is geostrophic, but otherwise arbitrary in the absence of friction. We show how weak friction, or starting the motion from rest, determines the mass transport by restricting circulation around closed geostrophic (f/h) contours. The resulting transport is quadratic in oscillatory quantities and depends on the friction type, but not on its (weak) magnitude. Comparison is made with earlier results in particular geometries. A tendency for anticyclonic circulation around shallow regions is found, and extends to large-amplitude oscillations where particle excursions exceed the topographic length scale. We suggest that numerical schemes for calculating tidal residuals should conserve mass and vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 367 - 387
Copyright
© 1981 Cambridge University Press

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References

Andrews, D. G. & McIntyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian mean flow. J. Fluid Mech. 89, 609–646.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bretherton, F. P. 1969 On the mean motion induced by internal gravity waves. J. Fluid Mech. 36, 785–803.Google Scholar
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129–154.Google Scholar
Colin de Verdière, A. 1979 Mean flow generation by topographic Rossby waves. J. Fluid Mech. 94, 39–64.Google Scholar
Hasselmann, K. 1970 Wave-driven inertial oscillations. Geophys. Fluid Dyn. 1, 463–502.Google Scholar
Heaps, N. S. 1978 Linearised vertically-integrated equations of residual circulation in coastal seas. Deut. Hydrogr. Zeit. 31, 147–169.Google Scholar
Hunt, J. N. & Johns, B. 1963 Currents induced by tides and gravity waves. Tellus 15, 343–351.Google Scholar
Huthnance, J. M. 1973a Tidal current asymmetries over the Norfolk Sandbanks. Est. Coastal Mar. Sci. 1, 89–99.Google Scholar
Huthnance, J. M. 1973b The influence of topography on tidal currents. Ph.D. thesis, University of Cambridge.
Ianniello, J. P. 1977 Tidally induced residual currents in estuaries of constant breadth and depth. J. Mar. Res. 35, 755–786.Google Scholar
Ianniello, J. P. 1979 Tidally induced residual currents in estuaries of variable breadth and depth. J. Phys. Oceanog. 9, 962–974.Google Scholar
Johns, B. 1973 The residual flow in a tidal stream. Pure & Appl. Geophys. 104, 594–607.Google Scholar
Johns, B. & Dyke, P. P. G. 1972 The structure of the residual flow in an offshore tidal stream. J. Phys. Oceanog. 2, 73–79.Google Scholar
Kagan, B. A. 1972 Resistance law of tidal flow. Izv. Atmos. Oceanic Phys. 8, 302–307.Google Scholar
Lamoure, J. & Mei, C. C. 1977 Effects of horizontally two-dimensional bodies on the mass transport near the sea bottom. J. Fluid Mech. 83, 415–431.Google Scholar
Liu, P. L.-F. 1977 Mass transport in the free-surface boundary layers. Coastal Engng 1, 207–219.Google Scholar
Loder, J. W. 1980 Topographie rectification of tidal currents on the sides of Georges Bank. J. Phys. Oceanog. 10, 1399–1416.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. Roy. Soc. A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1969 On the transport of mass by time-varying ocean currents. Deep-Sea Res. 16, 431–447.Google Scholar
Longuet-Higgins, M. S. 1970 Steady currents induced by oscillations round islands. J. Fluid Mech. 42, 701–720.Google Scholar
McIntyre, M. E. 1980 Towards a Lagrangian-mean description of stratospheric circulations and chemical transports. Phil. Trans. Roy. Soc. A 296, 129–148.Google Scholar
Moore, D. 1970 Mass transport velocity induced by free oscillations at a single frequency. Geophys. Fluid. Dyn. 1, 237–247.Google Scholar
Nihoul, J. C. J. 1975 Effect of the tidal stress on residual circulation and mud deposition in the Southern Bight of the North Sea. Pure & Appl. Geophys. 113, 577–581.Google Scholar
Ou, H. W. & Bennett, J. R. 1979 A theory of the mean flow driven by long internal waves in a rotating basin, with application to Lake Kinneret. J. Phys. Oceanog. 9, 1112–1125.Google Scholar
Pingree, R. D. & Maddock, L. 1977 Tidal residuals in the English Channel. J. Mar. Biol. Assoc. U.K. 57, 339–354.Google Scholar
Prandle, D. 1978 Residual flows and elevations in the southern North Sea. Proc. Roy. Soc. A 359, 189–228.Google Scholar
Rhines, P. B. 1976 The dynamics of unsteady currents. The Sea 6, 189–318.Google Scholar
Rhines, P. B. 1979 Geostrophic turbulence. Ann. Rev. Fluid Mech. 11, 401–441.Google Scholar
Rhines, P. B. & Holland, W. R. 1979 A theoretical discussion of eddy-driven mean flows. Dyn. Atmos. Oceans 3, 289–325.Google Scholar
Roach, P. J. 1976 Computational Fluid Dynamics. Albuquerque: Hermosa.
Sadourny, R. 1975 The dynamics of finite-difference models of the shallow-water equations J. Atmos. Sci. 32, 680–689.Google Scholar
Stern, M. E. & Shen, C. Y. 1976 Displacement and rectification of planetary fluids. Geophys. Fluid Dyn. 7, 81–118.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455.Google Scholar
Ursell, F. 1950 On the theoretical form of ocean swell on a rotating earth. Mon. Not. R. Astron. Soc., Geophys. Suppl. 6, 1–8.Google Scholar
Whitehead, J. A. 1975 Mean flow generated by circulation on a β-plane: an analogy with the moving flame experiment. Tellus 27, 358–363.Google Scholar
Zimmerman, J. T. F. 1978 Topographic generation of residual circulation by oscillatory (tidal) currents. Geophys. Astrophys. Fluid Dyn. 11, 35–47.Google Scholar
Zimmerman, J. T. F. 1979 On the Euler-Lagrange transformation and the Stokes drift in the presence of oscillatory and residual currents. Deep-Sea Res. 26, 505–520.Google Scholar