• Bowen, A. J., and R. A. Holman, 1989: Shear instabilities of the mean longshore current 1. Theory. J. Geophys. Res.,94, 18 023–18 030.

  • Dunkerton, T. J., D. P. Delisi, and M.-P. Lelong, 1998: Alongslope current generated by obliquely incident internal gravity waves. Geophys. Res. Lett.,25, 3871–3874.

  • Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res.,87, 525–538.

  • ——, 1985: Implications of ocean bottom reflection for internal wave spectra and mixing. J. Phys. Oceanogr.,15, 1145–1156.

  • ——, 1998: Internal wave reflection and mixing at Fieberling Guyot. J. Geophys. Res.,103, 2977–2994.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Hogg, N. G., 1971: Longshore currents generated by obliquely incident internal waves. Geophys. Fluid Dyn.,2, 361–376.

  • Phillips, O. M., 1966: The Dynamics of the Upper Ocean. Cambridge University Press, 261 pp.

  • Polzin, K. L., J. M. Toole, J. R. Ledwell, and R. W. Schmitt, 1997: Spatial variability of turbulent mixing in the abyssal ocean. Science,276, 93–96.

  • Slinn, D. A., and J. J. Riley, 1998: Turbulent dynamics of a criticallyreflecting internal gravity wave. Theor. Comput. Fluid Dyn.,11, 281–304.

  • Thorpe, S. A., 1968: On the shape of progressive internal waves. Philos. Trans. Roy. Soc. London,263A, 563–614.

  • ——, 1987: On the reflection of a train of finite amplitude internal waves from a uniform slope. J. Fluid Mech.,178, 279–302.

  • ——, 1992: Thermal fronts generated by internal gravity waves reflecting from a slope. J. Phys. Oceanogr.,22, 105–108.

  • ——, 1997: On the interactions of internal waves reflecting from slopes. J. Phys. Oceanogr.,27, 2072–2078.

  • ——, 1998a: The generation of alongslope currents by breaking internal waves. J. Phys. Oceanogr.,29, 29–35.

  • ——, 1998b: Some dynamical effects of internal waves and the sloping sides of lakes. Physical Processes in Lakes and Oceans, J. Imberger, Ed., AGU Coastal and Esturine Series, Vol. 54, Amer. Geophys. Union, 441–460.

  • ——, 1999: Fronts formed by obliquely reflecting internal waves at a sloping boundary. J. Phys. Oceanogr.,29, 2462–2467.

  • Toole, J. M., R. W. Schmitt, and K. L. Polzin, 1997: Near-bottom mixing above the flanks of a midlatitude seamount. J. Geophys. Res.,102, 947–959.

  • Wunsch, C., 1971: Note on some Reynolds stress effects of internal waves on slopes. Deep-Sea Res.,18, 538–591.

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The Effects of Rotation on the Nonlinear Reflection of Internal Waves from a Slope

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  • 1 School of Ocean and Earth Science, Southampton Oceanography Centre, Southampton, United Kingdom
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Abstract

The effect of rotation on the nonlinear reflection of internal waves from a sloping boundary is examined. The waves propagate at an angle β to the horizontal in an ocean of locally uniform buoyancy frequency N, and the boundary slopes at angle α to the horizontal. The following modifications are found when rotation is taken into account: 1) The modulus of the Lagrangian alongslope drift caused by the waves may be increased by an order of magnitude, and the level above the boundary at which the greatest drift is generated is no longer at z = 0, but depends on f/N where f is the Coriolis frequency, and the direction of the drift close to the boundary may be reversed. 2) Eulerian upslope currents associated with reflection are increased by a factor O(2). Particularly large currents are found to be generated for incident waves travelling almost directly downslope and when β > α. 3) The mean density and the vertical displacement of isopycnals caused by the waves are increased, possibly by factors O(2). 4) The generation of density fronts near the boundary is only slightly affected, except possibly when the incident wave direction β is close to values at which the second-order wave components are near critical when f/N = 0. Here rotation reduces the tendency for fronts to form.

Corresponding author address: Dr. Steve A. Thorpe, Bodfryn, Glanrafon, Llangoed, Anglesey LL58 8PH, United Kingdom.

Email: oss413@sos.bangor.ac.uk

Abstract

The effect of rotation on the nonlinear reflection of internal waves from a sloping boundary is examined. The waves propagate at an angle β to the horizontal in an ocean of locally uniform buoyancy frequency N, and the boundary slopes at angle α to the horizontal. The following modifications are found when rotation is taken into account: 1) The modulus of the Lagrangian alongslope drift caused by the waves may be increased by an order of magnitude, and the level above the boundary at which the greatest drift is generated is no longer at z = 0, but depends on f/N where f is the Coriolis frequency, and the direction of the drift close to the boundary may be reversed. 2) Eulerian upslope currents associated with reflection are increased by a factor O(2). Particularly large currents are found to be generated for incident waves travelling almost directly downslope and when β > α. 3) The mean density and the vertical displacement of isopycnals caused by the waves are increased, possibly by factors O(2). 4) The generation of density fronts near the boundary is only slightly affected, except possibly when the incident wave direction β is close to values at which the second-order wave components are near critical when f/N = 0. Here rotation reduces the tendency for fronts to form.

Corresponding author address: Dr. Steve A. Thorpe, Bodfryn, Glanrafon, Llangoed, Anglesey LL58 8PH, United Kingdom.

Email: oss413@sos.bangor.ac.uk

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