The Generation of Alongslope Currents by Breaking Internal Waves

S. A. Thorpe Department of Oceanography, Southampton Oceanography Centre, Southampton, United Kingdom

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Abstract

Internal gravity waves propagating in a fluid of constant buoyancy frequency and approaching a uniform sloping boundary from a direction that is not in a plane normal to the boundary, and dissipating energy on reflection, generate alongslope currents. The net radiation stress or momentum flux into the breaking region is proportional to the flux of energy lost from the waves. It is supposed that the stress is balanced by a frictional boundary stress so that a steady alongslope current is generated. The dependence of the strength of the current on the steepness, AIMI, of the incident wave and on its propagation direction is examined as a function of α and β, the inclination of the boundary to the horizontal and the angle between the incident wave group velocity vector and the horizontal, respectively. Alongslope currents of several centimeters per second, generally exceeding the Lagrangian drift produced by wave reflection alone, may be generated in the ocean or in lakes. Reflection of subcritical (α > β) waves with positive downward components of group velocity can lead to larger currents for the same values of the wave slope and of α and |αβ| than for the reflection of incident supercritical (α < β) waves. The vertical diffusion coefficient Kυ in the boundary layer where waves break is estimated using the Osborn empirical relationship between Kυ and ϵ, the rate of dissipation of turbulent energy per unit mass, and is found to exceed typical values found in the interior of oceans and lakes.

Corresponding author address: Prof. S. A. Thorpe, University of Southampton, Department of Oceanography, Southampton Oceanography Centre, Waterfront Campus, European Way, Southampton S014 3ZH, United Kingdom.

Abstract

Internal gravity waves propagating in a fluid of constant buoyancy frequency and approaching a uniform sloping boundary from a direction that is not in a plane normal to the boundary, and dissipating energy on reflection, generate alongslope currents. The net radiation stress or momentum flux into the breaking region is proportional to the flux of energy lost from the waves. It is supposed that the stress is balanced by a frictional boundary stress so that a steady alongslope current is generated. The dependence of the strength of the current on the steepness, AIMI, of the incident wave and on its propagation direction is examined as a function of α and β, the inclination of the boundary to the horizontal and the angle between the incident wave group velocity vector and the horizontal, respectively. Alongslope currents of several centimeters per second, generally exceeding the Lagrangian drift produced by wave reflection alone, may be generated in the ocean or in lakes. Reflection of subcritical (α > β) waves with positive downward components of group velocity can lead to larger currents for the same values of the wave slope and of α and |αβ| than for the reflection of incident supercritical (α < β) waves. The vertical diffusion coefficient Kυ in the boundary layer where waves break is estimated using the Osborn empirical relationship between Kυ and ϵ, the rate of dissipation of turbulent energy per unit mass, and is found to exceed typical values found in the interior of oceans and lakes.

Corresponding author address: Prof. S. A. Thorpe, University of Southampton, Department of Oceanography, Southampton Oceanography Centre, Waterfront Campus, European Way, Southampton S014 3ZH, United Kingdom.

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