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Interharmonics in internal gravity waves generated by tide-topography interaction

Published online by Cambridge University Press:  25 September 2008

ALEXANDER S. KOROBOV  and
KEVIN G. LAMB
ALEXANDER S. KOROBOV
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
KEVIN G. LAMB
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Canada
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Abstract

The dynamics and spectrum of internal gravity waves generated in a linearly stratified fluid by tidal flow over a flat-topped ridge are investigated at five different latitudes using an inviscid two-dimensional numerical model. The resulting wave field includes progressive freely propagating waves which satisfy the dispersion relation, and forced waves which are trapped non-propagating oscillations with frequencies outside the internal wave band. The flow is largely stable with respect to shear instabilities, and, throughout the runs, there is a negligibly small amount of overturning which is confined to the highly nonlinear regions along the sloping topography and where tidal beams reflect from the boundaries. The wave spectrum exhibits a self-similar structure with prominent peaks at tidal harmonics and interharmonics, whose magnitudes decay exponentially with frequency. Two strong subharmonics are generated by an instability of tidal beams which is particularly strong for near-critical latitudes where the Coriolis frequency is half the tidal frequency. When both subharmonics are within the free internal wave range (as in cases 0°–20° N), they form a resonant triad with the tidal harmonic. When at least one of the two subharmonics is outside of the range (as in cases 30°–40° N) the observed instability is no longer a resonant triad interaction. We argue that the two subharmonics are generated by parametric subharmonic instability that can produce both progressive and forced waves. Other interharmonics are produced through wave–wave interactions and are not an artefact of Doppler shifting as assumed by previous authors. As the two subharmonics are, in general, not proper fractions of the tidal frequency, the wave–wave interactions are capable of transferring energy to a continuum of frequencies.

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Papers
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Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 61 - 95
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Copyright © Cambridge University Press 2008

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