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Observations on the wavenumber spectrum and evolution of an internal wave attractor

Published online by Cambridge University Press:  25 February 2008

JEROEN HAZEWINKEL ,
PIETER VAN BREEVOORT ,
STUART B. DALZIEL  and
LEO R. M. MAAS
JEROEN HAZEWINKEL
Affiliation:
Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Texel, The Netherlands Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
PIETER VAN BREEVOORT
Affiliation:
Institute for Marine and Atmospheric research Utrecht, University Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
STUART B. DALZIEL
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
LEO R. M. MAAS
Affiliation:
Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Texel, The Netherlands Institute for Marine and Atmospheric research Utrecht, University Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Abstract

Reflecting internal gravity waves in a stratified fluid preserve their frequency and thus their angle with the gravitational direction. At boundaries that are neither horizontal nor vertical, this leads to a focusing or defocusing of the waves. Previous theoretical and experimental work has demonstrated how this can lead to internal wave energy being focused onto ‘wave attractors’ in relatively simple geometries. We present new experimental and theoretical results on the dynamics of wave attractors in a nearly two-dimensional trapezoidal basin. In particular, we demonstrate how a basin-scale mode forced by simple mechanical excitation develops an equilibrium spectrum. We find a balance between focusing of the basin-scale internal wave by reflection from a single sloping boundary and viscous dissipation of the waves with higher wavenumbers. Theoretical predictions using a simple ray-tracing technique are found to agree well with direct experimental observations of the waves. With this we explain the observed behaviour of the wave attractor during the initial development, steady forcing, and the surprising increase of wavenumber during the decay of the wave field after the forcing is terminated.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 373 - 382
Copyright
Copyright © Cambridge University Press 2008

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