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Numerical simulation of a two-dimensional internal wave attractor

Published online by Cambridge University Press:  16 October 2008

NICOLAS GRISOUARD ,
CHANTAL STAQUET  and
IVANE PAIRAUD
NICOLAS GRISOUARD
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, BP 53, 38041 Grenoble Cedex 9, France
CHANTAL STAQUET
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, BP 53, 38041 Grenoble Cedex 9, France
IVANE PAIRAUD
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, BP 53, 38041 Grenoble Cedex 9, France
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Abstract

Internal (gravity) wave attractors may form in closed containers with boundaries non-parallel and non-normal to the gravity vector. Such attractors have been studied from a theoretical point of view, in laboratory experiments and using linear numerical computations. In the present paper two-dimensional numerical simulations of an internal wave attractor are reported, based upon the nonlinear and non-hydrostatic MIT-gcm numerical code. We first reproduce the laboratory experiment of a wave attractor performed by Hazewinkel et al. (J. Fluid Mech. Vol. 598, 2008 p. 373) and obtain very good agreement with the experimental data. We next propose simple ideas to model the thickness of the attractor. The model predicts that the thickness should scale as the 1/3 power of the non-dimensional parameter measuring the ratio of viscous to buoyancy effects. When the attractor is strongly focusing, the thickness should also scale as the 1/3 power of the spatial coordinate along the attractor. Analysis of the numerical data for two different attractors yields values of the exponent close to 1/3, within 30%. Finally, we study nonlinear effects induced by the attractor.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 614 , 10 November 2008 , pp. 1 - 14
Copyright
Copyright © Cambridge University Press 2008

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