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Wave attractors in stratified and rotating media

Leo Maas
Royal Netherlands Institute for Sea Research, Texel & Utrecht University, the Netherlands

Abstract
Oceans and planetary and stellar atmospheres have in common that waves propagate in stratified, rotating environments in ‘non-trivially shaped’ fluid domains. To some approximation, stars consist of spherical shells that are either convectively mixed or density-stratified, due to radiation. The nontrivial aspect resides in the fact that the spherical shape of stars, imposed by gravity, breaks the cylindrical symmetry due to rotation. Because of this, (e.g. tidal) perturbations of these equilibrium states, i.e. linear waves, are subject to a strong focusing principle. This predicts their approach onto particular locations, wave attractors, where the waves intensify and interact with the mean state. Simple theory and laboratory experiments illustrate the generic appearance of wave attractors in symmetry-breaking fluid domains, which should therefore occur in lakes, oceans and stars alike. Wave attractors are interesting physically and mathematically. Physically, because they appear to attract particles too. This may contribute to a rapid exchange of material across stratification, and thus to a resetting of the mean state over long time-scales. Mathematically, because these problems, while linear, appear to be riddled with features normally associated with nonlinear dynamical systems only.

2011 February 16, 13:30

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