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Inertial wave rays in rotating spherical fluid domains

Published online by Cambridge University Press:  10 October 2014

Anna Rabitti  and
Leo R. M. Maas
Anna Rabitti*
Affiliation:
Department of Physical Oceanography, NIOZ Royal Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands
Leo R. M. Maas
Affiliation:
Department of Physical Oceanography, NIOZ Royal Netherlands Institute for Sea Research, PO Box 59, 1790 AB Texel, The Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

The behaviour of inertial waves in a rotating spherical container, filled with homogeneous fluid, is here investigated by means of a three-dimensional ray tracing algorithm, in a linear, inviscid framework. In particular, the classical, two-dimensional association between regular modes and periodic trajectories is addressed here for the first time in a fully three-dimensional setting. Three-dimensional, repelling periodic trajectories are found and classified on the basis of the associated frequency and spatial structure, although associated frequencies are hardly reconcilable to Bryan’s (Proc. R. Soc. Lond., vol. 45, 1889, pp. 42–45) classical solutions for inertial waves in the sphere. The normalized squared frequency $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\omega ^2 = 1/2$ appears to divide the frequency range into two different trajectory regimes, where critical latitudes play a different role. Chaotic orbits are not found, as expected, while invariant, non-domain-filling orbits (whispering gallery modes) constitute the majority of the trajectories in the sphere. From ray tracing alone, the wavefield is still far from being completely reconstructed, and a study performed in such a simplified setting is clearly far from any realistic application, however, it appears that three-dimensional ray dynamics constitutes a valid approach to infer information on the spectrum and regularity properties of a system, and is then able to bring new insight in a variety of fundamental problems of geophysical and astrophysical relevance, once its power and limitations have been recognized.

JFM classification

Mathematical Foundations: General fluid mechanics Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 621 - 654
Copyright
© 2014 Cambridge University Press 

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