Inertial wave rays in rotating spherical fluid domains
In: Journal of Fluid Mechanics. Cambridge University Press: London. ISSN 00221120; eISSN 14697645, meer
 
Author keywords 
general fluid mechanics; internal waves; waves in rotating fluids 
Abstract 
The behaviour of inertial waves in a rotating spherical container, filled with homogeneous fluid, is here investigated by means of a threedimensional ray tracing algorithm, in a linear, inviscid framework. In particular, the classical, twodimensional association between regular modes and periodic trajectories is addressed here for the first time in a fully threedimensional setting. Threedimensional, 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 $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\omega ^2 = 1/2$?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, nondomainfilling 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 threedimensional 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. 
