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Gravito-inertial waves in a differentially rotating spherical shell

Published online by Cambridge University Press:  01 July 2016

G. M. Mirouh ,
C. Baruteau ,
M. Rieutord  and
J. Ballot
G. M. Mirouh*
Affiliation:
Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
C. Baruteau
Affiliation:
Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
M. Rieutord
Affiliation:
Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
J. Ballot
Affiliation:
Université de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
*
†Email address for correspondence: giovanni.mirouh@irap.omp.eu
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Abstract

The gravito-inertial waves propagating over a shellular baroclinic flow inside a rotating spherical shell are analysed using the Boussinesq approximation. The wave properties are examined by computing paths of characteristics in the non-dissipative limit, and by solving the full dissipative eigenvalue problem using a high-resolution spectral method. Gravito-inertial waves are found to obey a mixed-type second-order operator and to be often focused around short-period attractors of characteristics or trapped in a wedge formed by turning surfaces and boundaries. We also find eigenmodes that show a weak dependence with respect to viscosity and heat diffusion just like truly regular modes. Some axisymmetric modes are found unstable and likely destabilized by baroclinic instabilities. Similarly, some non-axisymmetric modes that meet a critical layer (or corotation resonance) can turn unstable at sufficiently low diffusivities. In all cases, the instability is driven by the differential rotation. For many modes of the spectrum, neat power laws are found for the dependence of the damping rates with diffusion coefficients, but the theoretical explanation for the exponent values remains elusive in general. The eigenvalue spectrum turns out to be very rich and complex, which lets us suppose an even richer and more complex spectrum for rotating stars or planets that own a differential rotation driven by baroclinicity.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 800 , 10 August 2016 , pp. 213 - 247
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© 2016 Cambridge University Press 

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