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Compressible fluid modes in rigid ellipsoids: towards modal acoustic velocimetry

Published online by Cambridge University Press:  07 January 2020

Jérémie Vidal Open the ORCID record for Jérémie Vidal [Opens in a new window] ,
Sylvie Su Open the ORCID record for Sylvie Su [Opens in a new window]  and
David Cébron Open the ORCID record for David Cébron [Opens in a new window]
Jérémie Vidal*
Affiliation:
Department of Applied Mathematics, University of Leeds, LeedsLS2 9JT, UK
Sylvie Su
Affiliation:
Université Grenoble Alpes, CNRS, ISTerre, Grenoble, France
David Cébron
Affiliation:
Université Grenoble Alpes, CNRS, ISTerre, Grenoble, France
*
†Email address for correspondence: j.n.vidal@leeds.ac.uk
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Abstract

Motivated by planetary-driven applications and experiments in non-spherical geometries, we study compressible fluid modes in rotating rigid ellipsoids. Such modes are also required for modal acoustic velocimetry (MAV), a promising non-invasive method to track the velocity field components in laboratory experiments. To calculate them, we develop a general spectral method in rigid triaxial ellipsoids. The description is based on an expansion onto global polynomial vector elements, satisfying the non-penetration condition on the boundary. Then, we investigate the diffusionless compressible modes in rotating (and magnetised) rigid ellipsoids. The spectral description is successfully benchmarked against three-dimensional finite-element computations and analytical predictions. A spectral convergence is obtained. Our results have direct implications for MAV in experiments, for instance in the ZoRo experiment (gas-filled rigid spheroid). So far, deformation and rotational effects have been theoretically considered separately, as small perturbations of the solutions in non-rotating spheres. We carefully compare the perturbation approach, in this illustrative geometry, to the polynomial solutions. We show that second-order ellipticity effects are often present, even in weakly deformed ellipsoids. Moreover, high-order effects due to rotation and/or ellipticity should be observed for some acoustic modes in experimental conditions. Thus, perturbation theory should be used with care in MAV. Instead, the spectral polynomial method paves the way for future MAV applications in fluid experiments with rigid ellipsoids.

JFM classification

Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 885 , 25 February 2020 , A39
Copyright
© 2020 Cambridge University Press

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