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Article Dans Une Revue Journal of the Acoustical Society of America Année : 2021

Acoustic modes of rapidly rotating ellipsoids subject to centrifugal gravity

Résumé

The acoustic modes of a rotating fluid-filled cavity can be used to determine the effective rotation rate of a fluid (since the resonant frequencies are modified by the flows). To be accurate, this method requires a prior knowledge of the acoustic modes in rotating fluids. Contrary to the Coriolis force, centrifugal gravity has received much less attention in the experimental context. Motivated by on-going experiments in rotating ellipsoids, we study how global rotation and buoyancy modify the acoustic modes of fluid-filled ellipsoids in isothermal (or isentropic) hydrostatic equilibrium. We go beyond the standard acoustic equation, which neglects solid-body rotation and gravity, by deriving an exact wave equation for the acoustic velocity. We then solve the wave problem using a polynomial spectral method in ellipsoids, which is compared with finite-element solutions of the primitive fluid-dynamic equations. We show that the centrifugal acceleration has measurable effects on the acoustic frequencies when $M_\Omega \gtrsim 0.3$, where $M_\Omega$ is the rotational Mach number defined as the ratio of the sonic and rotational time scales. Such a regime can be reached with experiments rotating at a few tens of Hz, by replacing air with a highly compressible gas (e.g. SF$_6$ or C$_4$F$_8$).
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Dates et versions

hal-03329702 , version 1 (31-08-2021)

Identifiants

Citer

Jérémie Vidal, David Cébron. Acoustic modes of rapidly rotating ellipsoids subject to centrifugal gravity. Journal of the Acoustical Society of America, 2021, 150 (2), pp.1467-1478. ⟨10.1121/10.0005909⟩. ⟨hal-03329702⟩
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