Acoustic modes of rapidly rotating ellipsoids subject to centrifugal gravity

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