Gyroscopic analogy of a rotating stratified flow confined in a tilted spheroid with a heavy symmetrical top with the top axis misaligned from the axis of symmetry

We address the suppression of the gravitational instability of rotating stratified flows in a confined geometry. A rotating flow of a stratified fluid confined in an ellipsoid, subject to gravity force, whose velocity and density fields are linear in coordinates, bears an analogy with a mechanical system of finite degrees of freedom, that is, a heavy rigid body. An insight is gained into the mechanism of system rotation for the ability of a lighter fluid of sustaining, on top of it, a heavier fluid when the angular velocity is greater than a critical value. The sleeping top corresponds to such a state. We show that a rotating stratified flow confined in a tilted spheroid is equivalent to a heavy symmetrical top with the symmetric axis tilted from the top axis. The effect of this misalignment on the linear stability of the sleeping top and its bifurcation is investigated in some detail.

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