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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

Hamiltonian systems, from topology to applications through analysis II November 26, 2018 - November 30, 2018

November 29, 2018 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Yasuhide Fukumoto (Institute of Mathematics for Industry)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Heavy Symmetrical Top

  • Seeping top

  • Misalignment

  • Rotating Stratified Flow

  • Spheroid

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Video

15-Fukumoto

Abstract

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.

Supplements
Asset no preview Notes 3.01 MB application/pdf Download
Video/Audio Files

15-Fukumoto

H.264 Video 15-Fukumoto.mp4 126 MB video/mp4 Download
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