Convective instability of a rotating fluid

G. F. Shaidurov, M. I. Shliomis, G. V. Yastrebov

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Abstract

A physical system may be in thermodynamic equilibrium when participating as a whole in uniform rotational motion [1]. In particular, mechanical equilibrium of a liquid in a cavity rotating about a stationary axis with the constant angular velocity Ω ("solid-body" rotation of the liquid) is possible. If the liquid is uniform in composition and isothermal, then such equilibrium, as shown in [2], is stable for all Ω. However, in the case of a nonuniformly heated liquid, stability of the solid-state rotation is, generally speaking, impossible. The appearance of two steady-state force fields is associated with uniform rotation: the centrifugal field and the Coriolis force field. The former field forces the liquid elements which are less heated and therefore more dense to move away from the axis of rotation, displacing the less dense liquid layers (centrifugation). If we maintain in the liquid a temperature gradient which prevents the establishment of equilibrium stratification of the liquid, then with a suitable value of this gradient (the magnitude obviously depending on Ω) undamped flows-convection-will develop in the liquid. Thus, while in conventional gravitational convection the gravity field is the reason for the appearance of the Archimedes buoyant forces, in the rotating cavity the mixing of the nonuniformly heated liquid is caused by the centrifugal field. As soon as the convective flows arise the Coriolis forces come into play. Account for the latter, as is shown below, prevents reducing in a trivial fashion the study of convective stability of rotating liquid to the well-studied problems of gravitational convection.

Original languageEnglish
Pages (from-to)55-58
Number of pages4
JournalFluid Dynamics
Volume4
Issue number6
DOIs
StatePublished - 1 Nov 1969
Externally publishedYes

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