Stability of Taylor-Couette Flow with Radial Heating

Abstract

Beginning with Taylor’s [1] classical study of the motion of a viscous fluid in an annular gap driven by differential rotation of the coaxial cylinders, circular Couette flow has provided a rich testing ground for both linear and nonlinear stability theory. The present study employs linear stability theory to investigate the more complex problem of viscous fluid motion in a vertical annulus driven by the combined agencies of cylinder rotation and radial heating. With one exception, all previous infinite aspect ratio theoretical attacks on this problem have neglected the crucial role of gravity. These include studies by Yih [2], Becker and Kaye [3], Walowit, Tsao and DiPrima [4], Bahl [5], and Soundalgekar, Takhar, and Smith [6]. These analyses showed that isothermal Taylor cells are destabilized (stabilized) by positive (negative) radial heating gradients across the annular gap. Roesner [7] properly included the effect of gravity in the Boussinesq approximation but, like most his predecessors, considered only axisymmetric disturbances. Roesner’s results contrast those neglecting gravity: isothermal Talylor cells are stabilized by both positive and negative radial heating and the stability boundary is symmetric with respect to the sense of radial heating.