Author: Ronald Lee Duty

Publisher:

Published: 1961

Total Pages: 1

ISBN-13:

The stability of Couette flow is discussed in the case in which the cylinders rotate in opposite directions by an asymptotic method in which the Taylor number is treated as a large parameter. On assuming the principle of exchange of stabilities to hold, the problem is then governed by a sixth-order differential equation with a simple turning point. It is then shown how the solutions of this equation can be represented asymptotically in terms of the solutions of a basic reference equation. The solutions of this basic reference equation have recently been tabulated; this is an explicit representation of the solution of the stability problem in terms of tabulated functions. Detailed results for the critical Taylor number and wave-number at the onset of instability and the associated eigenfunctions are given for a limiting case. In this case there exists an infinite number of cells between the cylinders but that the amplitude of the secondary motion in all but the innermost cell is small. (Author).