Existence of secondary solutions to a generalized Taylor problem
Abstract
In this paper the existence of secondary solutions to a generalization of the classical Taylor problem is considered. A viscous liquid is assumed to occupy the region interior to a right circular cylinder and exterior to a surface formed by rotating a smooth, positive, periodic function about the axis of the cylinder. The cylinder is fixed while the inner surface rotates with a constant angular velocity. The existence of axisymmetric cellular solutions is established by a generalization of the method of Lyapunov and Schmidt. By treating the branching equation as a function of three complex variables it is shown that a critical Re number exists and that for Re numbers less than this critical value, the problem has a unique solution, while for Re numbers slightly above this value, positive and small there are three solutions.
 Publication:

Applicable Analysis
 Pub Date:
 July 1974
 Bibcode:
 1974AppAn...4..145Z
 Keywords:

 Boundary Value Problems;
 Circular Cylinders;
 Existence Theorems;
 NavierStokes Equation;
 Rotating Cylinders;
 Viscous Flow;
 Angular Velocity;
 Complex Variables;
 Liquid Flow;
 Operators (Mathematics);
 Periodic Functions;
 Reynolds Number;
 Rotating Fluids;
 Fluid Mechanics and Heat Transfer