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;
- Navier-Stokes Equation;
- Rotating Cylinders;
- Viscous Flow;
- Angular Velocity;
- Complex Variables;
- Liquid Flow;
- Operators (Mathematics);
- Periodic Functions;
- Reynolds Number;
- Rotating Fluids;
- Fluid Mechanics and Heat Transfer