On the nonlinear stability of rotating Newtonian and non-Newtonian fluids
Abstract
The effect of superimposed rigid body rotations on the nonlinear stability of an arbitrary base flow is examined from a theoretical standpoint for incompressible Newtonian and non-Newtonian fluids. It is proven mathematically, from an analysis of the full nonlinear equations of motion, that instabilities which depend on the state of rotation of the fluid must arise from variations in the velocity disturbances along the axis of rotation of the fluid. Consequently, it follows that Squire's theorem cannot, under any circumstances, apply to rotationally dependent instabilities. The consistency of these results with previous work on Couette flow and rotating plane Poiseuille flow is discussed briefly.
- Publication:
-
Acta Mechanica
- Pub Date:
- 1983
- Bibcode:
- 1983AcMec..49..263S
- Keywords:
-
- Flow Stability;
- Newtonian Fluids;
- Nonnewtonian Fluids;
- Rotating Fluids;
- Base Flow;
- Flow Velocity;
- Incompressible Flow;
- Laminar Flow;
- Nonlinear Equations;
- Two Dimensional Flow;
- Fluid Mechanics and Heat Transfer