Finite-difference solutions of Taylor instabilities in viscous plane flow
Abstract
An integration algorithm is presented for the numerical solution of a linear, sixth-order eigenvalue problem associated with hydrodynamic stability of viscous flows between rotating planes. The highest derivative of the eigensolutions is approximated by passing a third-degree polynomial through three backward and one forward point, and formulas for the lower derivatives are obtained by integration of the polynomial approximation. Neutrally stable eigensolutions associated with Taylor-type vortex instabilities are calculated for plane Couette and Poiseuille flows in a rotating system, and are found to be in agreement with solutions obtained by series-expansion methods.
- Publication:
-
Computers and Fluids
- Pub Date:
- March 1975
- Bibcode:
- 1975CF......3..103L
- Keywords:
-
- Finite Difference Theory;
- Flow Stability;
- Rotating Fluids;
- Taylor Instability;
- Two Dimensional Flow;
- Viscous Flow;
- Algorithms;
- Couette Flow;
- Eigenvalues;
- Laminar Flow;
- Numerical Integration;
- Polynomials;
- Fluid Mechanics and Heat Transfer