Finitedifference solutions of Taylor instabilities in viscous plane flow
Abstract
An integration algorithm is presented for the numerical solution of a linear, sixthorder eigenvalue problem associated with hydrodynamic stability of viscous flows between rotating planes. The highest derivative of the eigensolutions is approximated by passing a thirddegree 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 Taylortype 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 seriesexpansion 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