A selective iteration procedure for Taylor's stability problem
Abstract
An iteration method applicable to threedimensional instability problems in hydrodynamics near the first critical point is described, which yields the stable solution 'with probability one' and the unstable solution at most on a proper submanifold. An application of the method to the stability problem of the Couette flow is given. The application yields the Taylorvortex flow for a large domain of Reynolds numbers. Numerical results for physical data such as the mean torque and the shear are presented. The iteration scheme used in this concrete case is described in detail and numerical results are shown. For discretization a Galerkin method is taken.
 Publication:

Luft und Raumfahrt
 Pub Date:
 1977
 Bibcode:
 1977LR.........176S
 Keywords:

 Flow Stability;
 Hydrodynamics;
 Iterative Solution;
 Taylor Instability;
 Boundary Value Problems;
 Couette Flow;
 Galerkin Method;
 Incompressible Flow;
 Reynolds Number;
 Steady Flow;
 Viscous Flow;
 Vortices;
 Fluid Mechanics and Heat Transfer