Instability of timeperiodic flows
Abstract
The instabilities of some spatially and/or timeperiodic flows are discussed, in particular, flows with curved streamlines which can support TaylorGortler vortices are described in detail. The simplest flow where this type of instability can occur is that due to the torsional oscillations of an infinitely long circular cylinder. For more complicated spatially varying timeperiodic flows, a similar type of instability can occur and is spatially localized near the most unstable positions. When nonlinear effects are considered it is found that the instability modifies the steady streaming boundary layer induced by the oscillatory motion. It is shown that a rapidly rotating cylinder in a uniform flow is susceptible to a related type of instability; the appropriate stability equations are shown to be identical to those which govern the instability of a boussinesq fluid of Prandtl number unity heated time periodically from below.
 Publication:

National Aeronautics and Space Administration Report
 Pub Date:
 October 1985
 Bibcode:
 1985nasa.reptT....H
 Keywords:

 Circular Cylinders;
 Rotating Fluids;
 Taylor Instability;
 Vortices;
 Boussinesq Approximation;
 Kinematics;
 Nonlinearity;
 Time Dependence;
 Viscosity;
 Fluid Mechanics and Heat Transfer