Taylor vortex flow under harmonic modulation of the driving force.

Abstract

Time-periodic Taylor vortex flow between two concentric cylinders is studied. With the outer cylinder at rest and the inner one rotating with angular velocity \ensuremath{\Omega}(t)=\ensuremath{\Omega}(1+\ensuremath{\Delta} cos\ensuremath{\omega}t), the stability boundary of circular Couette flow and the fully nonlinear Taylor vortices are investigated. Results are obtained by a finite-difference numerical simulation of the full Navier-Stokes equations for a radius ratio \ensuremath{\eta}=0.65 and by an analytical Galerkin approximation with four modes for arbitrary gap width. Data obtained by both methods agree very well. Modulation is found to destabilize the basic flow in agreement with earlier theoretical results. The time dependence of Taylor vortices is determined in detail and compared with recent experiments. Their response to the modulated driving is elucidated and explained by investigating various limiting behaviors and by comparison with the amplitude equation. Subharmonic response is found for large modulation amplitudes when the driving \ensuremath{\Omega}(t) becomes supercritical in both rotation directions during one period. Differences and similarities of linear and nonlinear flow properties with modulated convection in Rayleigh-B\'enard systems are discussed in detail. That low-frequency small-amplitude modulation stabilizes the basic conductive state in the latter system while it destabilizes circular Couette flow is shown to be caused by the different coupling of the driving to the secondary flow field.