Delaying transition in Taylor–Couette flow with axial motion of the inner cylinder

Abstract

Periodic axial motion of the inner cylinder in Taylor–Couette flow is used to delay transition to Taylor vortices. The outer cylinder is fixed. The marginal stability diagram of Taylor–Couette flow with simultaneous periodic axial motion of the inner cylinder is determined using flow visualization. For the range of parameters studied, the degree of enhanced stability is found to be greater than that predicted by Hu & Kelly (1995), and differences in the scaling with axial Reynolds number are found. The discrepancies are attributed to essential differences between the base flow in the open system considered by Hu & Kelly, where mass is conserved over one period of oscillation, and the base flow in the enclosed experimental apparatus, where mass is conserved at all sections at all times.

Spatial and temporal resonances in a periodically forced hydrodynamic system

“…The experiments and theoretical analysis of the model problem [14,25] clearly demonstrated the effectiveness of the parametric forcing in stabilizing the basic flow and delaying the onset of the centrifugal instability. These works also provided insight into the physical mechanisms involved.…”

“…1). This system has been investigated experimentally [25] and theoretically [7,12,14]. The system is governed by a number of non-dimensional parameters.…”

“…These parameters are combined to give the following non-dimensional governing parameters: the radius ratio e = r i /r o , the Couette flow Reynolds number R i = dr i Ω i /ν, the axial Reynolds number R a = dU/ν, the non-dimensional frequency ω = d 2 Ω/ν, where ν is the kinematic viscosity of the fluid. The experimental apparatus [25] has a radius ratio e = 0.905, and we have used this same value in all the numerical computations presented in this paper.…”

“…Our basic state, consisting of a superposition of circular Couette flow and annular Stokes flow, is independent of the axial and azimuthal directions, and time-periodic with the period of the forcing. Over an extensive range of parameter space, the primary bifurcation is to an axisymmetric state that is periodic in the axial direction and time, with the same temporal period as the forcing [14,25]. Due to the symmetries of the system, the bifurcation is not the generic fold or saddle-node bifurcation, but a pitchfork for periodic orbits ( [11], Theorem 7.12, p. 287).…”

“…When the basic solution loses stability, two time-periodic solutions resembling Taylor vortices appear; the symmetry S transforms one to the other. The previous works on this problem [7,14,25] focused on delaying the onset of the centrifugal instability of the circular Couette flow by imposing an adequate level of annular Stokes flow, and have considered relatively small amplitude forcing where only synchronous bifurcations resulted. Here, we explore the direct competition between the two mechanisms and how their competition leads to resonance behavior.…”