TY - JOUR

T1 - Centrifugal instability of a stokes layer

T2 - Subharmonic destabilization of the taylor vortex mode

AU - Hall, P.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - The centrifugal instability of a Stokes layer has been investigated by Seminara & Hall (1976, 1977). It was found that the Stokes layer on a torsionally oscillating circular cylinder is unstable to perturbations periodic along the axis of the cylinder when the Taylor number for the flow exceeds a certain critical value. The weakly nonlinear theory given by Seminara & Hall showed that, if nonlinear effects are considered, at this Taylor number a stable axially periodic equilibrium flow bifurcates from the basic circumferential flow. It is known experimentally that this equilibrium flow becomes unstable to disturbances having a longer axial wavelength at a second critical Taylor number about 10 % greater than the first critical value. Moreover it is known that, in the initial stages of this destabilization, a mode having twice the axial wavelength of the fundamental is present. In this paper we investigate the linear stability of the bifurcating solution to such a subharmonie mode. An approximate solution of the linear stability problem shows that the subharmonic becomes unstable at a Taylor number remarkably close to the experimentally measured second critical Taylor number.

AB - The centrifugal instability of a Stokes layer has been investigated by Seminara & Hall (1976, 1977). It was found that the Stokes layer on a torsionally oscillating circular cylinder is unstable to perturbations periodic along the axis of the cylinder when the Taylor number for the flow exceeds a certain critical value. The weakly nonlinear theory given by Seminara & Hall showed that, if nonlinear effects are considered, at this Taylor number a stable axially periodic equilibrium flow bifurcates from the basic circumferential flow. It is known experimentally that this equilibrium flow becomes unstable to disturbances having a longer axial wavelength at a second critical Taylor number about 10 % greater than the first critical value. Moreover it is known that, in the initial stages of this destabilization, a mode having twice the axial wavelength of the fundamental is present. In this paper we investigate the linear stability of the bifurcating solution to such a subharmonie mode. An approximate solution of the linear stability problem shows that the subharmonic becomes unstable at a Taylor number remarkably close to the experimentally measured second critical Taylor number.

UR - http://www.scopus.com/inward/record.url?scp=17144474776&partnerID=8YFLogxK

U2 - 10.1017/S0022112081003327

DO - 10.1017/S0022112081003327

M3 - Article

AN - SCOPUS:17144474776

SN - 0022-1120

VL - 105

SP - 523

EP - 530

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -