TY - JOUR
T1 - The linear stability of high-frequency flow in a torsionally oscillating cylinder
AU - Blennerhassett, P.J.
AU - Bassom, Andrew
PY - 2007
Y1 - 2007
N2 - The linear stability of the Stokes layer induced in a fluid contained within a long cylinder oscillating at high frequency about its longitudinal axis is investigated. The disturbance equations are derived using Floquet theory and the resulting system solved using pseudo-spectral methods. Both shear modes and axially periodic centripetal disturbance modes are examined and neutral stability curves and corresponding critical conditions for instability identified. For sufficiently small cylinder radius it is verified that the centripetal perturbations limit the stability of the motion but that in larger-radius configurations the shear modes associated with the Stokes layer take over this role. These results suggest a possible design, free of entry-length effects, for experiments intended to examine the breakdown of oscillatory boundary layers.
AB - The linear stability of the Stokes layer induced in a fluid contained within a long cylinder oscillating at high frequency about its longitudinal axis is investigated. The disturbance equations are derived using Floquet theory and the resulting system solved using pseudo-spectral methods. Both shear modes and axially periodic centripetal disturbance modes are examined and neutral stability curves and corresponding critical conditions for instability identified. For sufficiently small cylinder radius it is verified that the centripetal perturbations limit the stability of the motion but that in larger-radius configurations the shear modes associated with the Stokes layer take over this role. These results suggest a possible design, free of entry-length effects, for experiments intended to examine the breakdown of oscillatory boundary layers.
U2 - 10.1017/S0022112007004831
DO - 10.1017/S0022112007004831
M3 - Article
SN - 0022-1120
VL - 576
SP - 491
EP - 505
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -