Bifurcations to three-dimensional flows in a periodically driven cylindrical cavity

Consider a Newtonian fluid of kinematic viscosity ν and density ρ confined in a finite cylinder of radius R and height H, whose sidewall oscillates harmonically in the axial direction, with period T and maximum axial velocity Vmax, while the top and bottom lids remain at rest. There are three non-dimensional parameters in this problem: the aspect ratio, Γ = H/R, the Reynolds number, Re = VmaxR/ν , and the Stokes number, St = R2/νT . In the current study, the aspect ratio is fixed at Γ = 2. The flow is governed by the usual Navier-Stokes equations: ( ∂ ∂ t +u ·∇ ) u=− 1 ρ ∇p+ν∇2u, (1a)