Existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow

We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier–Stokes equations numerically. Three wide-gap clearance ratios, β= (R₂- R₁) / R₁= 0.33 , 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio β= 0.18 at Reynolds number Re= 700 as the initial conditions and suddenly increasing β to the target value, we can compute Taylor vortices for the three wide gaps. For β= 0.33 , Taylor vortices exist in the range 450 ≤ Re≤ 2050. With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at Re= 1850 , and then become periodic at Re= 2000. When Re> 2050 the flow returns back to the steady basic flow state with no Taylor vortices. For β= 0.38 , Taylor vortices can exist in the range 500 ≤ Re≤ 1400. With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at Re= 1200 , and then the flow evolves into the steady basic flow for Re> 1400. For β= 0.42 , Taylor vortices can exist in the range 650 ≤ Re≤ 1300. With increasing Re, steady asymmetric Taylor vortices occur at Re= 1150 , and then the flow evolves into the steady basic flow for Re> 1300. The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the (β, Re) plane for β≥ 0.33 and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time.