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

Abstract

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, b ¼ R 2 À R 1 ð Þ =R 1 ¼ 0:33, 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio b ¼ 0:18 at Reynolds number Re ¼ 700 as the initial conditions and suddenly increasing b to the target value, we can compute Taylor vortices for the three wide gaps. For b ¼ 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 ¼ 1850, and then become periodic at Re ¼ 2000. When Re [ 2050 the flow returns back to the steady basic flow state with no Taylor vortices. For b ¼ 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 ¼ 1200, and then the flow evolves into the steady basic flow for Re [ 1400. For b ¼ 0:42, Taylor vortices can exist in the range 650 Re 1300. With increasing Re, steady asymmetric Taylor vortices occur at Re ¼ 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 ðb; ReÞ plane for b ! 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. Keywords Spherical Couette flow Á Wide gap Á Symmetric Taylor vortices Á Asymmetric Taylor vortices