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, $$\beta =\left( R_{2}-R_{1}\right) /R_{1}=0.33$$ , 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio $$\beta =0.18$$ at Reynolds number $${Re}=700$$ as the initial conditions and suddenly increasing $$\beta$$ to the target value, we can compute Taylor vortices for the three wide gaps. For $$\beta =0.33$$ , Taylor vortices exist in the range $$450\le {Re}\le 2050$$ . 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 $$\beta =0.38$$ , Taylor vortices can exist in the range $$500\le {Re}\le 1400$$ . 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 $$\beta =0.42$$ , Taylor vortices can exist in the range $$650\le {Re}\le 1300$$ . 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 $$(\beta ,{Re})$$ plane for $$\beta \ge 0.33$$ and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time.