Numerical study of bifurcation solutions of spherical Taylor-Couette flow (Q1919046)

The steady bifurcation flows in a spherical gap with rotating inner and stationary outer spheres are simulated numerically by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for \(775 \leq \text{Re} \leq 1220\) and three steady stable flows with 0, 1, or 2 vortices for \(1220 < \text{Re} \leq 1500\). The mechanism of development of a saddle point in the meridional plane at higher Reynolds numbers and its role in the formation of two-vortex flow are analyzed.