On the structure and formation of spiral Taylor-Görtler vortices in spherical Couette flow (Q2710582)

The authors present results of direct numerical simulation of Couette flow between inner rotating and outer stationary spheres. A second-order accurate finite difference method is used to solve incompressible three-dimensional time-dependent Navier-Stokes equations in spherical polar coordinates. Decoupling between the velocity and pressure is achieved by an approximate factorization method. Three-dimensional spherical shell is divided into a number of grids \(22\times 361\times 91\) in radial, meridional and azimuthal directions, respectively. Time integration is carried out until the steady or time-periodic state is obtained. The axisymmetric solution of the so-called 1-vortex flow has been chosen as initial condition to simulate the supercritical spiral Taylor-Görtler vortex flow. The authors give a time sequence of visualizations of iso-surfaces of azimuthal vorticity component to illustrate the temporally and spatially growing structure of spiral Taylor-Görtler vortices. Vortex tearing, splitting, tilting, reconnecting, stretching, and compressing are observed during the formation of the spiral vortices.