Simulation of different flow regimes in a narrow-gap spherical Couette flow

The spherical Couette flow (SCF) system with the flow between two concentric rotating spheres is one of the most convenient example in exploring the laminar-turbulent transition. The transitions occurred in this flow phenomena has a great relevance with the geophysical motions and has applications in hydrodynamic problems. In the present work, we numerically study different flow instabilities in a narrow-gap SCF between two concentric spheres with only inner sphere rotating and the outer sphere is fixed. The time dependent three-dimensional incompressible Navier-Stokes equations (INSEs) along with a parallelized line Gauss-Seidel(LGS) solver has been used for the simulation of different flow instabilities in a narrow-gap clearance ratios(CR), β=(R₂−R₁)/R₁=0.10. The flow instabilities have been investigated for a range of Reynolds numbers (Re) 170≤Re≤12000. For this narrow-gap CR, first we obtain the 0-,1-,2-,3-, and 4-vortex flows at Re=1430,1440,1460,1750 and 1950 respectively by using the Stokes flow (SF) as an initial condition. Further increasing the Re using the same initial condition the flow becomes wavy, spiral wavy, then return back to supercritical basic flow and finally becomes turbulent at higher Re. The computed numerical results have a good agreement with the existing numerical and experimental results. Further more, we have noticed some new flow states which have not been observed in the previous numerical and experimental studies.