Direct calculation of turbulent flow formation in a spherical layer with oscillating counter-rotating boundaries

We have numerically studied the transition to turbulent flow in a layer of a viscous incompressible fluid confined between concentric spherical boundaries performing counter-rotational oscillations. The rotation speeds of both spheres were modulated at the same frequency and amplitude. The transition to turbulence was caused by an increase in the amplitude of velocity modulation beginning with the state of rest. Using the concept of instantaneous frequency/phase of flow, it is established that the turbulence develops in a limited region of liquid layer, outside which the flow remains laminar. The turbulent region of flow exhibits intermittency of the chaos-chaos type.