Transitions to chaos in the spherical couette flow due to periodic variations in the rotation velocity of one of the boundaries

The results of an experimental investigation of unsteady viscous incompressible flows in a spherical gap, when the rotation velocity of one sphere varies in accordance with the harmonic law, while that of the other sphere remains constant, are presented. The modulation amplitudes and frequencies are small compared with the mean rotation velocities of the spheres. Transition to chaos is studied in a layer, whose thickness is equal to the inner sphere radius, in the case of counter rotation of the spherical boundaries. A periodic flow generated as a result of the mutual synchronization of the frequencies of a three-frequency regime preceding that under study at lower Reynolds numbers is taken as the original state. It is shown that certain properties of turbulent flows near the threshold of their formation essentially depend on the modulation frequency.