Shift of the Flow Stability Limit in the Presence of Random Rotational Velocity Fluctuations

Nonlinear stability of isothermal 3D flows of a viscous incompressible nonstratified fluid in the rotating spherical layer in the presence of noise is studied numerically. The transition between a stable nonstationary flow and the unstable flow in the form of traveling azimuthal waves is considered. Small-amplitude noise is introduced into the flow by random broadband perturbations of the rotational velocity of the inner sphere relative to the average value constant in time, while the outer sphere is fixed. An approach is proposed to simplify the determination of the critical Reynolds number corresponding to the stability limit in the presence of noise. The results obtained using the proposed method are compared with the results obtained by well-known methods.