Nonlinear stability of the isothermal three-dimensional flows of viscous incompressible fluid in the rotational spherical layer with the noise presence was studied numerically. Transition between stable non-stationary flow and unstable flow in the form of travelling azimuthal waves is under consideration. Small-amplitude noise inserted to the flow by random broadband disturbances of the inner sphere rotational rate about constant at time averaged value, outer sphere is fixed. An approach is proposed to simplify finding the critical Reynolds number, corresponding to the stability limit in the presence of noise. The results obtained by the proposed and well known methods are compared. Keywords: noise, rotational flows, spherical Couette flow, instability control.
The results of an experimental study of the effects of noises on flows in a rotating spherical layer are presented. Noise is introduced into the flow in the form of random fluctuations of the inner sphere rotational rate relative to a time constant mean value. The flow velocity was measured with a laser Doppler anemometer. It was found that the noises of the equal amplitude, but with different spectra cause the generation of mean flows of different intensity. It is shown that the increase in the average velocities under the action of the noise is larger for the stable flows compared to unstable ones Keywords: noise, flows with rotation, spherical Couette flow.
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