Scaling of variation intensity of flows under the influence of external noise

The effect of noise on the change of intensity of axisymmetric flows of viscous incompressible fluid in spherical layers at rotation of boundaries with equal angular velocities is numerically investigated. Noise is introduced into the flows by adding random fluctuations with zero mean value to the time constant mean rotation velocity of the inner sphere. The response of the flows to the introduction of two types of noise with different spectra was investigated. Power laws between the increase in the time-averaged parameters of the flows and the increase in the noise amplitude were found, which qualitatively retain their form when the noise spectrum, the thickness of the spherical layer, and the Reynolds numbers are changed. It was found that noises with the same amplitude, but with different types of spectra, lead to relative changes in the time-averaged values of friction force moments, kinetic energy of the flows, and RMS deviations of kinetic energy that differ by more than an order of magnitude.