The spherical Taylor–Couette flow

• The electrodiffusion method was applied for the first time in the flow between two concentric spheres in rotation.
• The evolution of the flow patterns was illustrated by the wall velocity gradients and their fluctuations.
• The visualization of each flow state was quantified by the power spectra of wall velocity gradients.

The instability modes that lead to turbulence between two concentric spheres, the inner one rotating while the outer is at rest, are investigated through visualization and using the electrodiffusion (ED) method. The wall velocity gradients are measured for the first time in a spherical shell by ED method. The exploration of the flow regimes is carried out for a dimensionless gap width δ=(R2−R1)/R1 of 0.107, an aspect ratio Γ=H/dΓ=H/d over the interval (17–21) and a Taylor number in the range (22–1500). The influence of these parameters on the apparition of instabilities is elucidated. The evolution of the flow patterns is visualized and also quantified by the wall velocity gradients and their fluctuations. Using the fast Fourier transform, the time series of velocity gradient obtained by the ED method permitted analysis and identification of the fundamental frequencies and their evolution associated with each flow state.

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