Shear instability from differential rotation in precessing cylinder flow

Cyclones and differential rotation are ubiquitous features in rotating fluid and occur particularly in both geophysical and astrophysical flows. For a certain value of the forcing parameter, cyclones regime has been observed in our experiment involving water in a precessing cylinder. They result from an instability with mushroom-like shape. . We propose here to study the nature of this so-called instability. We showed that the mode coupling of two inertial waves with azimuthal wavenumber m =0 and m =1 (mode forced by the precession) in the inviscid regime (at high Reynolds number limit) creates a differential rotation regime. It has been experimentally observed at small enough Poincaré number ɛ (ratio of the precession to the rotation frequencies). Furthermore, the radial profile of the corresponding axial mean flow vorticity shows an inflexion point leading to a localized inflectional secondary instability. There is a competition between centrifugal and shear instability.

In this study, we show that when ɛ is increased from low values the forced mode m =0 becomes the most instable in this induced differential rotation in relation to an extended instability criterion, which can be responsible for the observed eruptions of jets from the lateral walls of the cylinder leading to the cyclones formation within the volume from the development of an inviscid secondary shear instability.