Experimental study of the interaction between convective and elliptical instabilities

The reciprocal influence of convective and elliptical instabilities is studied experimentally in an elliptically deformed rotating cylindrical shell with an imposed temperature at the inner cylinder using the centrifugal force to mimic a radial gravity field. When the temperature contrast is stabilizing, we observe that the elliptical instability can grow and that the heat flux scales as the inverse of the viscous boundary layer depth. When the temperature profile is destabilizing, we observe (i) that the elliptical instability can still grow on the established convective motions, (ii) that for the experimental range of parameters, its growth rate progressively decreases when the intensity of convection increases, and (iii) that the elliptical instability modifies the heat transfer when the viscous boundary layer is smaller than the thermal one. Scaling laws for both cases are derived analytically and validated experimentally. We conclude that in geophysical and astrophysical systems, thermal effects have...