Elliptical instability in a rotating spheroid

Abstract

This paper concerns the elliptical instability of a flow in a rotating deformed sphere. The aim of our work is to analyse the characteristics of this instability experimentally and to provide a theoretical model which accounts for the observations. For this purpose, an elastic and transparent hollow sphere has been moulded in a silicone gel block. The flow is visualized using Kalliroscope flakes illuminated with a laser sheet as the sphere is set into rotation and compressed by two rollers. The elliptical instability occurs by the appearance of the so-called ‘spin-over’ mode whose growth rate and saturation amplitude are measured by video image analysis at different Ekman numbers. Growth rates are predicted well by the linear stability analysis. A nonlinear model is developed and is shown to describe correctly the saturated regimes observed in the experiments. At low Ekman numbers, a secondary instability leading to an intermittent regime is also discovered.