ELLIPTICAL INSTABILITY

In this review we describe the discovery and development of understanding of the so-called elliptical instability. This is the name given to the linear instability mechanism that tends to break up regions of elliptical streamlines in a rotating flow. The instability is discussed in the three different contexts—an unbounded strained vortex, a localized strained vortex, and a triaxial ellipsoid—where it was originally discovered and then rediscovered. These make it clear that the instability is one of parametric resonance where a normal mode, or pair of normal modes, of the undistorted rotating flow resonates with the underlying strain field. The effects of additional physics on the instability process are examined before its nonlinear evolution is discussed. Various applications of the instability in nature are then reviewed.