Compressing an Elliptic Vortex: Transition to Turbulence by Tumble Breakdown

Stability of the elliptic vortex attracted interest in the past decade. Cambon (1982), and Cambon, Teissedre and Jeandel (1985) have studied the stability of such flows with spatially uniform velocity gradient, and have provided RDT solutions for a wide range of the parameter S/Omega (where the strain rate S and the vorticity 2 Omega define the velocity gradient matrix). The range studied included those of hyperbolic streamlines (strain dominated, S/Omega is greater than 1), linear streamlines (simple shear, S/Omega = 1), and elliptical streamlines (vorticity dominated, S/Omega is less than 1). The latter class has more recently attracted interest and several studies appeared (Pierrehumbert 1986, Bayly 1986, Craik and Criminale 1986). These studies will be collectively referred to as PBCC.