Tricritical spiral vortex instability in cross-slot flow

Abstract

We examine fluid flow through cross-slot devices with various depth to width ratios alpha. At low Reynolds number, R-e, flow is symmetric and a sharp boundary exists between the two incoming fluid streams. Above an alpha-dependent critical value, Re-c(alpha), a steady symmetry-breaking bifurcation occurs and a spiral vortex structure develops. Order parameters characterizing the instability grow according to a sixth-order Landau potential, and show a progression from second- to first-order transitions as alpha increases beyond a tricritical value of alpha approximate to 0.55. Flow simulations indicate the instability is driven by vortex stretching at the stagnation point.