Tricritical spiral vortex instability in cross-slot flow

We examine fluid flow through cross-slot devices with various depth to width ratios α. At low Reynolds number, Re, flow is symmetric and a sharp boundary exists between the two incoming fluid streams. Above an α-dependent critical value, Re(c)(α), 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 α increases beyond a tricritical value of α ≈ 0.55. Flow simulations indicate the instability is driven by vortex stretching at the stagnation point.