Transition to chaos in a square vortex flow

We present a combined numerical and experimental study of transition to chaos in a quasi two dimenisonal flow composed of approximately square vortices. Such a flow (at low Reynolds numbers) is generated by driving a shallow fluid layer using an electromagnetic force that is nearly sinusoidal in both lateral directions. With increasing forcing strength the flow undergoes a sequence of symmetry breaking bifurcations that lead to steady, periodic, or quasi-periodic temporal dynamics. By constructing first recurrence maps we analyze how the dynamics of the quasi-periodic solution change with increasing Reynolds number. Our analysis reveals several narrow Reynolds number windows where the dynamics are characterized by resonance and frequency locking.We finally show that the flow transitions to chaos via the break-up of the two-torus.