Chaotic diffusion in steady wavy vortex flow-Dependence on wave state and correlation with Eulerian symmetry measures

A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the 'escape basins' (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low R regime after the breakup of all KAM tori, the outflow basin (γO) is larger than the inflow basin (γI), and both γO and γI are (approximately) independent of R. In the large R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates (γOrO,γIrI) with Reynolds number was in excellent qualitative agreement with the variation of ((ϕ¯θ)O,(ϕ¯θ)I).