The direct enstrophy cascade of two-dimensional soap film flows
We investigate the direct enstrophy cascade of two-dimensional decaying turbulence in a flowing soap film channel. We use a coarse-graining approach that allows us to resolve the nonlinear dynamics and scale-coupling simultaneously in space and in scale. From our data, we verify an exact relation due to Eyink [“Local energy flux and the refined similarity hypothesis,” J. Stat. Phys. 78, 335–351 (1995); Eyink “Exact results on scaling exponents in the 2D enstrophy cascade,” Phys. Rev. Lett. 74, 3800–3803 (1995)] between traditional 3rd-order structure function and the enstrophy flux obtained by coarse-graining. We also present experimental evidence that enstrophy cascades to smaller (larger) scales with a 60% (40%) probability, in support of theoretical predictions by Merilees and Warn [“On energy and enstrophy exchanges in two-dimensional non-divergent flow,” J. Fluid Mech. 69, 625–630 (1975)] which appear to be valid in our flow owing to the ergodic nature of turbulence. We conjecture that their kinemati...