Orthonormal Divergence-Free Wavelet Analysis of Nonlinear Energy Transfer in Rolling-Up Vortices

Abstract

Orthonormal divergence-free wavelet analysis of nonlinear transfer in some isolated vortices, which evolve from the instability of a thin shear layer, suggests that the rolling-up vortices are relevant to the energy cascade to smaller scales. A graphical representation method for the wavelet nonlinear interactions is developed so that the spatial scale and location information of the wavelets are depicted with enstrophy isosurfaces of vortices and vortex axis lines. It is found that the active nonlinear interactions are very closely distributed around the axis of rolling-up vortices irrespective of the forward or backward transfers and that the dominant nonlinear interactions are “local” in the sense of distance.