Orthonormal Divergence-Free Wavelet Analysis of Spatial Correlation between Kinetic Energy and Nonlinear Transfer in Turbulence

Abstract

Helical Meyer wavelet, an orthonormal divergence-free vector wavelet basis[1] is applied to the analysis of direct numerical simulation (DNS) data of incompressible isotropic turbulence. In the present study we focus our analysis on the correlation between the scale-location wavelet energy spectrum and nonlinear energy transfers relevant to its dynamics. Since helical Meyer wavelets are orthonormal and solenoidal, we can evaluate precisely the magnitude of nonlinear energy transfer between the wavelet modes with retaining the detailed energy balance. It is found that the magnitude of scale-location energy spectrum is positively correlated to those of relevant nonlinear energy transfers, i.e. nonlinear energy transfer actively occurs mainly in such domains that the fluid motions of assigned scale are intense. Batchelor and Townsend conjectured that intermittency of energy distribution in small scales may persist if the amount of energy transferred from a certain scale to smaller scales is determined by the energy density on the spot[2]. Our observation supports that such hypothetical process actually occurs as a result of the Navier-Stokes dynamics.