"Wavelet Transforms of the Navier-Stokes Equations and the Generalized Dimensions of Turbulence"

by
Lewalle, J.

ABSTRACT

The generalized dimensions D_q defined in the multifractal description of turbulence are related to the Navier-Stokes equations, and equations are presented for D_q and its evolution. In order to reach this result, the equations for incompressible flows are wavelet-transformed. When the analyzing wavelets belong in the Gaussian family, the pressure and momentum equations are transformed into first-order wave equations, for which the characteristics are obtained explicitly. Formal integration is carried out. As in Meneveau (1991), fractal statistics are then constructed from the local energy spectrum.