"Wavelet Transforms of the Navier-Stokes Equations and the
Generalized Dimensions of Turbulence"
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.
Appl. Sci. Res. 51, 109-113, 1993.
Jacques Lewalle, firstname.lastname@example.org