"Energy Dissipation in the Wavelet-Transformed Navier-Stokes Equations"

by
Lewalle, J.

ABSTRACT

The wavelet transformation has been successfully applied to the Navier-Stokes equations. In the case of Gaussian wavelets, a different light is shed on the role of convective terms, pressure and viscous terms. This note focusses ont he energy dissipation term in the resulting energy equation. It is shown that a k^2 term, analogous to the dissipation rate in Fourier space, results for wavelets of all orders except the first. For g_1-transforms, the coefficient of the dissipation term vanishes, leaving only a viscous diffusion term toward small scales.