ENERGY-DISSIPATION IN THE WAVELET-TRANSFORMED NAVIER-STOKES EQUATIONS

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, pressure, and viscous terms. This note focuses on the energy dissipation term in the resulting energy eq uation. It is shown that a kappa2 term, analogous to the dissipation r ate in Fourier space, results for wavelets of all orders except the fi rst. For g1 transforms, the coefficient of the dissipation term vanish es, leaving only as spectral diffusion term toward small scales.