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 equation. It is shown that a κ² term, analogous to the dissipation rate in Fourier space, results for wavelets of all orders except the first. For g₁ transforms, the coefficient of the dissipation term vanishes, leaving only a spectral diffusion term toward small scales.