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Energy dissipation in the wavelet-transformed Navier-Stokes equations. (English) Zbl 0777.76025

Summary: 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 \(\kappa^ 2\) 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 spectral diffusion term toward small scales.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
76F99 Turbulence
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[1] DOI: 10.1017/S0022112091003786 · Zbl 0749.76033 · doi:10.1017/S0022112091003786
[2] DOI: 10.1146/annurev.fl.24.010192.002143 · doi:10.1146/annurev.fl.24.010192.002143
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