Viscosity-dependent inertial spectra of the Burgers and Korteweg-deVries-Burgers equations.

We show that the inertial range spectrum of the Burgers equation has a viscosity-dependent correction at any wave number when the viscosity is small but not zero. We also calculate the spectrum of the Korteweg-deVries-Burgers equation and show that it can be partially mapped onto the inertial spectrum of a Burgers equation with a suitable effective diffusion coefficient. These results are significant for the understanding of turbulence.

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