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

摘要

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.