RG Analysis of the Kolmogorov Cascade in Isotropic Turbulence

We review the application of renormalization group (RG) methods to the problem of isotropic turbulence, with attention to Kolmogorov’s phenomenological scaling law. We see that RG reproduces the form of the 5/3 law and can also be used to obtain estimates of the Kolmogorov constant that agree with experiment and numerical simulation. The articles reviewed also confirm the universality of the scaling law and the constant. Finally, we posit a new form for correlations in Fourier space motivated by Kolmogorov’s theory and use it to apply RG to a modified Navier-Stokes equation.