Theory of ${\omega }^{-4/3}$ law of the power spectrum in dissipative flows

Abstract

It is demonstrated that ${\omega }^{-4/3}$ law of the power spectrum with the angular frequency $\omega$ in dissipative flows is produced by the emission of dispersive waves from the antikink of an congested domain. The analytic theory predicts the spectrum is proportional to ${\omega }^{-2}$ for relatively low frequency and ${\omega }^{-4/3}$ for high frequency.

11 pages, 2 figures