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

TL;DR

This paper presents an analytic theory explaining the $\, ext{-}4/3$ power spectrum law in dissipative flows, attributing it to dispersive wave emission from antikinks, with predictions matching observed frequency-dependent behaviors.

Contribution

It introduces a theoretical framework linking dispersive wave emission to the $\, ext{-}4/3$ power spectrum law in dissipative flows, providing frequency-dependent predictions.

Findings

Spectrum proportional to $\, ext{-}2$ at low frequency

Spectrum proportional to $\, ext{-}4/3$ at high frequency

Analytic theory matches observed spectral behavior

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.