Nonuniversal power-law spectra in turbulent systems

TL;DR

This paper investigates nonuniversal power-law spectra in turbulent systems using a modified Kuramoto-Sivashinsky equation, revealing scale-independent power laws with nonuniversal exponents through semi-analytical and numerical methods.

Contribution

It introduces a simplified model demonstrating nonuniversal power-law spectra in turbulence, expanding understanding beyond traditional universal inertial range theories.

Findings

Power-law spectra with nonuniversal exponents observed

Spectral range where nonlinear and linear time scales are scale-independent

Semi-analytical and numerical methods confirm nonuniversal power laws

Abstract

Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be observed. As a simple model for such situations, a modified version of the Kuramoto-Sivashinsky equation is studied. By means of semi-analytical and numerical studies, one finds power laws with nonuniversal exponents in the spectral range for which the ratio of nonlinear and linear time scales is (roughly) scale-independent.