The Universality of Dynamic Multiscaling in Homogeneous, Isotropic Turbulence

TL;DR

This paper demonstrates that dynamic multiscaling exponents in turbulence are universal, remaining consistent across different models and whether turbulence is steady or decaying, through analytical and numerical analysis.

Contribution

It provides the first comprehensive evidence that dynamic multiscaling exponents are universal across models and turbulence states, unifying steady and decaying turbulence behaviors.

Findings

Normalised structure functions eliminate dependence on measurement origin.

Bridge relations between exponents hold for both steady and decaying turbulence.

Exponents and relations are consistent across models and turbulence types.

Abstract

We systematise the study of dynamic multiscaling of time-dependent structure functions in different models of passive-scalar and fluid turbulence. We show that, by suitably normalising these structure functions, we can eliminate their dependence on the origin of time at which we start our measurements and that these normalised structure functions yield the same linear bridge relations that relate the dynamic-multiscaling and equal-time exponents for statistically steady turbulence. We show analytically, for both the Kraichnan Model of passive-scalar turbulence and its shell model analogue, and numerically, for the GOY shell model of fluid turbulence and a shell model for passive-scalar turbulence, that these exponents and bridge relations are the same for statistically steady and decaying turbulence. Thus we provide strong evidence for dynamic universality, i.e., dynamic-multiscaling exponents do not depend on whether the turbulence decays or is statistically steady.