Dynamic Multiscaling in Two-dimensional Fluid Turbulence

TL;DR

This paper uses extensive simulations to analyze multiscaling behavior in two-dimensional fluid turbulence, revealing how different methods of extracting time scales relate to multiscaling exponents and verifying bridge relations.

Contribution

It introduces a detailed analysis of dynamic multiscaling in 2D turbulence, establishing relations between time-dependent and equal-time structure functions through bridge relations.

Findings

Different methods yield distinct dynamic-multiscaling exponents.

Bridge relations between exponents are verified within error margins.

Results enhance understanding of multiscaling in 2D turbulence.

Abstract

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that differ- ent ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.