Multi-Time Multi-Scale Correlation Functions in Hydrodynamic Turbulence

TL;DR

This paper investigates multi-time and multi-scale correlation functions in high Reynolds number turbulence, revealing dynamic multiscaling and complex temporal behaviors through advanced numerical simulations.

Contribution

It introduces a systematic measurement approach using a quasi-Lagrangian frame to analyze multi-time correlations in turbulent flows, highlighting multiscaling phenomena.

Findings

Evidence of dynamic multiscaling in turbulence

Multi-time correlation functions have infinite characteristic times

Reduction of large-scale sweeping effects in measurements

Abstract

High Reynolds numbers Navier-Stokes equations are believed to break self-similarity concerning both spatial and temporal properties: correlation functions of different orders exhibit distinct decorrelation times and anomalous spatial scaling properties. Here, we present a systematic attempt to measure multi-time and multi-scale correlations functions, by using high Reynolds numbers numerical simulations of fully homogeneous and isotropic turbulent flow. The main idea is to set-up an ensemble of probing stations riding the flow, i.e. measuring correlations in a reference frame centered on the trajectory of distinct fluid particles (the quasi-Lagrangian reference frame introduced by Belinicher & L'vov, Sov. Phys. JETP 66, 303 (1987)). In this way we reduce the large-scale sweeping and measure the non-trivial temporal dynamics governing the turbulent energy transfer from large to small scales. We present evidences of the existence of dynamic multiscaling: multi-time correlation functions are characterized by an infinite set of characteristic times.