Multi-time multi-scale correlation functions in hydrodynamic turbulence

L. Biferale, E. Calzavarini, F. Toschi

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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 and 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 the dynamic multiscaling properties of turbulence - first proposed by L’vov et al. [Phys. Rev. E 55, 7030 (1997)] - in which multi-time correlation functions are characterized by an infinite set of characteristic times.
Original languageEnglish
Article number085107
Pages (from-to)085107-1/6
Number of pages6
JournalPhysics of Fluids
Volume23
Issue number8
DOIs
Publication statusPublished - 2011

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