Scale locality of the energy cascade using real space quantities

Abstract

The classical energy cascade in turbulence as described by Richardson and Kolmogorov is predominantly a conjecture relying on the locality of interactions between scales of turbulence. This picture is generally accepted and assumes that energy and enstrophy transfers occur between neighbouring scales of turbulence and that vortex stretching plays a major role in the dynamics of this energy cascade. Direct numerical simulation data for Re λ ranging from 37 to 1131 is used to gather evidence for the cascade by investigating the energy and enstrophy fluxes between scales and the interplay between vorticity at one scale and strain at an adjacent scale. This is achieved by using a bandpass filter to educe the turbulent structures at various length scales allowing one to determine the fluxes between these scales and to interrogate the role of non-local (in physical-space) vortex stretching. It is shown that the structures of a length scale L mostly transfer their energy to structures of size 0.3L and that most of the enstrophy flux goes from structures of scale L to 0.3L. Furthermore, vortical structures of a length scale L ω are stretched mostly by straining structures of size 3 to 5L ω and the stretching by eddies of sizes larger than 10L ω is negligible. The stretching is dominated by the most extensive principal strain rate of the straining structures. These observations are found to be independent of Re λ for the range investigated in this study. These results provide strong evidence for the classical view of an energy cascade transferring energy from large to small scales through a hierarchy of steps, each step consisting of the stretching of vortices by somewhat larger structures.

A physical model of turbulence cascade via vortex reconnection sequence and avalanche

“…From the spectral perspective, the energy cascade is understood as the interaction between adjacent wavenumbers (Obukhov 1941;Domaradzki & Carati 2007). From the spatial perspective, energy transfer across different scales is often assumed to be due to vortex stretching, in which vortical structures of a given scale are stretched and intensified by larger vortices (Taylor & Green 1937;Goto 2008;Mao & Hussain 2017;Doan et al 2018). However, the link between these two approaches is still unclear.…”

“…One important aspect in classical turbulent energy cascade is the locality of interactions between different scales (Taylor & Green 1937;Domaradzki & Rogallo 1990). From the physical space perspective, it suggests that a vortex of a given size is stretched primarily by the strain from structures that are three to five times larger (Leung, Swaminathan & Davidson 2012;Doan et al 2018). It is therefore appropriate to investigate the scale locality in vortex reconnection.…”

“…It is therefore appropriate to investigate the scale locality in vortex reconnection. The scale-by-scale transfer and interaction is analysed by following the method proposed by Davidson, Morishita & Kaneda (2008) (see also Doan et al (2018)) -summarized as follows. The velocity u and vorticity ω are decomposed into large and small scales such that u = u L + u S and ω = ω L + ω S , where the superscripts L and S respectively denote the larger and smaller structures compared to a selected scale.…”

Gabor mode enrichment in large eddy simulations of turbulent flow

“…While the discussion in this section regarding interscale energy transfer has been presented from the perspective of single-point statistical measures targeted for modelling, the interested reader is referred to the substantial array of literature on interscale energetics in turbulent flows. Recent work by Doan et al (2018) has addressed the role of non-local vortex stretching in interscale transfer of enstrophy flux for a wide range of Reynolds numbers and Johnson (2020) introduced an exact relationship between interscale energy transfer and vorticity-strain interactions. Johnson (2020) shows that scale non-local vortex stretching (large-scale strain on small-scale vorticity) and strain self-amplification play a more important role in interscale transfers than scale local vortex stretching.…”

Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows1

“…. As stressed recently by Doan et al [115], the rate of generation of enstrophy, by vortex stretching, is often taken as a proxy for the spectral energy transfer process [116][117][118][119][120][121] in physical space [122,123].…”