Dissipation range of the energy spectrum in high Reynolds number turbulence

Abstract

We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to R λ = 650, with excellent small-scale resolution of k max η ≈ 6, and additionally at R λ = 1300 with k max η ≈ 3, where k max is the maximum resolved wave number and η is the Kolmogorov length scale. We find that for a limited range of wave numbers k past the bottleneck, in the range 0.15 kη 0.5, the spectra for all R λ display a universal stretched exponential behavior of the form exp(−k 2/3), in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range 1 kη 4, but one that persistently decreases with increasing R λ. This region serves as the intermediate dissipation range between the exp(−k 2/3) region and the far dissipation range kη 1 where analytical arguments as well as DNS data with superfine resolution [S. Khurshid et al., Phys. Rev. Fluids 3, 082601 (2018)] suggest a simple exp(−kη) dependence. We briefly discuss our results in connection to the multifractal model.

Self-attenuation of extreme events in Navier–Stokes turbulence

“…It is instructive to note that the mathematical results typically obtained in R 3 can be readily generalized to our simulation in the T 3 torus. Using the largest grid sizes currently feasible in turbulence simulations, of up to 12288 3 points 21,22 , the Taylor-scale Reynolds number R λ , which quantifies the turbulence intensity, is varied from 140 to 1300 in our simulations (corresponding to fully developed turbulence). Special attention is given to faithfully resolve the small scales and hence the extreme events 12 , keeping the grid spacing smaller than the Kolmogorov length scale, η ¼ ðν 3 =hϵiÞ 1=4 , based on the mean dissipation rate of kinetic energy 〈ϵ〉, where the average 〈 ⋅ 〉 is taken over the 3D spatial domain and also multiple realizations.…”

Langevin based turbulence model and its relationship with Kappa distributions

“…That being said, the differences between the best fit using -distribution and large amplitude velocity fluctuations at high values of k (see Fig. 2 ) shows that other non-extensive distributions such as stretched exponential 39 – 41 or regularized -distributions 42 , 43 may be considered in order to extend the scope of the use of CMLs to characterize turbulent flows. Moreover, the CML also lacks nonlinear interactions between scales, or coupling between increments at different spatial locations either, all important effects to be considered to further characterize turbulence.…”

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

“…1993; Saddoughi & Veeravalli 1994; Sirovich, Smith & Yakhot 1994; Ishihara et al. 2005; Khurshid, Donzis & Sreenivasan 2018; Buaria & Sreenivasan 2020), and the effect of the Gaussian filter moves this exponential-like decay to lower wavenumbers. The unfiltered spectrum shows agreement with the standard Kolmogorov spectrum, over a limited range of wavenumbers .…”