Spectral energetics of a quasilinear approximation in uniform shear turbulence
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Accepted version
Author(s)
Hernandez, Carlos
Hwang, Yongyun
Type
Journal Article
Abstract
The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the meanare fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascadeis shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. It is also found that the streamwise wave number spectra of turbulent transport, obtained with the classical Reynolds decomposition, statistically characterizes the instability of the linearised fluctuation equations. Further supporting evidence of this claim is presented by carrying out a numerical experiment, in which the QL model with single streamwise Fourier mode is found to generate the strongest turbulence for Lx/Lz= 1∼3, consistent with previous findings (Lx and Lz are the streamwise and spanwise computational domains, respectively). Finally, the QL model is shown to completely ignore the role of slow pressure in the fluctuations, resulting in a significant damage of pressure-strain transport at all length scales. This explains the anisotropic turbulence of the QL model throughout the entire wavenumber space as well as the inhibited nonlinear regeneration of streamwise vortices in the self-sustaining process.
Date Issued
2020-12-10
Date Acceptance
2020-08-05
Citation
Journal of Fluid Mechanics, 2020, 604 (A11), pp.A11-1-A11-26
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
A11-1
End Page
A11-26
Journal / Book Title
Journal of Fluid Mechanics
Volume
604
Issue
A11
Copyright Statement
© The Author(s), 2020. Published by Cambridge University Press. This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2020.678. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works.
Sponsor
The Leverhulme Trust
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/spectral-energetics-of-a-quasilinear-approximation-in-uniform-shear-turbulence/8B2A4CC37BCE43FC98209CD2E67FA07E
Grant Number
RPG-2019-123
Subjects
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status
Published online
Date Publish Online
2020-10-06