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Local modulated wave model for the reconstruction of space–time energy spectra in turbulent flows

Published online by Cambridge University Press:  14 January 2020

Ting Wu
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China
Guowei He*
Affiliation:
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing100049, China
*
Email address for correspondence: hgw@lnm.imech.ac.cn

Abstract

A statistical model is developed to reconstruct space–time energy spectra in turbulent flows from a non-extensive dataset comprising a time series of velocity fluctuations at a finite number of measurement points. This model is based on a higher approximation of energetic flow structures and developed by using local modulated waves. As a result, it can correctly predict the mean wavenumbers and spectral bandwidths. In contrast, Taylor’s frozen-flow hypothesis incorrectly predicts the spectral bandwidths to be zero, and the local wavenumber model significantly under-predicts the spectral bandwidths. An analytical example is formulated to illustrate the present model, and datasets from direct numerical simulations of turbulent channel flows are used to validate this model. The present statistical model is also discussed in terms of the dominating processes of temporal decorrelation in turbulent flows.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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