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Characteristics of space-time energy spectra in turbulent channel flows

Ting Wu1,2, Chenhui Geng1,2, Yichen Yao3, Chunxiao Xu3, and Guowei He1,2,*

  • 1The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
  • 2School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • 3Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

  • *Corresponding author: hgw@lnm.imech.ac.cn
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Phys. Rev. Fluids 2, 084609 – Published 31 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084609

Abstract

An energy spectrum is preliminarily characterized by its mean and standard deviation. In this study, we derive exact expressions for the means and bandwidths of space-time energy spectra at fixed frequencies. The mean wave numbers are used to determine the phase velocities that bridge from temporal spectra to space-time spectra. The bandwidths are used to measure the well-known spectral broadening. We show that phase velocities alone are insufficient to determine the bandwidths of energy spectra. As a result, the cross-spectral method predicts narrower bandwidths of energy spectra. Therefore, in addition to phase velocities, amplitudes are used to rescale the space-time energy spectra, leading to the correct bandwidths. Existing data from direct numerical simulations of turbulent channel flows validate the rescaling approach.

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Phys. Rev. Fluids 2, 084609– Published 31 August, 2017
  • Received 18 January 2017

©2017 American Physical Society

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