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  A note on Taylor's hypothesis under large-scale flow variation

Wilczek, M., Xu, H., & Narita, Y. (2014). A note on Taylor's hypothesis under large-scale flow variation. Nonlinear Processes in Geophysics, 21, 645-649. doi:10.5194/npg-21-645-2014.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-0F31-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-DEAC-2
Genre: Journal Article

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 Creators:
Wilczek, Michael1, Author              
Xu, Haitao2, Author              
Narita, Yasuhito, Author
Affiliations:
1Max Planck Research Group Theory of Turbulent Flows, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2266693              
2Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063287              

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 Abstract: Experimental investigations of turbulent velocity fields often invoke Taylor's hypothesis (also known as frozen turbulence approximation) to evaluate the spatial structure based on time-resolved single-point measurements. A crucial condition for the validity of this approximation is that the turbulent fluctuations are small compared to the mean velocity, in other words, that the turbulence intensity must be low. While turbulence intensity is a well-controlled parameter in laboratory flows, this is not the case in many geo- and astrophysical settings. Here we explore the validity of Taylor's hypothesis based on a simple model for the wavenumber-frequency spectrum that has recently been introduced as a generalization of Kraichnan's random sweeping hypothesis. In this model, the fluctuating velocity is decomposed into a large-scale random sweeping velocity and small-scale fluctuations, which allows for a precise quantification of the influence of large-scale flow variations. For turbulence with a power-law energy spectrum, we find that the wavenumber spectrum estimated by Taylor's hypothesis exhibits the same power-law as the true spectrum, yet the spectral energy is overestimated due to the large-scale flow variation. The magnitude of this effect, and specifically its impact on the experimental determination of the Kolmogorov constant, are estimated for typical turbulence intensities of laboratory and geophysical flows.

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Language(s): eng - English
 Dates: 2014-06-02
 Publication Status: Published in print
 Pages: -
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 Table of Contents: -
 Rev. Method: Peer
 Identifiers: eDoc: 702114
DOI: 10.5194/npg-21-645-2014
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Title: Nonlinear Processes in Geophysics
  Alternative Title : Nonlin. Processes Geophys.
Source Genre: Journal
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Pages: - Volume / Issue: 21 Sequence Number: - Start / End Page: 645 - 649 Identifier: -