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Compact representation of wall-bounded turbulence using compressive sampling

Bourguignon, J.-L. and Tropp, J. A. and Sharma, A. S. and McKeon, B. J. (2014) Compact representation of wall-bounded turbulence using compressive sampling. Physics of Fluids, 26 (1). Art. No. 015109. ISSN 1070-6631. http://resolver.caltech.edu/CaltechAUTHORS:20140320-104900351

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Abstract

Compressive sampling is well-known to be a useful tool used to resolve the energetic content of signals that admit a sparse representation. The broadband temporal spectrum acquired from point measurements in wall-bounded turbulence has precluded the prior use of compressive sampling in this kind of flow, however it is shown here that the frequency content of flow fields that have been Fourier transformed in the homogeneous spatial (wall-parallel) directions is approximately sparse, giving rise to a compact representation of the velocity field. As such, compressive sampling is an ideal tool for reducing the amount of information required to approximate the velocity field. Further, success of the compressive sampling approach provides strong evidence that this representation is both physically meaningful and indicative of special properties of wall turbulence. Another advantage of compressive sampling over periodic sampling becomes evident at high Reynolds numbers, since the number of samples required to resolve a given bandwidth with compressive sampling scales as the logarithm of the dynamically significant bandwidth instead of linearly for periodic sampling. The combination of the Fourier decomposition in the wall-parallel directions, the approximate sparsity in frequency, and empirical bounds on the convection velocity leads to a compact representation of an otherwise broadband distribution of energy in the space defined by streamwise and spanwise wavenumber, frequency, and wall-normal location. The data storage requirements for reconstruction of the full field using compressive sampling are shown to be significantly less than for periodic sampling, in which the Nyquist criterion limits the maximum frequency that can be resolved. Conversely, compressive sampling maximizes the frequency range that can be recovered if the number of samples is limited, resolving frequencies up to several times higher than the mean sampling rate. It is proposed that the approximate sparsity in frequency and the corresponding structure in the spatial domain can be exploited to design simulation schemes for canonical wall turbulence with significantly reduced computational expense compared with current techniques.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://scitation.aip.org/content/aip/journal/pof2/26/1/10.1063/1.4862303PublisherArticle
http://dx.doi.org/10.1063/1.4862303DOIArticle
ORCID:
AuthorORCID
Tropp, J. A.0000-0003-1024-1791
Sharma, A. S.0000-0002-7170-1627
McKeon, B. J.0000-0003-4220-1583
Additional Information:© 2014 American Institute of Physics Publishing LLC. Received 6 March 2013; accepted 20 December 2013; published online 22 January 2014. This work was supported by the National Science Foundation (NSF) under CAREER Award No. CBET-0747672. We are extremely grateful to Dr. Xiaohua Wu for his generosity in performing new runs of the pipe flow DNS and providing us with the data used in this study. We thank the anonymous reviewers for critiques that led to significant improvements in this paper.
Group:GALCIT
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Funding AgencyGrant Number
NSFCBET-0747672
Record Number:CaltechAUTHORS:20140320-104900351
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140320-104900351
Official Citation:Compact representation of wall-bounded turbulence using compressive sampling J.-L. Bourguignon, J. A. Tropp, A. S. Sharma and B. J. McKeon Phys. Fluids 26, 015109 (2014); http://dx.doi.org/10.1063/1.4862303
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44408
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:20 Mar 2014 18:06
Last Modified:09 Oct 2017 23:09

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