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Published October 2014 | Published
Journal Article Open

On the origin of frequency sparsity in direct numerical simulations of turbulent pipe flow


The possibility of creating reduced-order models for canonical wall-bounded turbulent flows based on exploiting energy sparsity in frequency domain, as proposed by Bourguignon et al. [Phys. Fluids26, 015109 (2014)], is examined. The present letter explains the origins of energetically sparse dominant frequencies and provides fundamental information for the design of such reduced-order models. The resolvent decomposition of a pipe flow is employed to consider the influence of finite domain length on the flow dynamics, which acts as a restriction on the possible wavespeeds in the flow. A forcing-to-fluctuation gain analysis in the frequency domain reveals that large sparse peaks in amplification occur when one of the possible wavespeeds matches the local wavespeed via the critical layer mechanism. A link between amplification and energy is provided through the similar characteristics exhibited by the most energetically relevant flow structures, arising from a dynamic mode decomposition of direct numerical simulation data, and the resolvent modes associated with the most amplified sparse frequencies. These results support the feasibility of reduced-order models based on the selection of the most amplified modes emerging from the resolvent model, leading to a novel computationally efficient method of representing turbulent flows.

Additional Information

© 2014 AIP Publishing LLC. Received 10 July 2014; accepted 20 October 2014; published online 31 October. The authors acknowledge financial support from the Australian Research Council through the ARC Discovery Project No. DP130103103, and from Australia's National Computational Infrastructure via Merit Allocation Scheme Grant No. D77. B.J.M., R.M., and M.L. are grateful for the support of the U.S. Air Force Office of Scientific Research under Grant No. FA9550-09-1-0701 (Program Manager R. Ponnappan). D.M. Smith is gratefully acknowledged for provision of his DMD code.

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August 20, 2023
August 20, 2023