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

• Main Authors: Gomez, F. (Author), Blackburn, H.M (Author), Rudman, M. (Author), McKeon, B.J (Author), Luhar, M. (Author), Moarref, R. (Author), Sharma, A.S (Author)
• Format: Article
• Language: English
• Published: 2014-10-31.
• Subjects: Article
• Online Access: Get fulltext

 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.