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Coherent large-scale structures from the linearized Navier–Stokes equations

Published online by Cambridge University Press:  20 June 2019

Anagha Madhusudanan Open the ORCID record for Anagha Madhusudanan [Opens in a new window] ,
Simon. J. Illingworth Open the ORCID record for Simon. J. Illingworth [Opens in a new window]  and
Ivan Marusic Open the ORCID record for Ivan Marusic [Opens in a new window]
Anagha Madhusudanan*
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
Simon. J. Illingworth
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
Ivan Marusic
Affiliation:
Department of Mechanical Engineering, University of Melbourne, VIC 3010, Australia
*
†Email address for correspondence: amadhusudana@student.unimelb.edu.au
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Abstract

The wall-normal extent of the large-scale structures modelled by the linearized Navier–Stokes equations subject to stochastic forcing is directly compared to direct numerical simulation (DNS) data. A turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=2000$ is considered. We use the two-dimensional (2-D) linear coherence spectrum (LCS) to perform the comparison over a wide range of energy-carrying streamwise and spanwise length scales. The study of the 2-D LCS from DNS indicates the presence of large-scale structures that are coherent over large wall-normal distances and that are self-similar. We find that, with the addition of an eddy viscosity profile, these features of the large-scale structures are captured by the linearized equations, except in the region close to the wall. To further study this coherence, a coherence-based estimation technique, spectral linear stochastic estimation, is used to build linear estimators from the linearized Navier–Stokes equations. The estimator uses the instantaneous streamwise velocity field or the 2-D streamwise energy spectrum at one wall-normal location (obtained from DNS) to predict the same quantity at a different wall-normal location. We find that the addition of an eddy viscosity profile significantly improves the estimation.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence theory

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JFM Papers
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Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 89 - 109
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© 2019 Cambridge University Press 

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