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Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels
Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels
We study the Reynolds number scaling of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. We establish that the resolvent formulation admits three classes of wave parameters that induce universal behavior with Reynolds number on the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (Re ? ? 10³-10¹?). Results from this low rank model of the Navier-Stokes equations compare favorably with experimental results in the literature.
mathematical foundations, navier–stokes equations, turbulent boundary layers
0022-1120
275-316
Moarref, Rashad
18ab57ac-e2ea-4733-ab4a-c40d1dae59e0
Sharma, Ati S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Tropp, Joel A.
1ea65229-d3e3-4614-bcd3-4ccf4e1d1dc2
McKeon, Beverley J.
d3dd4f29-f65b-46c2-9d6d-f974cbb66fc2
Moarref, Rashad
18ab57ac-e2ea-4733-ab4a-c40d1dae59e0
Sharma, Ati S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
Tropp, Joel A.
1ea65229-d3e3-4614-bcd3-4ccf4e1d1dc2
McKeon, Beverley J.
d3dd4f29-f65b-46c2-9d6d-f974cbb66fc2

Moarref, Rashad, Sharma, Ati S., Tropp, Joel A. and McKeon, Beverley J. (2013) Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels. Journal of Fluid Mechanics, 734, 275-316. (doi:10.1017/jfm.2013.457).

Record type: Article

Abstract

We study the Reynolds number scaling of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (2010), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier-Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. We establish that the resolvent formulation admits three classes of wave parameters that induce universal behavior with Reynolds number on the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (Re ? ? 10³-10¹?). Results from this low rank model of the Navier-Stokes equations compare favorably with experimental results in the literature.

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e-pub ahead of print date: 9 October 2013
Published date: November 2013
Keywords: mathematical foundations, navier–stokes equations, turbulent boundary layers
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 350308
URI: http://eprints.soton.ac.uk/id/eprint/350308
ISSN: 0022-1120
PURE UUID: 1e9bd646-502d-43aa-89df-bdcd535cceee
ORCID for Ati S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 25 Mar 2013 12:22
Last modified: 21 Nov 2021 03:08

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Contributors

Author: Rashad Moarref
Author: Ati S. Sharma ORCID iD
Author: Joel A. Tropp
Author: Beverley J. McKeon

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