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On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis

On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis
On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis
We generate predictions for the fluctuating pressure field in turbulent pipe flow by re-formulating the resolvent analysis of McKeon & Sharma (2010) in terms of the so-called primitive variables. Under this analysis, the nonlinear convective terms in the Fourier-transformed Navier-Stokes equations are treated as a forcing that is mapped to a velocity and pressure response by the resolvent of the linearized Navier-Stokes operator. At each wavenumber-frequency combination, the turbulent velocity and pressure field are represented by the most-amplified (rank-1) response modes, identified via a singular value decomposition of the resolvent. We show that these rank-1 response modes reconcile many of the key relationships between the velocity field, coherent structure (i.e., hairpin vortices), and the high-amplitude wall-pressure events observed in previous experiment and DNS. A Green’s function representation shows that the pressure fields obtained under this analysis correspond primarily to the fast pressure contribution arising from the linear interaction between the mean shear and the turbulent wall-normal velocity. Recovering the slow pressure requires an explicit treatment of the nonlinear interactions between the Fourier response modes. By considering the velocity and pressure fields associated with the triadically-consistent mode combination studied by Sharma & McKeon (2013), we identify the possibility of an apparent amplitude modulation effect in the pressure field, similar to that observed for the streamwise velocity field. However, unlike the streamwise velocity, for which the large scales of the flow are in phase with the envelope of the small-scale activity close to the wall, we expect there to be a ?/2 phase difference between the large scale wall-pressure and the envelope of the small-scale activity. Finally, we generate spectral predictions based on a rank-1 model assuming broadband forcing across all wavenumber-frequency combinations. Despite the significant simplifying assumptions, this approach reproduces trends observed in previous DNS for the wavenumber spectra of velocity and pressure, and for the scale-dependence of wall-pressure propagation speed.
0022-1120
1-33
Luhar, M.
7972fd0e-2eb8-4c6d-aac0-8ef9b0540cff
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B.J.
2e685015-292a-42a7-8c9e-7cc27cf2da67
Luhar, M.
7972fd0e-2eb8-4c6d-aac0-8ef9b0540cff
Sharma, A.S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, B.J.
2e685015-292a-42a7-8c9e-7cc27cf2da67

Luhar, M., Sharma, A.S. and McKeon, B.J. (2014) On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis. Journal of Fluid Mechanics, 1-33.

Record type: Article

Abstract

We generate predictions for the fluctuating pressure field in turbulent pipe flow by re-formulating the resolvent analysis of McKeon & Sharma (2010) in terms of the so-called primitive variables. Under this analysis, the nonlinear convective terms in the Fourier-transformed Navier-Stokes equations are treated as a forcing that is mapped to a velocity and pressure response by the resolvent of the linearized Navier-Stokes operator. At each wavenumber-frequency combination, the turbulent velocity and pressure field are represented by the most-amplified (rank-1) response modes, identified via a singular value decomposition of the resolvent. We show that these rank-1 response modes reconcile many of the key relationships between the velocity field, coherent structure (i.e., hairpin vortices), and the high-amplitude wall-pressure events observed in previous experiment and DNS. A Green’s function representation shows that the pressure fields obtained under this analysis correspond primarily to the fast pressure contribution arising from the linear interaction between the mean shear and the turbulent wall-normal velocity. Recovering the slow pressure requires an explicit treatment of the nonlinear interactions between the Fourier response modes. By considering the velocity and pressure fields associated with the triadically-consistent mode combination studied by Sharma & McKeon (2013), we identify the possibility of an apparent amplitude modulation effect in the pressure field, similar to that observed for the streamwise velocity field. However, unlike the streamwise velocity, for which the large scales of the flow are in phase with the envelope of the small-scale activity close to the wall, we expect there to be a ?/2 phase difference between the large scale wall-pressure and the envelope of the small-scale activity. Finally, we generate spectral predictions based on a rank-1 model assuming broadband forcing across all wavenumber-frequency combinations. Despite the significant simplifying assumptions, this approach reproduces trends observed in previous DNS for the wavenumber spectra of velocity and pressure, and for the scale-dependence of wall-pressure propagation speed.

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Published date: 20 May 2014
Organisations: Aeronautics, Astronautics & Comp. Eng

Identifiers

Local EPrints ID: 364753
URI: https://eprints.soton.ac.uk/id/eprint/364753
ISSN: 0022-1120
PURE UUID: 13d1f581-ec33-4150-a38b-92148dcd0570
ORCID for A.S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

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Date deposited: 21 May 2014 10:39
Last modified: 06 Jun 2018 12:25

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