Use of eddy viscosity in resolvent analysis of turbulent channel flow
Use of eddy viscosity in resolvent analysis of turbulent channel flow
The predictions obtained from resolvent analysis with and without an eddy viscosity model for turbulent channel flow at Reτ=550 are compared to direct numerical simulation data to identify the scales and wave speeds for which resolvent analysis provides good predictions. The low-rank behavior of the standard resolvent identifies energetic regions of the flow whereas the eddy resolvent is low rank when the resulting projection of the leading eddy resolvent mode onto the leading mode from spectral proper orthogonal decomposition is maximum. The highest projections are obtained for structures that are associated with the near-wall cycle and structures that are energetic at z=±0.5. It is argued that these types of structures are likely to be correctly predicted for any friction Reynolds number due to the inner and outer scaling of the Cess eddy viscosity profile. The eddy resolvent also correctly identifies the most energetic wave speed for these two scales. For all other scales, neither analysis reliably predicts the most energetic wave speed or mode shapes. The standard resolvent tends to overestimate the most energetic wave speed while the eddy resolvent underestimates it. The resulting eddy resolvent modes are overly "attached" to the wall since the wall-normal gradient of the eddy viscosity overestimates the transport of energy towards the wall. These observations have direct implications for future work towards estimating turbulent channel flows using resolvent analysis and suggest that the Cess profile can be further optimized for individual scales to provide better low-order models of turbulent channel flows.
Symon, Sean
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Madhusudanan, Anagha
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Illingworth, Simon J.
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Marusic, Ivan
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1 June 2023
Symon, Sean
2e1580c3-ba27-46e8-9736-531099f3d850
Madhusudanan, Anagha
72799cee-c433-4145-b943-9f99413ce4d4
Illingworth, Simon J.
0e1c7b04-2c41-4152-996f-6aa92583bf5b
Marusic, Ivan
b54cc588-2523-44e8-b4af-989b835fcd9e
Symon, Sean, Madhusudanan, Anagha, Illingworth, Simon J. and Marusic, Ivan
(2023)
Use of eddy viscosity in resolvent analysis of turbulent channel flow.
Physical Review Fluids, 8 (6), [064601].
(doi:10.1103/PhysRevFluids.8.064601).
Abstract
The predictions obtained from resolvent analysis with and without an eddy viscosity model for turbulent channel flow at Reτ=550 are compared to direct numerical simulation data to identify the scales and wave speeds for which resolvent analysis provides good predictions. The low-rank behavior of the standard resolvent identifies energetic regions of the flow whereas the eddy resolvent is low rank when the resulting projection of the leading eddy resolvent mode onto the leading mode from spectral proper orthogonal decomposition is maximum. The highest projections are obtained for structures that are associated with the near-wall cycle and structures that are energetic at z=±0.5. It is argued that these types of structures are likely to be correctly predicted for any friction Reynolds number due to the inner and outer scaling of the Cess eddy viscosity profile. The eddy resolvent also correctly identifies the most energetic wave speed for these two scales. For all other scales, neither analysis reliably predicts the most energetic wave speed or mode shapes. The standard resolvent tends to overestimate the most energetic wave speed while the eddy resolvent underestimates it. The resulting eddy resolvent modes are overly "attached" to the wall since the wall-normal gradient of the eddy viscosity overestimates the transport of energy towards the wall. These observations have direct implications for future work towards estimating turbulent channel flows using resolvent analysis and suggest that the Cess profile can be further optimized for individual scales to provide better low-order models of turbulent channel flows.
Text
PhysRevFluids.8.064601
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Published date: 1 June 2023
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Local EPrints ID: 480521
URI: http://eprints.soton.ac.uk/id/eprint/480521
ISSN: 2469-990X
PURE UUID: f4ce4950-c414-4e49-81ac-28253a29e3dc
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Date deposited: 03 Aug 2023 17:25
Last modified: 17 Mar 2024 03:49
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Author:
Anagha Madhusudanan
Author:
Simon J. Illingworth
Author:
Ivan Marusic
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