Estimating uncertainty in homogeneous turbulence evolution due to coarse-graining

Reynolds Averaged Navier Stokes (RANS) closures assume that the state of the turbulent flow field can be uniquely described using a finite set of tensors. However, these tensors are averaged statistics, and thus, varied turbulent flow fields with different internal structuring can correspond to the...

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Bibliographic Details
Published in:Physics of fluids (1994) 2019-02, Vol.31 (2)
Main Authors: Mishra, Aashwin Ananda, Duraisamy, Karthik, Iaccarino, Gianluca
Format: Article
Language:English
Subjects:
Boundary value problems
Closures
Computational fluid dynamics
Dependence
Evolution
Fluid dynamics
Granulation
Homogeneous turbulence
Ill posed problems
Parameter uncertainty
Physics
Reynolds averaged Navier-Stokes method
Tensors
Turbulent flow
Uncertainty analysis
Velocity gradient
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Summary:Reynolds Averaged Navier Stokes (RANS) closures assume that the state of the turbulent flow field can be uniquely described using a finite set of tensors. However, these tensors are averaged statistics, and thus, varied turbulent flow fields with different internal structuring can correspond to the same values for this finite tensor basis. This causes the modeled initial value problem governing turbulence evolution to be ill-posed. This non-unique specification of the initial turbulent flow field may lead to non-unique evolution for the real turbulent flow at this level of description, introducing epistemic uncertainty in the RANS modeling problem. In this investigation, we show that for homogeneous turbulence, there is a range of possible evolution of a real turbulent flow field if only a finite set of local tensors are specified. Furthermore, this range can include diametrically opposite behavior of the flow. The dependence of this uncertainty is analyzed and quantified for different mean velocity gradients and at different flow parameters. It is exhibited that this uncertainty is engendered by the linear mechanisms in turbulence physics. The magnitude of sensitivity of flow evolution on flow history is explained, using the spectral space structure of the linear instabilities manifested for different mean flows.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.5080460