Estimating uncertainty in homogeneous turbulence evolution due to coarse-graining

Abstract

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.