On the von Karman Length Scale as a Triggering Parameter in Eddy-Resolving Simulations of Turbulent Flows

Abstract

The von Karman length scale ${\text{L}}_{\text{vK}} =\upkappa{\text{S}}/\left| {\nabla^{2} {\text{U}}} \right|$ represents a key element in triggering the flow to generate resolved turbulence in Scale-Adaptive Simulations (SAS) [8, 9, 12] analog to the role of grid spacing $\Delta \left( { = \sqrt[3]{{\Delta _{\text{x}}\Delta _{\text{y}}\Delta _{\text{z}} }}} \right)$ in Large-Eddy Simulation (LES). Accordingly, the ${\text{L}}_{\text{vK}}$ parameter mimics the length scale characterizing the resolved motion within the SAS framework. It represents a flow variable of decisive importance in additional source term providing selective enhancement of the dissipation rate production, mostly in the separated shear layer regions. The main objective of the present work is the visualization of the structural properties of the ${\text{L}}_{\text{vK}}$ length scale in some internal and external flow configurations subjected to different straining originating from the boundary layer separation from sharp-edged and continuous curved surfaces. Furthermore, the present work attempts to establish a relationship between the ${\text{L}}_{\text{vK}}$ length scale and grid resolution (in terms of grid spacing $\Delta$) in relation to the flow unsteadiness characterization, identifying the SAS method capabilities of capturing appropriately the fluctuating turbulence.