Clipping over Dissipation in Turbulence Models

Abstract

Clipping refers to adding 1 line of code $A ⇐ {\rm min}\{A, B\}$ to force the variable $A$ to stay below a present bound $B.$ Phenomenological clipping also occurs in turbulence models to correct for over dissipation caused by the action of eddy viscosity terms in regions of small scales. Herein we analyze eddy viscosity model energy dissipation rates with 2 phenomenological clipping strategies. Since the true Reynolds stresses are $O(d^2)$ ($d$ = wall normal distance) in the near wall region, the first is to force this near wall behavior in the eddy viscosity by $ν_{turb}⇐ {\rm min}\{ν_{turb}, \frac{\kappa}{T_{ref}}d^2\}$ for some preset $\kappa$ and time scale $T_{ref}.$ The second is Escudier’s early proposal to clip the turbulence length scale in a common specification of $ν_{turb},$ reducing too large values in the interior of the flow. Analyzing respectively shear flow turbulence and turbulence in a box (i.e., periodic boundary conditions), we show that both clipping strategies do prevent aggregate over dissipation of model solutions.