The length scale equation in turbulence models

Abstract. The question of which length scale equation to use in models of turbulence has long been controversial and several approaches have been suggested and used in the past. In this paper, we demonstrate that all these approaches are equivalent and the inconsistencies in the use of some of these approaches arise from improper modeling of the diffusion term in the length scale equation. We formulate a general length scale equation, which encompasses all current approaches. This equation is devoid of inconsistencies and should prove useful in its general form, or one of its subsets, in turbulence closure modeling.