On the sensitization of turbulence models to rotation and curvature

Empirical alterations of eddy-viscosity turbulence models to account for system rotation and streamline curvature an discussed. Except in a narrow class of flows, the streamline curvature itself is an inadequate entry into a model, because it is not Galilean-invariant. We propose a measure of the extra influence on the turbulence which is invariant, fully defined in three dimensions, and unifies rotation and curvature effects. This is at the expense of involving higher derivatives than the ''traditional'' (non-invariant) terms do. It is closely related to an idea of Knight & Saffman [1]. Its interpretation is straightforward, at least in two dimensions, and coincides with the classical measures in a few ''building-block'' flows such as rotating shear flow or a curved boundary layer. It can be used in one-equation, two-equation, and similar models in conjunction with empirical functions which depend on the model; an example is given.