Invariance of turbulent closure models

Abstract

The invariance of second moment turbulent closure under a change of frame is examined. It is shown that the Reynolds stresses and the higher turbulence correlations based on an ensemble mean are frame‐indifferent while the Reynolds stress transport equations are frame dependent. As a result of this incompatibility, second moment closure cannot form a general foundation for the study of turbulence. Alternative approaches that are properly invariant are discussed.