A rigorous framework for Leslie's model of homogeneous anisotropic turbulence

Abstract

Leslie, in the book Developments in the Theory of Turbulence (1973 Oxford: Clarendon), offered a very simple and intuitively founded model for the case of homogeneous anisotropic turbulence. Here, we offer a rigorous reformulation of Leslie's model leading to a general form for the velocity correlation tensor that satisfies realizability conditions like symmetry in its tensor indices and the condition of solenoidality arising from the incompressibility condition. The anisotropic part of the correlation tensor involves two non-dimensional constants—one arising from the pure strain term and the other from the term that induces distortion in the wave vector space; the rapid pressure term does not contribute. The estimates for these non-dimensional constants yield encouraging results within this framework.