An Analytical Solution of the Pure Rotation Problem: Rapid Distortion Theory of an Initially Axisymmetric Turbulence

Abstract

The calibration of turbulent models for the rapid part of the pressure strain tensor is generally based on rapid distorsion theory for which analytical solutions for irrotational strain and pure shear are available (see e.g. Lee, 1989). Such solutions may be developed in time with respect to an initially isotropic situation. In the following, we examine the case of pure rotation starting from an axisymmetric situation. Although it confirms that a functional dependence of the rapid pressure-strain tensor with respect of the anisotropy tensor b cannot fulfill, even for small times, the solution of the linear problem (except in the case of irrotational strain), the analysis of the solution for the pure rotation problem provides new arguments for modelling.