Abstract
A curvature correction for explicit algebraic Reynolds stress models (EARSMs), based on a formal derivation of the weak-equilibrium assumption in a streamline oriented curvilinear co-ordinate system is presented. The curvature correction is given from the rotation rate of the curvilinear co-ordinate system following the mean flow. Two methods for defining that rotation rate are proposed, one is derived from the strain-rate tensor, and the other is derived from the local mean acceleration vector. Both methods are fully three-dimensional and Galilean invariant and the correction vanishes in cases without curvature or rotation effects. The EARSM proposed by Wallin and Johansson (J. Fluid Mech. 403 (2000) 89) was extended with the proposed curvature corrections and recalibrated in such a way that the original model was retrieved in cases without curvature or rotation effects. Rotating homogeneous turbulent shear flows with vanishing mean vorticity should be close to neutral stability according to linear stability theory, also observed from large eddy simulations. This was used for the recalibration. The importance of the curvature correction and the proposed recalibration is shown for rotating homogeneous shear and rotating channel flows.
Published Version
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