On Euclidean invariance of algebraic Reynolds stress models in turbulence

Abstract

This article shows how Euclidean invariance can be preserved in the so-called algebraic Reynolds stress model (ARSM) approximation. This approximation is used to reduce the transport equation for the Reynolds stresses to an explicit algebraic relation. A number of known models, which make use of this approximation, are not form-invariant under transformations to rotating coordinate systems. A simple extension is presented to show how this artifact can be removed.