On Algebraic Second Moment Models

Abstract

Equilibrium and bifurcation analysis is used to explore algebraic second moment models. It is shown that the three-dimensional, explicit algebraic stress solution for the anisotropy tensor precludes rotational stabilization unless two invariants of the mean velocity gradient vanish. If these vanish the irrotational part of the flow must be a plane strain: essentially the model can only bifurcate and stabilize in two-dimensional mean flow. However, it is also shown that those same two invariants must vanish if the mean flow is steady. The full equilibrium analysis described herein provides a consistent picture of a model with equilibria that respond appropriately to rotation.