RÉSUMÉ

In complex turbulent flows, it is argued that the standard pressure-strain correlation model must be augmented by additional tensors to accurately account for complicating influences (such as system rotation, streamline curvature, buoyancy, etc.). This leads to the question, how many tensors do we need to adequately represent the pressure strain correlation. Representation theory indicates that a complete function-space representation of pressure-strain correlation in terms of Reynolds stress anisotropy, mean strain rate and mean rotation rate involves tens of basis tensors. On the other hand, purely from dimensional arguments it can be shown that at a given point in space, the pressure-strain correlation can be expressed completely in terms of only three basis tensors in two-dimensional mean flow and only five in three-dimensional flows. So is the number of basis tensors required thirty or is it five? In this paper, we will examine and explain the difference between the two numbers and how that impacts on modeling pressure-strain correlation or any other traceless symmetric second-order tensor in turbulence. Specifically we will compare merits of short and long tensor representations. We also derive mathematically equivalent shorter tensor representations of popular longer versions of pressure-strain correlation models.