Linear dependencies in fourth-rank turbulence tensor models Original Research Article

In turbulence modeling, and perhaps elsewhere, one encounters the need to model a fourth-rank tensor Mijpq, which is symmetric in ij and pq, in terms of a second-rank symmetric tensor bij. It has commonly been assumed that there are fifteen linearly independent tensor forms in the most general such model. Here we show that there are only twelve, and give the three linear dependencies.