  Structural subgrid stress models for large eddy simulation often allow for
backscatter of energy from unresolved to resolved turbulent scales, but
excessive model backscatter can eventually result in numerical instability. A
commonly employed strategy to overcome this issue is to set predicted subgrid
stresses to zero in regions of model backscatter. This clipping procedure
improves the stability of structural models, however, at the cost of reduced
correlation between the predicted subgrid stresses and the exact subgrid
stresses. In this article, we propose an alternative strategy that removes
model backscatter from model predictions through the solution of a constrained
minimization problem. This procedure, which we refer to as optimal clipping,
results in a parameter-free mixed model, and it yields predicted subgrid
stresses in higher correlation with the exact subgrid stresses as compared with
those attained with the traditional clipping procedure. We perform a series of
a priori and a posteriori tests to investigate the impact of applying the
traditional and optimal clipping procedures to Clark's gradient subgrid stress
model, and we observe that optimal clipping leads to a significant improvement
in model predictions as compared to the traditional clipping procedure.
