Towards lowering dissipation bounds for turbulent flows

We examine the background flow variational principle for calculating bounds on the energy dissipation rate in turbulent shear flow, and suggest to select this principle's test functions such that they comply with the small-scale smoothness of real turbulent velocity fields. A self-consistent algorithm implementing this requirement then yields an upper bound on the dimensionless dissipation coefficient which shows a weak power-law decrease at high Reynolds numbers, instead of approaching a nonzero constant, as it did in previous estimates.