Towards lowering dissipation bounds for turbulent flows

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