RIGOROUS BOUND ON THE PLANE-SHEAR-FLOW DISSIPATION RATE

The Doering-Constantin approach [Phys. Rev. Lett. 69, 1648 (1992)] to derive an upper bound on the dissipation rate in terms of a properly chosen stationary flow profile can be (slightly) improved by casting it in the form of a variational principle for the profile. Only Schwarz's inequality is needed to prove this. Its solution can be evaluated analytically. The mean dissipation bound is ≤U3L-1/9 2 provided the Reynolds number Re=UL/ν exceeds 12 2, and the mean transverse momentum flux is bounded by J31≤(νL-1)2Re2/9 2. © 1995 The American Physical Society.