Improved variational principle for bounds on energy dissipation in   turbulent shear flow
  We extend the Doering-Constantin approach to upper bounds on energy dissipation in turbulent flows by introducing a balance parameter into the variational principle. This parameter governs the relative weight of different contributions to the dissipation rate. Its optimization leads to improved bounds without entailing additional technical difficulties. For plane Couette flow, the high-Re-bounds obtainable with one-dimensional background flows are methodically lowered by a factor of 27/32. 
Rolf Nicodemus, Siegfried Grossmann, and Martin Holthaus (Fachbereich   Physik der Philipps-Universitaet Marburg)