Variational bounds on the energy dissipation rate in body-forced shear   flow
  A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations. 
Nikola P. Petrov, Lu Lu, Charles R. Doering