THE BACKGROUND HOW METHOD - PART 2 - ASYMPTOTIC THEORY OF DISSIPATIONBOUNDS

We study analytically the asymptotics of the upper bound on energy dis sipation for the two-dimensional plane Couette how considered numerica lly in Part I of this work, in order to identify the mechanisms underl ying the variational approach. With the help of shape functions that s pecify the variational profiles either in the interior or in the bound ary layers, it becomes possible to quantitatively explain all numerica lly observed features, from the occurrence of two branches of minimizi ng wavenumbers to the asymptotic parameter scaling with the Reynolds n umber. In addition, we derive a new variational principle for the asym ptotic bound on the dissipation rate. The analysis of this principle r eveals that the best possible bound can only be attained if the variat ional profiles allow the shape of the boundary layers to change with i ncreasing Reynolds number.