THE BACKGROUND FLOW METHOD - PART 1 - CONSTRUCTIVE APPROACH TO BOUNDSON ENERGY-DISSIPATION

We present a numerical strategy that allows us to explore the full sco pe of the Doering-Constantin variational principle for computing rigor ous upper bounds on energy dissipation in turbulent shear flow. The ke y is the reformulation of this principle's spectral constraint as a bo undary value problem that can be solved efficiently for all Reynolds n umbers of practical interest. We state results obtained for the plane Couette how and investigate in detail a simplified model problem that can serve as a definite guide for the application of the variational p rinciple to other flows. The most notable findings are a bifurcation o f the minimizing wavenumber and a pronounced minimum of the bound at i ntermediate Reynolds numbers, and a distinct asymptotic scaling of the optimized variational parameters.