VARIATIONAL BOUND ON ENERGY-DISSIPATION IN TURBULENT SHEAR-FLOW

We present numerical solutions to the extended Doering-Constantin vari ational principle for upper bounds on the energy dissipation rate in p lane Couette flow, bridging the entire range from low to asymptoticall y high Reynolds numbers. Our variational bound exhibits structure, nam ely a pronounced minimum at intermediate Reynolds numbers, and recover s the Busse bound in the asymptotic regime. The most notable feature i s a bifurcation of the minimizing wave numbers, giving rise to simple scaling of the optimized variational parameters, and of the upper boun d, with the Reynolds number.