  We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in plane Couette
flow, bridging the entire range from low to asymptotically high Reynolds
numbers. Our variational bound exhibits structure, namely a pronounced minimum
at intermediate Reynolds numbers, and recovers the Busse bound in the
asymptotic regime. The most notable feature is a bifurcation of the minimizing
wavenumbers, giving rise to simple scaling of the optimized variational
parameters, and of the upper bound, with the Reynolds number.
