Author:
NICODEMUS ROLF,GROSSMANN S.,HOLTHAUS M.
Abstract
We present a numerical strategy that allows us to explore the full
scope of the
Doering–Constantin variational principle for computing rigorous upper
bounds on
energy dissipation in turbulent shear flow. The key is the reformulation
of this
principle's spectral constraint as a boundary value problem that can
be solved
efficiently for all Reynolds numbers of practical interest. We state results
obtained
for the plane Couette flow, and investigate in detail a simplified model
problem that
can serve as a definite guide for the application of the variational principle
to other
flows. The most notable findings are a bifurcation of the minimizing wavenumber
and a pronounced minimum of the bound at intermediate Reynolds numbers,
and a
distinct asymptotic scaling of the optimized variational parameters.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
35 articles.
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