Variational bound on energy dissipation in plane Couette flow

Details Variational bound on energy dissipation in plane Couette flow Variational bound on energy dissipation in plane Couette flow

1998-04-24

arxiv.org/abs/cond-mat/9804274v1

Phys. Rev. E 56, 6774 (1997)

Physics

Condensed Matter

Soft Condensed Matter

22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from holthaus@stat.physik.uni-marburg.de

Scientific paper

10.1103/PhysRevE.56.6774

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.

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