Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895839 | Physica D: Nonlinear Phenomena | 2015 | 8 Pages |
Abstract
We investigate absolute limits on heat transport in a truncated model of Rayleigh-Bénard convection. Two complementary mathematical approaches-a background method analysis and an optimal control formulation-are used to derive upper bounds in a distinguished eight-ODE model proposed by Gluhovsky, Tong, and Agee. In the optimal control approach the flow no longer obeys an equation of motion, but is instead a control variable. Both methods produce the same estimate, but in contrast to the analogous result for the seminal three-ODE Lorenz system, the best upper bound apparently does not always correspond to an exact solution of the equations of motion.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Andre N. Souza, Charles R. Doering,