Transport bounds for a truncated model of Rayleigh-Benard convection

PHYSICA D-NONLINEAR PHENOMENA

卷:308

Article

Souza, Andre N.¹  Doering, Charles R.^1,2,3 

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Michigan, Ctr Study Complex Syst, Ann Arbor, MI 48109 USA

[3] Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USA

关键词: Rayleigh-Benard convection;    Lorenz equations;    Heat transport;    Optimal control;   

DOI  :  10.1016/j.physd.2015.05.009

来源: Elsevier

【 摘 要 】

We investigate absolute limits on heat transport in a truncated model of Rayleigh-Benard 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free