skip to content

Statistical stability arguments for maximum kinetic energy dissipation

Thursday 31st October 2013 - 17:00 to 17:35
INI Seminar Room 1
The hypothesis that stationary turbulent flows have maximal mean-flow kinetic energy dissipation (Max-D) is intriguing because mean-flow properties can be predicted without modelling the turbulent component of the flow. Our knowledge of Max-D is largely restricted to relatively simple laboratory flows. Measured Poiseuille flow profiles match Max-D predictions closely and, under these simplified conditions, Malkus's statistical stability argument provides some theoretical justification for Max-D [1]. However, it is not clear whether Max-D is applicable to more complicated fluid systems, like Earth's atmosphere [2]. Recent global climate model simulations have found that the calibrated values of important tunable parameters are indeed consistent with Max-D [3]. Furthermore, the maximum entropy framework [4], which naturally gives a Max-D principle in the case of simple laboratory flows, can be readily applied to more complicated systems. I will discuss attempts to gener alise the Malkus statistical stability argument and how this connects with maximum entropy arguments. In doing so I hope to compare the physical insights of statistical stability, which emphasises dynamical resilience to perturbations, with maximum entropy considerations, which ignore system dynamics.

[1] W. V. R. Malkus. Borders of disorder: In turbulent channel ow. Journal of Fluid Mechanics, 489:185{198, 2003. [2] Richard Goody. Maximum entropy production in climate theory. Journal of the atmospheric sciences, 64(7):2735-2739, 2007. [3] Salvatore Pascale, Jonathan M. Gregory, Maarten H.P. Ambaum, and Remi Tailleux. A parametric sensitivity study of entropy production and kinetic energy dissipation using the FAMOUS AOGCM. Climate Dynamics, 38(5-6):1211-1227, 2012. [4] Dewar R and Maritan A. A theoretical basis for maximum entropy production. 2013. In Beyond the Second Law: Entropy Production and Non-equilibrium Systems (eds. R Dewar, C Lineweaver, R Niven, K Regenauer-Lieb), Springer, In Press
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons