Abstract

Variational principles of fluid turbulence offer an attractive alternative to numerical solution of the Navier-Stokes equation, especially for global climate studies. I discuss the principle (Max-D) that certain stationary turbulent flows maximize the rate of kinetic energy dissipation of the mean flow. Following its conjecture as an organizational principle for atmospheric circulation [1], Max-D has gained numerical support from global climate model simulations [2]. Max-D has also been derived for turbulent shear flow in a channel from considerations of dynamic stability, and yields realistic predictions for the mean velocity profile at all Reynolds numbers [3]. Further theoretical support for Max-D in channel flow has emerged from the statistical principle of maximum entropy [4]. Tying these threads together may lead to a clearer understanding of the theoretical basis and range of validity of Max-D for global climate studies. I outline possible approaches to doing this.

[1] Lorenz EN (1955) Generation of available potential energy and the intensity of the general circulation. Scientific Report No. 1, UCLA Large Scale Synoptic Processes Project.

[2] Pascale S, Gregory JM, Ambaum MHP , Tailleux R (2012) A parametric sensitivity study of entropy production and kinetic energy dissipation using the FAMOUS AOGCM . Clim. Dyn. 38, 1211-1227 and references therein.

[3] Malkus WVR (2003) Borders of disorders: in turbulent channel flow. J. Fluid Mech. 489, 185-198.

[4] Dewar RC, Maritan A (2013) A theoretical basis for maximum entropy production. In Beyond the Second Law: Entropy Production and Non-equilibrium Systems (eds. RC Dewar, CH Lineweaver, RK Niven, K Regenauer-Lieb), Springer, in press.