Kinetic energy dissipation and the stability of stationary turbulent flows
Seminar Room 1, Newton Institute
AbstractVariational 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 , Max-D has gained numerical support from global climate model simulations . 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 . Further theoretical support for Max-D in channel flow has emerged from the statistical principle of maximum entropy . 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.  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.  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.  Malkus WVR (2003) Borders of disorders: in turbulent channel flow. J. Fluid Mech. 489, 185-198.  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.
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