Thermodynamics of fluid turbulence: A unified approach to the maximum transport properties

Abstract

Dissipative properties of various kinds of turbulent phenomena are investigated. Two expressions are derived for the rate of entropy increase due to thermal and viscous dissipation by turbulence, and for the rate of entropy increase in the surrounding system; both rates must be equal when the fluid system is in a steady state. Possibility is shown with these expressions that the steady-state properties of several different types of turbulent phenomena (Bénard-type thermal convection, turbulent shear flow, and the general circulation of the atmosphere and ocean) exhibit a unique state in which the rate of entropy increase in the surrounding system by the turbulent dissipation is at a maximum. The result suggests that the turbulent fluid system tends to be in a steady state with a distribution of eddies that produce the maximum rate of entropy increase in the nonequilibrium surroundings.