Anisotropic Redistribution of Turbulent Kinetic Energy in the Troposphere

A coupling between the velocity field and the Coriolis field in the troposphere can redistribute kinetic energy at very small scales even if the mean turbulent field is spatially homogeneous. The purpose of this presentation is to define a model for the Reynolds stress that provides a closure for the Reynolds Averaged Navier-Stokes equation for all inertial and non-inertial temporal frames-of-reference. Mixing and production of the turbulent kinetic energy and the turbulent dissipation depend on the Reynolds stress and the Cauchy stress. It is noteworthy that the Coriolis Theorem predicts that the strain rate is frame insensitive; and, that the Reynolds stress is frame sensitive. Consequently, the Cauchy stress and the Reynolds stress are not similar. This presentation will illustrate that the URAPS-closure for the Reynolds stress (see Koppula et al.,2009,Chem. Eng. Sci. 64,4611-4624; 2011,Ind.Eng.Chem.Res.,50(15),8905-8916; 2013,Physica Scripta,T155) predicts that the turbulent dispersion and the turbulent dissipation of kinetic energy are positive; and, that the "production" of kinetic energy could be either positive or negative. For homogeneous decay, anisotropic mixing of kinetic energy could produce hue differences in the sky. This phenomena may explain how foraging birds are able to return to their natal nest with fidelity.