Formulation of turbulence mechanics

Abstract

This paper presents a setup of turbulence mechanics for averaged description of turbulence, founded on laws of momentum, moment of momentum, and energy, complemented by common rheological principles for formulating constitutive relations between generalized forces and generalized velocities of the description. A kinematical-geometrical principle is adopted to determine internal rotating degrees of freedom of turbulent media generated by the eddy structure of turbulent flow fields. The connection between the formulated mechanics and some models (as K-epsilon model), widely used in practical engineering flow calculations, is established. As an example, the formulated mechanics is applied to describe some classical flow patterns.

Modelling Turbulence Effect in Formation of Zonal Winds

“…Neglecting, similar to the model discussed in [11], the effects of diffusion of the moment of momentum M , for the body force acting on the medium specified as the gravitational force, this equation in a non-rotating frame reads as [5][6][7] …”

“…The RAT theory [5][6][7][8][9] realizes a generalized setup of turbulence average description proceeding from distinguishing of the velocity fluctuations at each flow field point (in addition to their magnitude and orientation) by the curvature of the velocity fluctuation streamlines passing the point. The generalization is formalized by inclusion of the curvature radius of the velocity fluctuation streamlines R into the set of arguments of the probability distribution, specifying the applied averaging.…”

“…In particular, CTM does not account for effects caused by the preferred orientation of eddy rotation, which remarkably constricts its applicability. The theory in [5][6][7][8][9] (concisely outlined in Section 2 as the rotationally anisotropic turbulence (RAT) theory) removes the constriction. The RAT theory treats the turbulence according to the Richardson-Kolmogorov turbulence conception [21,22] as a stochastic form of fluids motion constituted by a hierarchy of eddies of different scales, whereas the eddies of the largest scales, immediately interacting with the average flow, have a preferred orientation of rotation.…”

Modeling a turbulence effect in formation of the Antarctic Circumpolar Current

“…The RAT theory (Heinloo, 2004) modifies the conventional turbulence mechanics (CTM) by accounting for the preferred orientation of eddy rotation. The modification is formalized by including the curvature radius R of the streamline of the turbulent flow velocity v and the fluctuating constituent v , into the arguments of the probability distribution which specifies the applied statistical averaging.…”

“…The discussion was based on the theory of rotationally anisotropic turbulence (RAT theory) (Heinloo, 2004), accounting for the preferred orientation of eddy rotation. Although the model that was suggested in Heinloo and Toompuu (2004) resulted in a turbulence-generated eastward zonal flow associated with density fronts, it disregarded the geostrophic constituent of the flow velocity.…”