Postclassical Turbulence Mechanics

Abstract

<p align="justify"> <span style="font-family:Verdana;">This paper surveys the formalism and applications of the postclassical turbulence mechanics (PCTM) grounded on the characterization of turbulent flow field in infinitesimal surroundings of the flow field points besides the flow velocity at these points also by the curvature of the velocity fluctuation streamlines passing these points. The PCTM applies this step to found the turbulence split into the orientated and the non-orientated constituents. The split specifies the competence of the classical turbulence mechanics (CTM) to the description of the non-orientated turbulence constituent and delegates the description of the orientated turbulence constituent (in the spirit of the theory of micropolar fluids) to the equation of moment-of-momentum. The concurrent presence of the orientated (relatively large scale) and the non-orientated (relatively small scale) turbulence constituents enables to compile the CTM and the conception of L. F. Richardson and A. N. Kolmogorov about the cascading turbulence (RK conception) within a conjoint formalism. The compilation solves the classical conflict between the CTM and the RK conception, though evinces a conflict of another type characterized as paradigmatic.</span> </p

Physics of Solution of Primary Task of the Turbulence Problem

“…Besides returning the turbulence problem to the physical background and demonstrating the efficiency of the classical physics principles in advancing the TM, the formulation of the PCTM also includes several future tasks including the modification of the statistical fluid mechanics replacing the characterization of flow field in infinitesimal surroundings of the flow field points by the flow velocity v with the pairs ( , ) v R and advancing the methods of turbulence measurements so far adjusted for the needs of the CTM. The formulation of the PCTM also increases the number of applications of TM, outlined in several examples reported and/or referred to in (Heinloo, 2013b(Heinloo, , 2008b(Heinloo, , 2004aHeinloo & Toompuu, 2013;Heinloo, Toompuu, & Lilover, 2012). The examples can be arranged into three groups.…”

“…The basic step to solve the primary task of the turbulence problem in the sense specified above is the definition of the turbulence spin. This task is solved in the setup of postclassical turbulence mechanics (PCTM) (Heinloo, 2004a(Heinloo, , 2013a(Heinloo, , 2013b. The solution is preceded by an axiomatic step constituting the need to include the curvature of velocity fluctuation streamlines passing the flow field points to the characteristics of the flow field states in the infinitesimal surroundings of the flow-field points (as random events) and is realized through the definition of the turbulence spin, M , as…”

“…Section 3 enlightens the prerequisite of the definition of the turbulence spin -inclusion of curvature of velocity fluctuation streamlines passing the flow field points to the characteristics of states of the flow field in the infinitesimal surroundings of the flow-field points. The outcome of solution of the primary task in the form of the postclassical turbulence mechanics (PCTM) (Heinloo, 2004a(Heinloo, , 2013a(Heinloo, , 2013b is commented. Section 4 characterizes the situation in the TM called fourth by the formulation of the PCTM as critical in respect to the classical turbulence mechanics (CTM).…”