Similarity and weak closing relations for symmetric free turbulence

Abstract

In [1, 2], similarity behavior of free turbulent flows at large Reynolds numbers was analyzed. Here, the term similarity was applied to distributions of averaged quantities that depend on the coordinate in the direction of the flow through two scaling functions of length1 (x) and velocity U(x). In the study [3] of flow on a self-propelled body (momentumless wake), Naudascher used a similarity concept of more general type. In the present work, which takes the point of view of similarity with one scaling function of length and different amplitude functions for different quantities, flows are analyzed that have arbitrary (including zero) deficit of the total momentum with respect to the momentum of the external flow. The similarity distributions satisfy the equations for the mean velocity and the single-point moments of second order only under the condition that certain connections (“weak closing relations”) hold between the amplitude functions. The relations are different depending on the dominant physical processes.