Abstract
The analytical framework based on the similarity hypotheses of Kolmogorov and Obukhov arguably provides an adequate description of homogeneous isotropic turbulence at very large Reynolds numbers. In the flows normally encountered in the laboratory, the Reynolds number is finite and other influences, for example those due to a mean shear or, more generally, inhomogeneities associated with the larger scales, are present. In this paper, we review and assess some of the current progress in using ‘exact’ two-point equations for analysing the manner in which small-scale turbulence is affected by different types of inhomogeneities that may be present. There is strong support for this approach from experimental and/or numerical data for decaying homogeneous isotropic turbulence and along the axis of a round jet where the Reynolds number remains constant. In each of these flows, the major source of inhomogeneity is the streamwise decay of energy. Overall implications are discussed in the context of results obtained in physical space, although the correspondence to the spectral domain is also commented on briefly.
Highlights
DEUTSCHE PHYSIKALISCHE GESELLSCHAFT where Cαn can be identified with the Kolmogorov ‘constants’
Local isotropy is satisfied by those terms which are present in a restricted scaling range (RSR) only, i.e. for the molecular diffusion and the advection terms
It is of interest to inquire into the similarity of all the scales on the axis of a round jet, since Rλ is expected to remain constant along the axis in the far field of a jet [53]
Summary
The major objective here is to gain some insight into the flow physics which results in an imbalance between the left and right sides of equation (6) and more especially equation (10), in nearly homogeneous flows. The jet axis is characterized mainly by a streamwise decay of energy, whereas several extra effects are present (shear, lateral diffusion, pressure) away from the axis. We will attempt to provide an overview of the large-scale effects in grid turbulence and the axis of a turbulent round jet. The inhomogeneities of these flows could be taken into account, local isotropy is still maintained for all the other (turbulent advection, molecular diffusion and pressure diffusion) terms. From a mathematical point of view, the extra inhomogeneous terms are introduced and manipulated within a quasi-isotropic context. The equations given can be regarded as ‘exact’
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