Exact Statistical Theory Of Isotropic Turbulence
Author(s)
Z. Ran
Abstract
The starting point for this paper lies in the results obtained by Sedov (1944) for
isotropic turbulence with the self-preserving hypothesis. A careful consideration
of the mathematical structure of the Karman-Howarth equation leads to an exact
analysis of all possible cases and to all admissible solutions of the problem. This
kind of appropriate manipulation escaped the attention of a number of scientists
who developed the theory of turbulence and processed the experimental data for
a long time. This paper revisits this interesting problem from a new point of
view. Firstly, a new complete set of solutions are obtained, and Sedov’s solution
is one special case of this set of solutions. Based on these exact solutions, some
physically significant consequences of recent advances in the theory of selfpreserved
homogenous statistical solution of the Navier-Stokes equations are
presented. New results could be obtained for the analysis on turbulence features,
such as the scaling behaviour, the energy spectra, and also the large scale
dynamics.
Keywords: isotropic turbulence, Karman-Howarth equation, exact solution.
1 Introduction
Homogeneous isotropic turbulence is a kind of idealization for real turbulent
motion, under the assumption that the motion is governed by a statistical law
invariant for arbitrary translation (homogeneity), rotation or reflection (isotropy)
of the coordinate system. This idealization was first introduced by Taylor [29]
and used to reduce the formidable complexity of statistical expression of
turbulence and thus made the subject feasible for theoretical treatment. Up to
now, a large amount of theoretical work has been devoted to this rather restricted
kind of turbulence. However, turbulence observed either in nature or in
laboratory has much more complicated structure. Although remarkable progress
Keywords
isotropic turbulence, Karman-Howarth equation, exact solution.
Related Book
Other papers in this volume
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