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1 - Small-Scale Statistics and Structure of Turbulence – in the Light of High Resolution Direct Numerical Simulation

Published online by Cambridge University Press:  05 February 2013

By
Yukio Kaneda  and
Koji Morishita
Edited by
Peter A. Davidson ,
Yukio Kaneda  and
Katepalli R. Sreenivasan
Yukio Kaneda
Affiliation:
Center for General Education Aichi Institute of Technology
Koji Morishita
Affiliation:
Kobe University
Peter A. Davidson
Affiliation:
University of Cambridge
Yukio Kaneda
Affiliation:
Aichi Institute of Technology, Japan
Katepalli R. Sreenivasan
Affiliation:
New York University
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Summary

Introduction

Fully developed turbulence is a phenomenon involving huge numbers of degrees of dynamical freedom. The motions of a turbulent fluid are sensitive to small differences in flow conditions, so though the latter are seemingly identical they may give rise to large differences in the motions.1 It is difficult to predict them in full detail.

This difficulty is similar, in a sense, to the one we face in treating systems consisting of an Avogadro number of molecules, in which it is impossible to predict the motions of them all. It is known, however, that certain relations, such as the ideal gas laws, between a few number of variables such as pressure, volume, and temperature are insensitive to differences in the motions, shapes, collision processes, etc. of the molecules.

Given this, it is natural to ask whether there is any such relation in turbulence. In this regard, we recall that fluid motion is determined by flow conditions, such as boundary conditions and forcing. It is unlikely that the motion would be insensitive to the difference in these conditions, especially at large scales. It is also tempting, however, to assume that, in the statistics at sufficiently small scales in fully developed turbulence at sufficiently high Reynolds number, and away from the flow boundaries, there exist certain kinds of relation which are universal in the sense that they are insensitive to the detail of large-scale flow conditions. In fact, this idea underlies Kolmogorov's theory (Kolmogorov, 1941a, hereafter referred as K41), and has been at the heart of many modern studies of turbulence. Hereafter, universality in this sense is referred to as universality in the sense of K41

Type
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Ten Chapters in Turbulence , pp. 1 - 42
Publisher: Cambridge University Press
Print publication year: 2012

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