Chapter Title

A review of the statistical theory of turbulence.

Authors

H L. Dryden

Publication Date

1942

Keywords

model studies, models, statistics, turbulence, turbulent

Start Page

115

End Page

132

Book Title

Turbulence: Classical Papers on Statistical Theory.

Editors

Friedlander SK;Topper L;

Publication Place

New York

Publisher

Interscience Publishers, Inc.

Abstract

Describes 'current' state of model developed by Taylor (1935), which is applicable to continuous movements and satisfies equations of motion. Flow Components: U, V, W = Average velocities in each of 3 dimensions; u, v, w = Instantaneous fluctuations, such that each read = U + u, V + v, W + w ('Navier-Stokes Equation', as in Behlke (1994)). Continuity of Turbulent Motion: Justifies use of fluid velocities as vector averages, but concedes that molecules are in fact discontinuous. Reynolds Stresses: Sresses in addition to Navier-Stokes Equations due to viscosity: -du2, -dv2, -dw2 (=eddy normal stress components); and -duv2, -dvw2, -duw2 (=eddy shearing stress components) -- each stress component equals the rate of transfer of momentum across corresponding surface by the fluctuation. Scale of Turbulence: defines method of assigning scale where l1 is defined as length = (root mean square of V) times (integral from 0 to T of Rtdt ), which = (root mean square of V)(integral from 0 to infinity of Rtdt), where Rt equals the autocorrelation of velocity of a given molecule over time, which approaches 0 as T approaches infinity. V is the component of velocity transverse to mean flow and in the direction of concern. Another variable, L, is described as defining the mean size of eddies. Isotropic Turbulence: simplest type of turbulence, intensity components equal in all directions. -- there is a strong tendency toward isotropy in all turbulent motions. Note: if turbulence is isotropic, then u2 = v2 = w2 (read u as 'mean value of u').



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