#### Chapter Title

A review of the statistical theory of turbulence.

#### 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').