The Fundamentals of the Statistical Theory of Turbulence

10.2514/8.350 ◽  
1937 ◽  
Vol 4 (4) ◽  
pp. 131-138 ◽  
Author(s):  
TH. VON KARMAN
Keyword(s):  
Statistical Theory ◽  
Statistical Theory Of Turbulence

scholarly journals Statistical theory of turbulence IV-Diffusion in a turbulent air stream

1935 ◽  
Vol 151 (873) ◽  
pp. 465-478 ◽  
Author(s):  
Geoffrey Ingram Taylor
Keyword(s):  
Thermal Conductivity ◽  
Statistical Theory ◽  
Line Source ◽  
Transverse Component ◽  
Lagrangian System ◽  
Principal Element ◽  
Air Stream ◽  
Heated Wire ◽  
The Mean ◽  
Statistical Theory Of Turbulence

It was pointed out in Part I that experiments on the spread of heat from a line source ( e.g ., an electrically heated wire) in a turbulent air stream may be expected to give two elements of the statistical specification of turbulence. If the spread is measured near the source the value of the mean transverse component of velocity √¯ v 2 or v ' in the notation of Part I, can be found. If the spread is examined further down-stream it should be possible to analyse the results to find the correlation function R η , which is the principal element of the representation of turbulence in the Lagrangian system. Spread of heat nearer line source Recently the spread of heat from a heated wire in a wind tunnel has been measured at points near to the source by Schubauer. The stream was made turbulent by means of grids of round bars arranged in square pattern. Their diameters were 1 /5 of the mesh length and M varied from 5 inches to 1/2 inch. The width of the heat wake was found by measuring the angle subtended at the source by the two positions where the temperature rise was half that in the centre of the wake. This angle, denoted by α, depends partly on the amount of turbulence and to a less extent on the spread of heat due to the thermal conductivity of the air. By assuming that the effect of turbulence is to communicate to the air an eddy conductivity β, which is additive to, and obeys the same law as, true thermal conductivity, a virtual angle α turb can be deduced by the relation α 2 turb = α 2 — α 2 0 ,

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