Mechanism of the production of small eddies from large ones

Abstract

The connexion between the statistical representation of turbulence and dissipation of energy has been discussed in relation to the decay of the isotropic turbulence which is produced in a wind tunnel by means of regular grids. It was shown that a length λ can be defined which may be taken as a measure of the scale of the small eddies which are responsible for dissipation. This λ can be found by measuring the correlation R y between the indications of two hot wire anemometers set at a distance y apart on a line perpendicular to the axis of the tunnel. Then 1/ λ 2 = Lt y→0 1 - R y / y 2 , and the mean rate of dissipation of energy per unit volume is W ¯ = 15 μ u 2 ¯ / λ 2 , (1) where u 2 ¯ is the mean of the square of one component of velocity. When turbulence is generated in a wind stream by a grid of regularly spaced bars it may be expected to possess a definite scale proportional to the linear dimensions of the grid. In any complete statistical description of turbulence this scale must be implicitly or explicitly involved. One way in which the scale can be defined is to measure the distance y apart by which the two hot wires must be separated before the correlation between the indications disappears. Another way is to define the scale as l 2 = ∫ 0 y R y d y . (2)