LXXXI. The eddy viscosity in turbulent shear flow

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Abstract
The comparative slowness of those processes in the turbulent wake which determine the turbulent energy balance makes it necessary to consider the whole wake flow in attempts to derive local values of such quantities as turbulent intensity and eddy viscosity. If the wake is in a state of moving equilibrium, i.e. the development involves processes controlling the intensity and eddy viscosity to values appropriate to the particular stage, of development, then the controlling mechanism must be of large scale both in space and time. It is suggested that the large slow eddies responsible for the phenomenon of intermittently turbulent flow form this mechanism, and a plausible control sequence is outlined in which the intensity of the large eddies controls the level of eddy viscosity. The detailed structure of these large eddies has been investigated by measuring the spectrum functions of the velocity fluctuation components in the wake of a circular cylinder. The group of large eddies is distinct, and it is possible to deduce that the large eddies are randomly placed in the mean stream direction, extend over most of one half of the wake, and have their vorticity roughly in the direction of maximum positive mean rate-of- strain. By a rough calculation it is shown that this type are near the state of energy equilibrium necessary for the operation of the suggested control process. Finally, the generation of Reynolds shear stresses by distortion of quasi-stationary turbulent fields is discussed, and possible reasons for the applicability of the eddy viscosity hypothesis are suggested.

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