Note on the distribution of turbulent velocities in a fluid near a solid wall

In their interesting paper “An Examination of Turbulent Flow with an Ultramicroscope,” Messrs. Fage and Townend have examined experimentally the manner in which the components of turbulent velocity die away to zero at the surface of a smooth pipe. In their experiments U, the mean velocity along the pipe at any fixed point, increased from zero at the walls to a maximum value Uc in the middle of the pipe. If axesxyz are taken,x being along the direction of mean flow,y perpendicular to the surface of the pipe, andz the transverse direction parallel to the surface, the maximum valuesu 1 ,v 1 ,w 1 , ofu, v, w , the components of turbulent velocity were measured. It was found (loc. cit ., fig. 7) that thoughu 1 ,v 1 ,w 1 become zero at the surface, yetu 1 /U,w 1 /U do not do so. In factu 1 /U tends to become constant as the surface is approached,w 1 /U increases to a maximum at the surface itself, whilev 1 /U decreases to zero. The purpose of the present work is to examine the significance of these observations.