Skin friction of the wind on the Earth's surface

Abstract

The mechanism by means of which momentum is transmitted to a solid surface, in order that it may exert a drag on a fluid flowing past it, is at present understood only very imperfectly. It seems certain, however, that the law of dynamical similarity is applicable to skin friction; if therefore it were possible to measure the tangential force exerted by the wind as it blows over a large tract of land, it should be equal to the skin friction on a similar small surface when subjected to the action of the very high wind which would correspond with the same value of l V/ v . In reducing the tract of land to a similar small flat plate, the trees and houses would be reduced to a mere roughness on the plate. It is to be expected therefore that, if the skin friction on unit area of the earth's surface be expressed in the form F = kp Q 2 s , (1) Q s being the wind velocity near the surface and p the density of air, the constant k will be the same as the constant which would be found in the laboratory by experimenting with a small, slightly roughened plate, if a sufficiently high value of l V/ v , could be obtained. It should be noticed, however, that the velocity which should be compared with is the velocity close to the solid surface and not the general velocity of the air in the case of a flat plate, or the mean velocity over a cross section in the case of flow in a pipe.