Abstract
It is generally accepted that the vorticity transport theory of turbulent motion initiated by G. I. Taylor takes some important place in the mechanism of momentum transfer in turbulent chaos. Its superior points have already been affirmed by various papers published by Taylor, but the mechanism is not yet affirmed satisfactorily enough to describe the details of turbulent motion as detected by L. Prandtl.
The application of Taylor's theory to the atmospheric field has been examined by the present writer with some success, though the principle of discussion adopted was not rigorous. Anyhow we see here that the vorticity transport theory is found to be reliable fairly well among the various theories hitherto postulated.
Prof. S. Fujiwhara has pointed out the existence of transverse resistance accompanying eddy motion long since the publication of his elaborate work on the vortical motion. His intention has partly been accomplished by S. Sakakibara and Y. Isimaru in their equations of transverse eddy viscosity.
In the present paper the writer shows that the term of transverse resistance is detectable from the vorticity transport theory under gradient wind condition. Denoting the mean motion by bar and the eddy motion by dash, the equations of motion of perfect fluid adopted by Taylor are, in steady state, where The deformation of vorticity of incompressible fluid is expressed by, in Lagrangian form. and the condition of conservation of vorticity is as follows: Thus Taylor arrived at the following equations: etc. Assuming the relations as realizable in the problem of gradient wind we have as the x-component of frictional resistance and as the y-component. Here If μ1=μ2, ν1=ν2and the coefficients are positive, the result becomes to coincide with Sakakibara-Isimaru's term.
Next the effect of compressibility has been considered. Discarding the terms of small order, the frictional term is approximately given by etc., where
