Turbulent Motion in the Atmosphere (first paper)

Abstract

Since the idea of eddy motion has been introduced in the domain of meteorology by G. I. Taylor and W. Schmidt, the studies of this problem are too manifold to enumerate and their transition is it that, as N. Shaw says, “In the past century we have noted contributions from the united states, Great Britain, France, Germany, Austria and the Scandinavian countries. In the latter part of the period Japan has taken a full share in the task of expressing the behavour of the atmosphere according to the laws of mathematical physics.”
Yet there remains an important discussion upon the mechanism of eddy motion undecidedly, namely, Taylor assumed the conservation of the vorticity of fluid and Prandtl the conservation of the momentum in turbulent motion. Their difference in the equation of motion consists in that the former adopts the form η ∂²_u/∂_z² and the latter ∂/∂_z η ∂_u/∂_z, whether η is variable or not, where η denotes the coefficient of eddy viscosity, u the mean horizontal velocity and z the co-ordinate directed vertically upwards. They coincide with each other when η is independent of z, but in general variation of η with z can never be made light of. After the authority of G. I. Taylor we discussed the question of eddies both theoretically and statistically, comparing with the S. Takaya's solution upon the problem of the same kind and proved out to some extent that we should adopt the form as the term of eddy turbulence so far as it concerns the transfer of momentum, we believe.