The following notation is used throughout. The co-ordinate axes are a right-handed rectangular system x, y, h, in which 0h is directed vertically upwards, and 0x lies in any azimuth which happens to be convenient. Elements of distance to east and to north are denoted by de, dn, so that they are special cases of, dx, dy. The atmospheric density is ρ, the pressure is p, acceleration of gravity is g, latitude ϕ is reckoned negative in the southern hemisphere, and ω is the angular velocity of the earth. Velocities are denoted by v with a suffix to indicate the direction towards which they blow. Momenta per unit volume are denoted by mx, mY, mH. The eddy-diffusivity is denoted by a capital K as in G. I. Taylor’s recent papers. Another, and in the author’s opinion a better, measure of turbulence is ξ discussed in a previous paper. The relation K to ξ is given by ∂/∂p(ξ ∂χ/∂p) ═ ∂χ/∂t ═ ∂2x/∂h2........(1) where χ is either potential temperature, or else mass of water or smoke per mass of atmosphere. If ρ and ξ were independent of height, then from (l) we should have ξ ═ g2 ρ 3K.............(2) It is suggested that ξ might be named “the turbulivity.” Its dimensions are: (mass)2 x (length)-2 x (time)-5.
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Lewis Fry Richardson (1921) studied this question.