Some Notes on the Structure of Wind in the Lowest Layer of the Atmosphere

Abstract

Based on Kolomogoroff's similarity hypothesis of locally isotropic turbulence, the correlation coefficient R_t of the velocity fluctuations at time points t₀ and t+t₀ is written as follows: R_t=1-(t/T₀)^2/3 . (1) where T₀ denotes the passing duration of the largest turbulent element which passes through the measuring point. Assuming that the correlation coefficient (R_t)_w, which is calculated from the vertical velocity fluctuations w' measured in the air layer near the ground, is expressed by the formula (1), the dependence of T₀ on the height of observation z and on the mean velocity u is obtained experimentally. From photographic records of vertical velocity fluctuations w' measured in the adiabatic atmosphere over level snow surfaces, R_t is calculated and is found to be well expressed by (1) in the range of small t's. It is concluded from the experimental data that T₀ is proportional to z. _??_ Consequently, the spectrum of turbulent energy in the space of wave-number k is expressed by (k/k₀)^-5/3, where k₀ is inversely proportional to z.