In this paper, the dispersion of atmospheric disturbances has been studied analytically. Particularly, the formation of a new trough over North America following an intense cyclogenesis in the Gulf of Alaska and the blocking action of atmospheric disturbances have been investigated, the former as a boundary value problem and the latter as an initial value problem. In the former problem. the method of Sommerfeld and Brillouin which was used in their study of the propagation of signals in a dispersive medium has been utilised. In the latter problem, using Airy's integral, we have obtained approximate solutions, some of which agree well with those obtained numerically by T. C. Yeh.
Recently Deacon1) has published a new formula a generalized exponential formula, so to speak, representing vertical distribution of wind velocity near the earth's surface deduced from many observational results (1) where (2) u denotes the wind velocity at height z, z0 the roughness height, β a parameter depending on the stability of the air layer, v* the fricti onal velocity, and k=0.4. The author congratulates him in that he has deduced a so simple formula which represents so many results in stable as well as in unstable conditions. But in two respects the author does not agree with him, i.e., (i) in respect to the constancy of z0, and (ii) in respect to the form of α. Deacon suggests from the observational results that the effect of stability on wind velocity becomes smaller as the earth's surface is approached, and hence he concludes that we should warrant to use a constant roughness parameter. From recent observational results such as Deacon's(l) or Pasquill's, (2) however, z0 seems to vary according to stability, i.e., decreases as the air layer becomes stable, which is contrary to the case of a simple logarithmic formula. For if the simple logarithmic formula is used and z0 is evaluated from observational results, z0 will be found to increase as the air layer becomes stable as described by Sutton(3) and the author.(4) But the author now recognizes both Deacon's formula and the recent experimental results. So he must seek for the reason that z0 decreases as the air layer becomes stable. But at the present stage of our knowledge he can not give a convincing reason, and gives only a hypothesis-that in a stable flow the roughness elements, such as leaves or twigs of vegetation, exert only a small effect on the air flow and consequently make the effective height of the roughness elements smaller. With regard to Deacon's suggestion that the effect of stability on wind velocity becomes smaller as the earth's surface is approached and hence z0 must be constant, the author wants to show that (4) =0.4). In this connection it may be remarked that Pasquill, trying to verify the equality of K and Kv (coefficient of eddy diffusivity for water vapour) experimentally, used (which is easily deduced from (1), (2) and (10)) and calculated this value from his wind observations and compared it with experimentally obtained Kv/z2∂u/∂z. He could conclude that K=Kv in the unstable as well as in the adiabatic cases, but could not conclude that K=Kv in the stable case as the values of K/z2∂u/∂z became too small. If, on the contrary, (1) and the corrected formulae (8) and (11) are used, we can obtain (12) Assuming the value of v*/U=1/14.4, which is obtained in the adiabatic case, is constant also for the non-adiabatic case, we can evaluate of K/z2∂u/∂z as shown in the table. It is seen that the values are in good agreement for all cases, though they are somewhat smaller especially in the unstable case. But it seems to the author that the experimental verification of the equality of K and Kv is given for all conditions of stability of the atmosphere. Adopted height is 75 cm.
The author discusses on some atmospheric phenomena of turbulent diffusion utilizing the following formula for the Lagrangian correlation coefficient R(ξ)=1-(ξ/τ0), obtained by the same author in a preceding paper. For the horizontal diffusion, τ0 usually means the lifetime of the effective largest turbulon which is proportional to the time duration T of observation, and τ0 becomes larger the longer the phenomenon persists. Thus the horizontal diffusion usually belongs to the I-class diffusion. Accordingly, the diffusing angle increases in proportion to T1/2 and the linear zone of diffusion continues farther. In this case, we again get the four-thirds power law for the diffusion coefficient. For the vertical diffusion, since the life-time of the vertical largest turbulon is elated with the height itself and is comparatively short, the II-class zone of turbulent diffusion is attained after a comparatively short time interval. The separating point between the two zones of diffusion is related to the length of the largest turbulon, and measuring this point we can estimate the length of the vertical largest turbulon (the mixing length) directly