The turbulent flow field of the natural wind is assumed to be composed of the mean flow and many ranks of eddies, which have the lengths A's and the velocities V's corresponding to their ranks. The movement of eddy which belongs to the n-rank is assumed to be influenced by some mutual actions between eddies. The effect of the mutual actions is assumed to be expressed by the surface friction which has the same form with the Stokes' friction law as follows: W=6πA (A/2)V, where A denotes the eddy viscosity coefficient and equals to ρVA. Under the assumptionn of the same rate of energy dissipation among all ranks of eddies, the negative five-thirds power law of the eddy-energy spectral function is obtained, and the result is compared with the observation which was carried out in the natural wind.
The theoretical studies of the disturbances in the westerlies have, so far, been based on the longitudinally uniform current taken as mean circulation. The problem of the disturbances in the jet stream (max. westerlies) which has eastward wind gradient is especially taken up in this paper, and the analytic solution of Laplaces' equation was given under the assumption that, as Platzman did, every motion has constant absolute vorticity and their perturbation is irrotational. As the first approximation of the solution, it was proved that the wave length of the perturbation is in agreement with the Rossby's result and the amplitude increases eastward, that is, in the direction of the decrease of zonal (sectional) index (the Namias' emperical law).
The present author pointed out that there is a marked descending motion in the rear of a typhoon at a distance of 100_??_200km from the centre of the typhoon. The type of the descending motion is quite different from the phenomena of the “eye” of storms. The existence of such descending motion in the field of tropical cyclones, even in the field of fully developed extra-tropical cyclones, would be quite interesting in the field of dynamic meteorology. This foehn effect (free foehn) may be explained as an isallobaric divergent motion due to the isallobaric high in the rear of typhoons.
The explanation of tables and figures. Tables 1 to 6 contain the necessary coefficients for the computation of insolation by the method of expansion for any long period and the results of computation by this method for summer half, winter half and total year. By such method as explained in Part I etc. we have obtained the daily amount as shown in tables 7 and 8, and the half and total yearly as shown in tables 9 and 10. There exists a satisfactory coincidence between both methods concerning the half and total year. Tables 7 and 8 are shown graphically in Figs. 1-6, in relation to the longitude of the sun, taking the earth's latitude as parameter. These are the annual variations of the amounts. Tables 9-10 are shown in Figs. 7-10 in relation to the latitude. Results concerning to planes are here omitted because they shall be given in the next paper on the insolation on the inclined plane.
Margules' formula for the slope of stationary discontinuous surface has two defects. One is the assumption inapplicable to the actual atmosphere. Inn the neighbourhood of discontinuous surface the acceleration of air is most pronounced and the vertical motion prevails. Because of this fact the discontinuous surface has an important meaning in meteorology, especially in weather analysis. Margules has however disregarded this fact. Then why is the fomula applicable in practice? The author investigated the reason. The other inconvenience in applying the formula is that, although the slope of the surface is known, yet the shape of its vertical section is not obvious. The author calculated first the formula which represents the shape of vertical section and then the angle of the shape. The result is that the shape of vertical section is approximately a parabola. The angle of slope thus derived agrees approximately with Margules'. § 1. Preliminary Remarks The author first examined the assumptions which Margules used to derive his formula. The author adopts only the following four assumptions: (a') The fluid is perfect (the effect of friction is later considered) (b') The motion is stationary (c') The motion is uniform in one direction. (d') The fluid is autobarotropy. It is shown that there is a possibility of obtaining intermediate integrals from the equations of motion. From the equation of continuity (4), v, w are represented as (5). Here Ψ is the stream function of momentum (v/s_??_w/s). § 2. Integrals for Stationary Motion Applying the above relations, the first intermediate integral (5) is derived, which means that the two quantity Ψ and u-2ω sin θ•y+2ω cosθ cosβ•z are both homotropy. From this formula we get (5') after neglecting the effect of Coriolis' force. From (5') or (5) we can deduce the following results. The stream line Ψ=constant, in the vertical section coincides with the isovel of the velocity component u, which cuts the section perpendicularly. In other words, the stream surface coincides with the iso-velocity surface of the velocity component which cuts the vertical section perpendicularly. That is, a stream uniform in one direction can not exist by itself in general, and accompanies a stream in the orthogonal section. Reversely a motion in the orthogonal section to the direction, in which the motion is considered to be uniform, accompanies also with it a motion in the latter direction. Therefore the actual current presents itself as one which runs spirally on a certain cylindrical surface. This result can be applied to the motion of air in a cyclone. If the cyclone is symmetrical about the central axis, the horizontally rotating current accompanies necessarily the convergent, divergent, ascending and descending currents (convective current). Reversely the convection accompanies necessarily the horizontally rotating air current. (The rigorous treatment on this subject will be described in future). By the same method as we obtained the equation (6), we can obtain the second, and further, the third intermediate integrals (7) and (8). These correspond respectively to the integral of vorticity and Bernouilli's integral of energy.