A. Schmidt, L. A. Bauer and others have pointed out that the small fraction of the earth's magnetic force is due to the electric current flowing in the magnetic field. From our observations of the magnetic force on the earth's surface, the vertical current is able to be calculated. In his treatments L. A. Bauer showed the existence of the vertical current of the order of 10-2amp/km2 over the whole earth. The direction of the current, however, changes itself at about latitudes 45°N and S. This fact necessarily leads us to the conclusion that the vertically upward currents at the polar caps and the vertically downward currents at the equatorial regions must close their circuits as was schematically indicated in the work of H. Hertz. Then the horizontal electric current should exist in the atmosphere and this current, too, will be calculated from the earth's magnetic force so far as the variation of the magnetic force with height is known to us. Unfortunately the magnetic observations in the free atmosphere were very scanty in number without giving us any expressions of the changes of magnetic forces with height. Recent investigations on the propagation of electric waves afford us the knowledge of the magnetic state at the ionosphere. From the experiments done by Appleton and Builder, we see that the magnetic force H in the atmosphere is expressed by to a first approximation, where H0 is the magnetic force on the earth's surface, h, the altitude in the atmosphere, small compared with the mean radius R of the earth. If this formula holds approximately good, the horizontal electric current is easily calculated by the next formulae. (density of eastwardly directed current) (density of southwardly directed current) If the magnetic forces and the length are given in C. G. S. units, the densities of current are expressed in amp/cm2-unit when multiplied by 10. In these expressions, _??_0 and _??_0 are the mean values of X, the north component of the magnetic force, and Y, the east component, at the earth's surface between two consecutive points, In the present paper the author calculated these mean values by the graphical method without serious error. Zo is the vertical component of the magnetic force. The meanings of other letters will be easily understood from Fig. 2 and 3 and the process of deduction of the above expressions was described in pages 5-7. It is worthy to note that the current is calculated from the magnetic forces on the earth's surface so far as h is small compared with R. This fact seems to us that the electric current thus calculated flows horizontally at every altitude on the earth, but this will be due to the above assumption of the variation of the magnetic force with height. This point will be discussed in the next paper. In this paper the present author calculated the horizontal current from the data of the magnetic forces given in a paper of A. Schmidt. The calculated values at various places over the globe were tabulated in Tables 1 and 2. Table 1 (p. 8) shows the eastwardly and southwardly directed mean currents, Whence we can conclude that the horizontal currents do not converge to nor diverge from certain points, showing the absences of the sink-and source-like points over the globe. Table 2. (p. 8) gives the values and direc_??_ions of currents at every points and a chart showing the distribution of the current was printed in page 9 (Fig. 4.) The distribution of current resembles, to a high degree, to the general circulation of the earth's atmosphere, but the magnitude of the electric current can not be explained from the ordinary ion current in the atmosphere. In the average state, the electric current flows westward at the equatorial region, rather a little north, while eastward at the higher latitudes. (Fig. 5 p. 10)
The famous studies of the motion of air and its vortex motion in the atmosphere(1) have been treated by the late Prof. Dr. D. Kitao about forty-five years ago. His treating was based in non viscous atmosphere which included the surf_??_ce frictional resistance terms by C. M. Guldberg and H. Mohn. Therofore, in this paper we retre_??_ted the same problems in the viscous atmosphere, starting from the following equation of motion with customary notations, In which, the axis of x to be taken southwards, y be eastwards in a horizontal surface and z to be drawn upwards in the direction opposite to that of the acceleration of gravity g only, and Ω be the potential of the extraneous forces, viz. Ω=gz, W is the vector of the angular velocity of earth's rotation, v is the Kinetic eddy viscosity and the symbol θ is the divergence of the vecter V, viz., We use to symbols £, η, ξ to denote the components of vorticity, ω is the angular velocity of the eartr's rotation, and φ be the latitude, then In these equations, the first and second terms on the right-hand sides express the component angular velocities of the mean rotation of an element of air and the third terms express the component angular velocity effected by the earth's rotation. In equation (1), we put where φ may be c_??_lled the ‘dynamen’ by Prof. D. Kitao, the surface of constant φ be the equal energy surface of air motion or this is so called ‘Isodynamical pressure surface’. From above equations we reduced to the convenient forms to calculate the relation of air motion or its vortex motion by using the auxiliary function. Firstly, we showed the balancing problem of the air motion in the viscous atmospherre. If we write the component of the frictional resistance Rx=-v∇2u, etc. in the stendy state. the equation (1) may be shown as follows; next, we assume to be the axis of n normal to the isodynamical pressure surface, α and β are the angle between wing direction and n axis and the frictional acting axis, respectively. Then we have, from (5) the angle (Vσ) be denoted between wind direction and the axis of the vorticity, and (δ) be the angle between the axis of n and the frictional resistance. Hence, from above equations (6), the wind velocity be shown as follows; At a great height we have this is the ‘dynamical pressure gradient wind’ parallel to the isodynamical pressure, which would prevail if there were no frictional resistance, viz. R=0. When the acceleration of velocities are existed in three dimensions, we put etc., therefore the total acceleration of velocity is Heuce, the equation of motion are The angles _??_, γ and ε are made the direction of acceleration of velocity with R, n, and V, respectively. Therefore, from equation (8), we have thence, after reduction, we have This formula (10) is just the same shape as equation (7) in the steady state, where to use β and δ in place of βε and δγ, respectively. In the case of the motion of air in two dimensions, we have in steady and in generaly Therefore, substituting from (11) in (7), we have If we put that the acceleration of veloeity may be linear change with time, viz. ∂2V/∂t2=0, hence, we have In the last section, we showed the atmospheric current due to the effect of the earth's rotation only, viz, In these, cases σ=2ω, sin (Vω)=sin (Vω), and the direction of axis of the deflecting air mass be determinded with the axis of earth's rotation.
Contents: § 1. introductory, & 2. the generation of vorticity and the transition from laminar to turbulent flow, §3. the freedom of eddying diffusion, § 4. the experimental fact supporting the existence of transverse resistance accompanying eddy motion, § 5. some criticisms on the theory of vorticitytransport in a turbulent field, § 6. the derivation of transverse force in a field of vorticity-transport, § 7. summary and concluding remarks. Abstract:- In the second paragraph is discussed the problem of the generation of vorticity and the transition from laminar to to bulent flow. In the well known theory of conservation of vorticity by Helmholtz four conditions are assum ed: 1. the fluid is free from viscosity. 2. the fluid is continuous in regard of velocity. 3. the fluid is under influence of force which has single valued potential. 4. the density of fluid is either uniform or a function of pressure only. In ordinary fluid such as air or water vortices are commonly generated even when the conditions 3 and 4 are fulfilled. Hence in such cases the violence of the condition 1 or 2 must be responsible for the production of vortices. On this point there are at present two dominant theories: One is the German school established by L. Prandtl and others in which the transition from laminar to turbulent flow or the generation of eddies is determined by the critical Reynolds number, the property of fluid being characterised by kinematic viscosity, but “es offen gelassen wird, ob sich die einzelnen Wirbel in der turbulenten Strömung entgegen der inneren Reibung durch Energieentnahme aus der Hauptströmung erhalten können, oder ob sie durch lokale äusseue Einflüsse, wie Wandrauhigkeit, immer erneut erregt werden (F. Noether)”. The other is the Japaese school developed j by S. Fujiwhara and his collaborators, in which is advocated velocity discontinuity as necessary condition. As already noticed by L. Prandtl and O. Tietjens it is necessary believed from theoretical stand-point of view to replace the “Differentialgleichungen” by “Differenzengleichungen” for the production of eddies and this coincides with the idea of discontinuity of the second kind termed by S. Fujiwhara. (Noether and Synge argue against this.) In the author's opinion the essential coincidence of the both theories is descriptively stated. In the third paragraph the freedom of eddy motion is discussed. The measurement by Taylor and Fage shows the equipartition of eddying energy in a field free from boundary effect (Screse's observation contradicts to this result). The above result is most important, because the transverse resistance derived by Sakakibara in mathematical form opposes against the theory of equipartition of eddying stress. We find here that the transverse resistance is formed by the motion of bound eddies affected by the special configuration of boundary. In the fourth paragraph are enumerated some observational facts supporting the existence of transverse resistance accompanying eddy motion. In the polar front theory for cyclogenesis the two distinct air masses are in juxtaposition and the two counter currents characterising them are balanced by geostrophic force. As noticed by T. Bergeron and Swoboda the presence of bulge on a polar front is not sufficient in itself to bring about cyclogenesis, but the mechanism of cyclonic convergency is also difficult to explain by the theory of air mass.
In this paper the present author investigated some relations between the movement of heat thunderstorms which occured in Kwantô district and its neighhourhoods and that of the upper air current by means of the pilot-balloon observations during 3 years from 1930 to 1933. It is concluded that: a) The direction of the movement of heat thunderstorms coincides with that of upper air current, but it has no relations to surface wind direction. b) The velocity of the movement of heat thunderstorm is nearly equal to that of the tipper wind. c) It is explained that the heat thunderstom whose velocity exceeds 43 km/hour is rarely experienced. d) The heat thunderstorm is easy to occur when the mean velocity of the upper current is less than 10 m/s, while it scarcely occurs when the mean velocity of the upper current exceeds 12 m/s. The present study on the relation between the heat thunderstorm and the upper air current may throw a light upon the warning of the thunderstorm, which is now being performed in the selected regions in Japan.