The transformation of the equations of motion of a viscous fluid to orthogonal curvilinear coordinates has been discussed by G. B. JEFFERY, and that of the equations of motion in dynamical meteorology to orthogonal curvilinear coordinates by the present authoi, out the analogous equations for the vorticity do not appear to have attracted the same attention. The first section of this paper deals with the transformation of the vorticity equations to the orthogonal curvilinear coordinates. The second section is devoted to applications to cylindrical and spherical polar coordinates.
In view of the suggested importance of lateral mixing, C=G. ROSSBY has given particular attention to the dynamics of the jet stream and its applications in meteorology and oceanography. But the conception of the absolute vorticity is often confused by several authors. The present author intends to give particular attention to the horizontal component of the total vorticity, as well as the so-called “absolute vorticity” which normally means the component about the vertical of the total vorticity.
The pressure, temperature, and density fields are theoretically derived from such a wind field that may be observed in the jet stream, and the outstanding features of the jet stream are theoretically explained. Especially theoretical relation between the jet stream and tropopause, which agrees with the observational results, is found.
Considering the variation with longitude of the basic current of westerlies in the upper troposphere, the problem of baroclinic disturbance is discussed on assumptions of non-divergent and adiabatic motion. It is shown from this investigation that a speed of trough is almost equal to the Rossby's result, and when the decreasing rate of the basic current with longitude exceeds a certain critical value, the disturbance becomes unstable.
Taking into account the adiabatic p ressure change due to the density change, the tendency equation is rewritten into a form where temperature advection is easily seen. As the temperature field is determined by the pressure and temperature field of two given levels, the surface pressure change and therefore moving velocity of pressure system may be calculated from this tendency equation.
Causes of descending current in valley are sought based on the theory that with the fall of separation point the current of foehn descends into the valley. II. WILD'S hypothesis is confirmed by ascending current in the lower boundary of turbulent mixing region of jet stream, by the quotation of W. TOLLMIEN's theory of stationary semi-infinite jet stream. It is shown that the effect of one of H. v. FICKER's theory and H. WILD's hypothesis must predominate on account of topographical influences.
From the physical point of view, it is desirable to deal the advection problem With the conservative property _??_ and differential method. As a result a formulae convenient in estimating the horizontal divergence is obtained. Introduction
The mechanism of the dissolution of the atmospheric chloride particles into rain drops by their mutual collision has been studied. The results obtained are as follows. 1. Relations among the chloride content per drop, the radius and the number of falling drops have been obtained, assuming that there is no supply of the chloride particles by an exchange or a flow of the air mass, and that the number of falling drops through the unit area per sec. and the radius of rain drops do not vary much. 2. A formula expressing the time variation in the amount of the chloride precipitation in a rain has been deduced. 3. The relation of the chlorinity, C, to the rainfall amount,P, can be expressed as follows: C·P=D(1-e-P⋅3σ/4γ) where, D is the total chloride content in the air column with the base of the unit area; sigma;, the rate of capture with which a rain drop captures salt particles; γ, the mean radius of rain drops. 4. The order of magnitude of the radius of the atmospheric chloride particles can be obtained by estimating the value ofsigma;in the above formula. The result agrees well with that of Wright.
We investigated various problems concerning the accuracy of the radiosonde which we designed and constructed on the principles described in our previous paper. In temperature measurement the position of the thermometer in the ventilator of the radiosonde is important because the heating effect of solar radiation upon the wall of the ventilator affects the temperature indication of the thermometer. The optimum position does not always coincide with the position of the highest air velocity. The effect of insolation on the temperature measurement is not remarkable up to the height of tropopause. The comparison of this type of radiosonde with U. S. A. radiosonde shows that there exists no systematic deviation of observed values between them.
In measuring the mobility-spectrum of the ions in the atmosphere, by means of the cylindrical condenser of the type of Gerdien's aspiration apparatus, we must calculate the second differential coefficient of the voltage-current characteristic curve. But it is very difficult to derive this from an experimental curve. Furthermore, the variation of ion contents during the observation can not be neglected without causing appreciable error to the result. I used Nolan's “Sub-divided Condenser”, and devised a method in which we have only to derive the first differential coefficient for this purpose.
A statistical survey of the sudden commencement of magnetic storms shows two remarkable properties; in the first place, the mean freauencv distribution of horizontal component H becomes non-symmetrical like the Pearson type, and in the second place, diurnal variation of H becomes W-type. After variation analysis we find that the variation in frequency distribution consists mainly of the energy variation of the corpuscular mass which is the cause of magnetic storm. This energy distribution is explained with an assumption that the sun-spot consists of a violent turbulence in which exists quasi-thermal motion by large scale masses of ionized gas which may be emitted from the sun as a unit. Wtype diurnal variation of H is explained as a complex phenomenon firstly with the primary field strength variation on the earth's surface produced by induced current on the front surface of corpuscular mass, and secondly the shielding effect of the ionosphere of the earth. The corpuscular theoy by Chapman and Ferraro is given support by our results even in numerical details, except that the conductivity of the earth's ionosphere must be by the order of 10-1-10-2 smaller than that expected from dynamo-theory of diurnal variation field. A rough estimation of the corpuscular mass is also attempted, and the values thus obtained are not so extravagant and inconsistent with that obtained up to this time.