If δQ1 is the total energy consumed or accumulated in unit volume of the lower atmosphere per unit time and δQ2 is that which enters in or comes out of this space per unit time δQ1 should be equal to δQ2. δQ1 and δQ2 are calculated by the following equations, We calculated numerically these equations of the atmosphere using the data obtained at Tokyo observatory. We made sure that the 1st law of thermodynamics holds satisfactorily good in the atmosphere.
The wind does not flow as a laminar motion, but as a very complex turbulent motion. One of the characters of such turbulent motion is the socalled “ turbulence ” Hence the present author tried to analyse the turbulence from the records of the daily observation of wind, such as those due to Dines' pressure tube anemometer and wind vane and obtained the following results. (1) The velocity distribution of tubulence in steady state is given by (2) Gustiness g, which is defined as the ratio of the velocity of turbulence to the mean wind velocity V, is given approximately by g=a+b/V where a and b are appropriate constants. (3) The greatest wind velocity in a given time interval, say an hour, is about twice of the mean velocity. (4) g is greater in day than in night. Generally the word “wind velocity” is not used in true sense of hydrodynamics, but it will mean some kind of average of the velocity of the air motion. In daily observation of wind velocity are used three anemometers that is, pilot balloon, Dines' anemometer and Robinson's anemometer. The motion of these anemometers are discussed here and it is found that they give different sorts of wind velocity so long as turbulence exists. The velocities which are measured by these anememeters are given respectively by (1) Pilot balloon: Vp=uo (2) Dine's anemometer: (3) Robinson's anemometer: hence we have Vp<Va<VrThe first means the velocity of the mass motion of the fluid, the second is the mean of the wind speed and not the mean of the velocity and the last is difficult to be explained physically, but it will be something like a mean energy of the wind. Thus, the velocity given by the Robinson's anemometer gives the greatest and that given by the pilot balloon the smallest, and hence, the Robinson constant shonld be taken smaller value than normal (about 0.8 times) to make the calculated value of velocity agree with the velocity obtained by pilot balloon. Then the wind velocity obtained by the Robinson anemometer will also become to have a rather natural meaning.
It is generally accepted that the vorticity transport theory of turbulent motion initiated by G. I. Taylor takes some important place in the mechanism of momentum transfer in turbulent chaos. Its superior points have already been affirmed by various papers published by Taylor, but the mechanism is not yet affirmed satisfactorily enough to describe the details of turbulent motion as detected by L. Prandtl. The application of Taylor's theory to the atmospheric field has been examined by the present writer with some success, though the principle of discussion adopted was not rigorous. Anyhow we see here that the vorticity transport theory is found to be reliable fairly well among the various theories hitherto postulated. Prof. S. Fujiwhara has pointed out the existence of transverse resistance accompanying eddy motion long since the publication of his elaborate work on the vortical motion. His intention has partly been accomplished by S. Sakakibara and Y. Isimaru in their equations of transverse eddy viscosity. In the present paper the writer shows that the term of transverse resistance is detectable from the vorticity transport theory under gradient wind condition. Denoting the mean motion by bar and the eddy motion by dash, the equations of motion of perfect fluid adopted by Taylor are, in steady state, where The deformation of vorticity of incompressible fluid is expressed by, in Lagrangian form. and the condition of conservation of vorticity is as follows: Thus Taylor arrived at the following equations: etc. Assuming the relations as realizable in the problem of gradient wind we have as the x-component of frictional resistance and as the y-component. Here If μ1=μ2, ν1=ν2and the coefficients are positive, the result becomes to coincide with Sakakibara-Isimaru's term. Next the effect of compressibility has been considered. Discarding the terms of small order, the frictional term is approximately given by etc., where
After examining 107 cyclones which had appeared near Japanese Islands in the winter of 1933 and 1934, we got the following results about their amalgamation. In Japanese vicinity and in winter (1) Cyclones have a tendency to amalgamate. (2) Cyclones have a tendency to develop. About 70% of all the cyclones had developed. (3) Amalgamation stimulates the development of cyclones. Of isolated cyclones, 62.5% developed, while of amalgamated cyclones 96.2% showed developement. (4) About 2/3 of cyclones which amalgamated other cyclones, had begun quick development in 18 or 24 hours before their amalgamation, but remaining 1/3 of them did not show any distinct growth in advance. (5) All of the cyclones had lower central depths at the points of amalgamation than that which they have before the amalgamation. The effect of amalgamation disappeared just after amalgamation in every case and then cyclones began their growth or decay under other (perhaps, thermal) conditions. (6) The growth of cyclones depends much more upon their courses than on amalgamation, viz. conditions of development are mainly settled by the course. (7) About 82% of cyclones changed the dircction of their march at their amalgamation. (8) The place where the amalgamation of two cyclones occurs is generally near the intersection of their courses and so that every course has its proper place of amalgamation.
The late Prof. K. Nakamura had calculated the number rainy days at Tôkyô for every day of the year for 44 years. In the present note the data for the following 17 years are added so as to be able to have the statistics for 61 years.