Je suppose que les postulates fondamentaux en hydrodynamique sont K. I.....K. 10 (§ 1), qui soot été employés par nombreux auteurs explicitement on implicitement pour deduire l'équation de NAVIER-STOKES (1.17). Il y a en § 2 quelques critiques pour les postulates K. I.....K. 10, et on obtient un nonvel terme turbulent fr (2.3). Il faut en conséquence développer le tenseur de viscosité Zrs en série des gradients de vitesse vr, s comme (2.5). Dans le cas du médium isotrope le coefficient de viscosité _??_rsmn n'est pas nécessairement symétrique, et on a un nouvel terme kr (2.7) additivement à côté droit de l'équation (2.11). Si on l'écrit vectoriellement, on obtient (2.9) pour kr comme l'expression vectorielle. J.y donne de plus une nouvelle expression (2.12), qui peut être employée au lieu de relation “Austausch” de Prandtl. On a quelques explications à phenomènes hydrodynamiques biers connues mais non expliqués jusqu'ici (§ 3). Enfin j'étudie sur la fondation d'équation (3.2) quand tourbillon se mouvoit le long de son axe, et explique géométriquement sa condition nécessaire et suffisante.
We define with xi (i=1, 2, 3) a cartesian coordinate system: i.e. horizontal axes x1=x, x2=y, and vertical x3=z. Then the fundamental equations of non-viscous fluid motion are where the index κ (and every index that is found twice in a term) shows the summation from 1 to 3 after the Einstein's expression, and Cik=-Cki is the coriolis-axiator. When the elements p, ρ and ui in the above equation are compounded of the temporal mean values and the fluctuations, i.e. ρ=_??_+ρ'_??_p=_??_+p', and ui=_??_+ui', we obtain by introducing these values into the equation (1) by using the equation of continuity Sometimes we can find the use of the terms which contain ρ', in the above equation. Next we must consider in detail about the 4th term in (2). For the horizontal turbulence Ertel as sumed where the mean values of ξi are considered as the components of the Prandtl's mixing-length. But according to the Prandtl's conception we must add to the equation (3) terms which depend on ∂ _??_/∂xi, that are the components of the direction of gradient of another velocity components. Here we consider that the above idea is insufficient, because the turbulence in the atmosphare arises in the direction, which even if the velocity gradient component does not exist in, parpendicular to the both directions of the mean flow and its velocity gradient. Moreover it is considered that the turbulence occurs not only from the velocity gradient, but also from the thermal convection, the eddy diffusion etc. So that for the most natural expression of ui' we assume where the additional terms εi represent the turbulence arising from agency other than velocity gradient. By using the above expression we can obtain the new equation which have a very expanded physical meaning for the eddy stresses that is The more extension in detail about the equation (4) will be found dlse where.
It is defined with xi (i=1, 2, 3) a orthogonal cartesian co-ordinate system. In turbulent flow the velocity component ui' are compounded of the mean (temporal) values and the fluctuations, and are writed _??_i=ui+ui'. For the pressure p=_??_+p'. Introducing these values into the Navier-Stokes' equation and neglecting the molecular viscosity and the fluctuation of density ρ, the fundamental equations are expressed as follows. where the index κ (and every index that is found twice in a term) shows the summation from 1 to 3 after the Einstein's expression. In anisotropic trubulence we put Cik=coriolis-axiator. _??_ik=-_??_ apparent (eddy) stresses. The mean values of §_??_are considered as the components of Prandtl's mixing-length. ε_??_ are the additional terms which represent the turbulence arising from agency other than velocity gradient. Using (2), the expressions for the apparent (eddy) stresses are introduced as follows: where Austaush coefficients or coefficients of eddy viscosity If we transform the equation (3) as follows, we can obtain new following expressions having the more clearer physical meaning for eddy stresses. where each notation is generally known. According to the expression (4), we can find a new physical improvement that the symmetric stress tensor is caused by rotation in addition to deformation. Introducing the equation (4) into the frictional term (by the eddy viscosity) in the equation of motion, we can obtain new general expressions for the resistance arising from the eddy transport of momentum in three dimentional anisotropic turbulent flow. When these new equations are applied to the horizontal wind motion whose variation in the horizontal components are negligibly small compared to vertical in the narrow region in the immediate neighbourhood of the ground, the new terms of the transverse resistance which are impossible to be found in the old theory are appeared in the following form. the equations (5) coinside with, the Sakakibara-Isimaru's equations. Moreover in this report the rate of dissipation of energy due to eddy viscosity only is computed, and it is found that the Dissipation Function contains the terms of rotation. Here the physical inspection of the Watanabe's Equation of motion in the “microgyrostatic field” is done.
Die bisber konstruierten, selbstregistrierenden Komponenten-Anemometer, um in relativ einfacher Weise die Windkomponenten zur Aufzeichnung zu gebracht haben. Nämlich z. B. Windwegen W als Abszissen, während cos θ die zugehorigen Richtungscosinus die Ordinaten bildete, so erhielt man Wcosθ (od. W sin θ ), die Komponenten des Windes, nicht als Linien, sondern als Flächen. Der Hauptvorteil der in Rede stehenden Neu-Konstruktion der Windcomponenten-Vorrichtung besteht darin, dass dieselbe, gerade die Wcosθ als eine Zahl, nicht als Flache, aufweisen kann. Fig. 4 zeigt Grund and Aufriss des Instrumentes. Hier also das Prinzip der Rollkugel, das sich erst Hele-Shawschen Kugelroll-Integrator benutzt hatte, in der gleichen Weise, in Verbindung mit der Windfahne and Schaalenkreuz Kontakten, anwendet. Bezeichnet φ den Drehwinkel des Rad R über beliebige Zeitraum ζ, dann φ ist proportional die Gesamtwindwegen, so erbält man nach der Fig. 3. und 4 die Windkomponenten als beiden (N und O) Messrollendrehungen φo und φn wo V die Windgeschwindigkeit, k eine Konstante ist. Also z. B. in die Quadranten wo cos θ<0 ist, φ (-n) bedeuten Sud-Komponente. Bei den zwei Messrollen werden vier Schreibfeder getriben und somit kann man die vier Komponenten zur Aufzeichnung zu bringen.
There are, at present, three kinds of apparatus for the production of a picture of a view subtending 180° on a flat plate or film-Wood's fish eye camera, Bond's hemispherical lens and Hill's convexo-concave lens. To the best of our knowledge, a spherical mirror has not been used in practice for such a purpose. So, it may be of value to give a short description of the apparatus and to show some photographs taken with it. A convex spherical mirror with a large aperture is arranged to face vertically upwards, and an ordinary photographic camera is placed at some distance above and looking into the mirror to photograph the image of clouds appearing in the mirror. We used a silvered round glass bottle as a spherical mirror. Of course, the perfect sphericity of the mirror cannot be expected from such an ordinary bottle. The surfaces of some glass bottles used by us are, however, nearly spherical. For example, one of them has, excluding the portion near the neck of the bottle, the mean radius of 11.62±0.15cm. The defect of this, mirror is, however, that some small flaws usually exist somewhere on the surfaces. The ideal spherical mirror with a large aperture is most probably to be obtained by silvering the surfaces of a large condenser. This is, however, beyond the easy reach of the amateur photographer. Now let us study how large the aperture of a mirror is in order to photograph the whole sky. Denote the angle of the field of view of a photographic lens by ψ, the aperture of a mirror by φ, and the radius of the mirror by γ. The ray coming from the horizon is incident and reflected on A and A' on the mirror and reaches B at which point the lens is placed. (see Fig. 1. page 239). There is a relation between, ψ and φ. ψ=π-2φ_??_(1) If the distance of B from C which is the pole of the mirror is denoted by d, three parameters d, r and ψ are connected by an equation of In our case d=100cm, , ψ=30°. From (1) and (2) we obtain φ=75°, r=48.4cm. Therefore, the largest image of clouds is obtainable by using a spherical mirror of radius of only 48cm with the above mentioned camera. Some photographs taken by this method are shown in Fig. 2, 3, 4, 5. It is to be noted that the surrounding view below the horizon appears in those pictures. It is wonderful that though the pictures are distorted except near the center, they are distinct even near the horizon in spite of the spherical aberration due to the large aperture of the mirror. The drawback of this method is that the image of the camera appears in the center of the picture. The damage coming from such an obstacle can however be lessened, if a mirror of large radius is chosen and the camera is placed at a considerable distance from the mirror, since, in this way, the image of the camera become smaller. This becomes evident, if Fig. 3 is compared with Fig. 4, where the former is taken with a large mirror, while Fig. 4 with a small one(1).
1. The correlation coefficient between the monthly number of sunspots and the late autumn rainfall in North Mauchuria is shown less than 0.351±0.144. (1898-1935). 2. There is the inverse correlation as high as -0.698±0.064 (1907-1936) between the monthly means of atmospheric pressure of May and the amount of rainfall of October in Harbin. Besides there are higher correlation between the May pressure in Harbin and the October rainfall in Antah, Yaomen, Sansing and Kungchuling. Therefore the air pressure of May in Harbin is able to predict the late autumn rainfall of various regions in North Manchuria. 3. It was found that the predic_??_ing formula of October rainfall in Harbin Y1=569.0-12.8 X1, showed less deviation in forecasting than that of another places.
In the semi-infinite elastic body with a superficial layer, it is a well known phenomenon that a group of Love-type's waves can be generated. The present author, assuming the boundary conditions to be “half-slip”, introduces another type of elastic waves mathematically.