In this paper, the author has determined empirically the height of the upheaval of the sea level caused by an approaching typhoon, only from the practical point of view. The result may be quite unsatisfactory giving only the lowest limit of the upheaval which may actually occur, because the upheaval due to the astronomical tide and the wind waves of very short period which may play an important role in the disaster over the coastal district has been neglected. The principal results can be judged only by common sense, and summarized as follows: (1) The time of maximum upheaval of the sea surface generally coincides with the time of the lowest barometric pressure at the station. In other words, owing to the general character of the typhoon that attacks Japan and moves northward along the Pacific coast, the highest water usually occurs when the center of the typhoon has reached the nearest distance from the station, as expected by the common sense. And at that time N-NE winds are generally the strongest. And when S-SW wind begins to blow, the sea level begins to lower very rapidly. (2) Dividing the elevation into two parts, i. e., the elevation due to the suction of low pressure and the elevation due to the drift of the wind, it was found that the latter is almost negligible for the wind force less than Beaufort's scale 4, however long such weak wind may persist. But as soon as the wind force exceeds that speed, the sea surface begins to rise very rapidly. (3) The total elevation is proportional to the difference between the normal barometric pressure at that place and the lowest pressure of the typhoon on its track, and is inversely proportional to the shortest distance from the center to that station, to which the typhoon approaches.
As an application of the study of Pellew and Southwell on maintained convective motion in a fluid heated from below, the author makes an attempt to draw the stream lines of the vertical sections of a regular hexagon, which is of great interest in relation to our thermal problem, because it appears from Bénard's experiments that hexagonal cells characterize the permanent regime in a layer of unlimited extent. If the midpoint of a layer is taken as origin and the directions of the axes of the cartesian coordinates x, y, z are drawn so that the x-axis is perpendicular to the side of the hexagon, the y axis coincides with the diagonal and the z axis is vertical, and if u, vw denote the component velocities, the function Ψ which decides the direction of the stream line is not an ordinary stream function, that is, denotes, for example, w=- ∂Ψ/∂x, u=∂Ψ/∂z, because u=0 but ∂v/∂y_??_0 Therefore, we do not get Ψ from the differential equation w/dz=u/dx as usual, but put w and u in the following form w=- ∂Ψ/∂xA(x, z), u=- ∂Ψ/∂zA(x, z) and then from the equation of continuity A(x, z) can be decided. As a result A(x, z) has a physical meaning of inversely proportional to the width of the stream tube and Ψ denotes an ordinary stream function when w', u' are adopted instead of w, u (where w'=w/A, u'=u/A). Finally Ψ1, Ψ2 and A(x, z) (at z=0) are drawn in figures, where Ψ1 is the stream line on the vertical section along the straight line through the origin and perpendicular to each side of the hexagon.
This paper is an abstract of the same author's “Studies on Atmospheric Pressure Variation”(unpublished). The motion of individual air particle is obtained for a stationary concentric cyclone, and then the development of divergence, convergence and vertical current is discussed from the Lagrangian point of view. The mechanism of the atmospheric pressure variation is discussed in terms of the accumulation of vorticity, convergence at low level divergence at upper level, vertical stability, horizontal density advection by adiabatic process, and the trajectories of each air particle. The reader who wishes a more complete and datailed treatment must be referred to the original paper (to be published in the Memoirs of the Central Meteorological Observatory).
In order to explain the connection between the horizontal and vertical structures of wind, the concept of the coupling eddy is postulated. The coupling eddy in the vertical structure is coincident with the vertical largest eddy. The movements of the coupling eddy in the horizontal and vertical directions are thought to be completely correlated with each other, and the correlation coefficient between two velocities u* and w* of the coupling eddy is assumed to be given by the following relation The turbulent velocities u and w which are observed in the wind contain not only the components of coupling eddy but also many components of eddies of other ranks, The correlation coefficient Ruw between u and w can be related with Ru*w*. For the natural wind, the effective largest eddy in horizontal plane usually increases its scale simultaneously with the increase in the time duration T of observation. Thus, as the time duration is prolonged, Ruw decreases in the following relation This relation is examined by the practical observation.