Kinematical Analysisの理論と其應用

抄録

Suppose a geometrical space and draw the surfaces z=p(x, y, t). We take the axes of x and y in the two principal directions at the pressure centre, then the velocity C(C_x, C_y) of the pressure cerrtre is given by C_x=-p₁₀₁/p₂₀₀ and C_y=-p₀₁₁/p₀₂₀, and the axes of x and y are at right angles to one another. Next we consider the well-known formula by S. Petterssen on the displacements (x and y) of the pressure centre:
Eliminating t from the above equations we get the following expression as the equation representing the track of the pressure centre:
This represents a parabola when A_xC_y-C_xA_y≠0. Its vertex is located at and the pressure-centre would reach there at the time t=-(C_xA_x+C_yA_y)/(A_x²+A_y²). The time rate of change of the resultant velocity V is given by so the resultant velocity of the pressure centre becomes minimum at the vertex. If(A_xC_x+A_yC_y)>0, then V increases as t increases and a pressure centre has no tendency to recurve. If(A_xC_x+C_yA_y)<0, then V decreases as t increases and a pressure centre will recurve in future.
If the tendency profiles are curved cyclonically, i.e., p₂₀₁>0 and p₀₂₁>0, then (after S. Petterssen) a cyclonic centre increases in strength and it is retarded. Under the same condition, it is also concluded that the cyclonic centre tends to recurve in future. If the tendency profiles are curved anticyclonically, i.e., p₂₀₁<0 and p₀₂₁<0 than (after S. Petterssen) a cyclonic centre decreases in strength and it is accelerated. Under the same condition, it is also concluded that the cyclonic centre has no tendency to recurve.
As for example, typhoons first travel westward and away from the Equator. In the vicinity of the tropic or a little beyond it, they sometimes recurve. They gradually slacken in their progressive movement and increases in their strength until they reach the point of recuvature. After recurvature, they travel to the northeastward and pass into middle latitudes, travelling at a great rate and decaying rapidly.
It is also discussed on the low type and the high type of a cyclonic centre. And it is concluded that the estimated field of pressure at the level 3 Km of height is often useful to prognosticate the sudden deepening of a cyclonic centre.