The Structure of Stationary Discontinuous Surface (I)

[摘要] Margules' formula for the slope of stationary discontinuous surface has two defects. One is the assumption inapplicable to the actual atmosphere. Inn the neighbourhood of discontinuous surface the acceleration of air is most pronounced and the vertical motion prevails. Because of this fact the discontinuous surface has an important meaning in meteorology, especially in weather analysis. Margules has however disregarded this fact. Then why is the fomula applicable in practice? The author investigated the reason. The other inconvenience in applying the formula is that, although the slope of the surface is known, yet the shape of its vertical section is not obvious. The author calculated first the formula which represents the shape of vertical section and then the angle of the shape. The result is that the shape of vertical section is approximately a parabola. The angle of slope thus derived agrees approximately with Margules'.§ 1. Preliminary RemarksThe author first examined the assumptions which Margules used to derive his formula. The author adopts only the following four assumptions:(a') The fluid is perfect (the effect of friction is later considered)(b') The motion is stationary(c') The motion is uniform in one direction.(d') The fluid is autobarotropy.It is shown that there is a possibility of obtaining intermediate integrals from the equations of motion. From the equation of continuity (4), v, w are represented as (5). Here Ψ is the stream function of momentum (v/s_??_w/s).§ 2. Integrals for Stationary MotionApplying the above relations, the first intermediate integral (5) is derived, which means that the two quantity Ψ and u-2ω sin θ•y+2ω cosθ cosβ•z are both homotropy.From this formula we get (5') after neglecting the effect of Coriolis' force. From (5') or (5) we can deduce the following results.The stream line Ψ=constant, in the vertical section coincides with the isovel of the velocity component u, which cuts the section perpendicularly. In other words, the stream surface coincides with the iso-velocity surface of the velocity component which cuts the vertical section perpendicularly. That is, a stream uniform in one direction can not exist by itself in general, and accompanies a stream in the orthogonal section. Reversely a motion in the orthogonal section to the direction, in which the motion is considered to be uniform, accompanies also with it a motion in the latter direction. Therefore the actual current presents itself as one which runs spirally on a certain cylindrical surface. This result can be applied to the motion of air in a cyclone. If the cyclone is symmetrical about the central axis, the horizontally rotating current accompanies necessarily the convergent, divergent, ascending and descending currents (convective current). Reversely the convection accompanies necessarily the horizontally rotating air current. (The rigorous treatment on this subject will be described in future).By the same method as we obtained the equation (6), we can obtain the second, and further, the third intermediate integrals (7) and (8). These correspond respectively to the integral of vorticity and Bernouilli's integral of energy.

[学科分类] 大气科学