On the Slow Motion of Compressible Air near the Surface of Ground

[摘要] For a theoretical treatment of slow motions of the air near the surface of the ground, it is desirable to stand on the basis of the equations representing the motion of viscous, compressible fluid and the convection equilibrium of heat. But by using the latter equations, it is difficult to reach appropriate solutions, excepting cases where liquid is concerned; the equation of state of liquid is expressed in a comparatively simple form. To get rid of this difficulty, we introduced the equation of polytropic change and obtained examples in which a stream-line was parted into two branches, which joined again each other, enclosing eddy flows, without assumption of any discontinuous surface in the field of motion.The equations (1) represent the conditions of the static equilibrium, (2), (3) and (4) are the equations of motion, and (5) is the equation of state of the atmosphere, where x and z are horizontal and vertical co-ordinates, (u, w) velocity compo-nents, p0+p, T0+T and ρ0+ρ pressure, temperature and density respectively. The suffix 0 is attached to the quantity representing the static equilib-rium. (6) expresses polytropic condition. Under the assumption of the isothermal atmosphere, a particular solution with a general current U may be given by (19) and (20), where λ is determined by (16) or (17).Fig. 3 shows an illustation of a family of stream-lines schematically. When stream-lines are compelled to run upward or downward, an eddy flow may appear at their front or back respec-tively. In the same figure we may find an example of topographic effect on winds under conditions somewhat different from Pockels' case (F. Pockets: Met. ZS. 1901).If U is comparatively small, there appears a circulation in the air just above the trough of stream-lines, bearing some resemblance to the eddy at the head of a squall (Fig. 5). Finally, we examined shortly the case of progressing obstacles and proved that generally there must be an infinite number of horizontal, nodal lines in the air, but the general characters of circumstances were not essentially altered.

[学科分类] 大气科学