Abstract
Take the x-and y-axis east-and northwards respectively, and let the general westerly wind be U(y), then Here u and υ denote the velocity components associated with wave motion. The equation of continuity is then the instability of wave motion sets in only when β is complex.
The vorticity of the steady motion is 1/2 dU/dy If throughout any layer the vorticity is constant, d2U/dy2 vanishes and wherever β+αU does not also vanish. When there are several layers in each of which the steady vorticity is constant the various solution of the form (4) are to be fitted together, the arbitrary constants being so chosen as to satisfy certain boundary conditions. The first of these conditions is evidently The second may be obtained from the continuity of pressure across the boundary. Thus when U(y) is continuous across the boundary. At a fixed wall, of course Under these circumstances the examinations of stability coincides with Lord Rayleigh's investigation on the stability of certain fluid motions. Thus it may be concluded that in the isolated system of west wind zone the wave motion of any wave length is stable and has no chance of transforming into vortical motion, but on coupling with the east wind zone such as the equatorial trade wind zone or the polar east wind zone, the wave motion becomes unstable and transforms into vortical motion when the wave length is large compared with the breadth of the wind zone. The critical wave length is estimated to be about 10, 000km, which is too large compared with the cyclone wave of wave length 1000km. This discordance may be ascribed to the much simplified assumptions adopted here.
