Abstract
The system of partial differe n tial equations which shows the one-dimensional unsteady airflow over the mountains under the inversion layer is hyperbolic type, and has two families of characteristic lines. Using this nature, the system of basic equations is integrated numerically along each characteristic line. The following three initial conditions are given: (1) subcritical flow for all intervals, (2) subcritical flow for all intervals, but critical flow at the mountain crest, and (3) supercritical flow for all intervals. In all cases the bight of the inversion increases on the windward side and decreases on lee side. And a jump arises on the lee side after some time-steps. The higher the initial speed, the farther downward the jump appears, which suggests the possibility of a fall wind. That the swell is higher with increasing initial speed explains the abnormal pressure difference between the windward and the lee side. In order to determine the position of the lee side jump, a method for extending the characteristic lines through the jump region is devised and described. Some characteristics of propagation of the jump or drop whose shape is unchanged are discussed analytically. These analytical results can explain the propagation of the disturbances observed in numerical solutions.
