In an attempt to understand the dynamical influence of the earth's orography upon the large-scale motion of the atmosphere, the system of “shallow water” equations on the rotating earth is integrated numerically. The model consists of an incompressible, homogeneous, hydrostatic and inviscid fluid. The “beta-plane” approximation is used to simplify the model. The fluid is confined in a channel bounded on the north and south by two parallel “walls” extending in the cast-west direction. Periodicity is the boundary condition applied at the east and west boundaries to simulate the cyclic continuity of the zone with longitude. A circular obstacle of parabolic shape is placed at the bottom in the middle of the channel. The steady-state solutions in the absence of the obstacle are used as the initial conditions of the problem. Five different cases are investigated in detail. All computations were performed for an interval of 20 days (some cases were run longer) with a time step of 6 minutes.
The following main results were obtained: 1) Westerly flows past the obstacle produced a train of long waves on the lee side, which can be identified as “planetary” waves. On the other hand, easterly flows are little disturbed by the obstacle and long waves do not appear; 2) The number of waves produced in the westerly cases agrees with the number expected from the steady-state Rossby-Haurwitz wave formula for various intensities of zonal flow past the obstacle.
The results of the present calculations agree qualitatively with the data obtained in the early 1950's by Fultz, Long and Frenzen in laboratory experiments on the flow past a barrier in a rotating hemispherical shell. Finally, a theoretical consideration is given to explain the characteristic differences between westerly and easterly flows past the obstacle as observed in the numerical experiments.