Abstract

In an attempt to understand the dynamical influence of the earth's topography 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 flui... Show moreIn an attempt to understand the dynamical influence of the earth's topography 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 by two parallel "walls" extended to the west and east directions. Periodic boundary conditions are applied to simulate the cyclic continuity of the channel in the 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 up to 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 the zonal flow past the obstacle. The results of the present calculations are compared favourably with those obtained in the early 1950's by Fultz, Long and Frenzen in the laboratory experiments of the flow past a barrier in a rotating hemispherical shell. Finally, a theoretical consideration was given to explain characteristic differences between westerly and easterly flows past the obstacle observed in the numerical experiments. Show less