NOTES ON THE THEORY OF LARGE-SCALE DISTURBANCES IN ATMOSPHERIC FLOW WITH APPLICATIONS TO NUMERICAL WEATHER PREDICTION
AIR FORCE CAMBRIDGE RESEARCH LABS HANSCOM AFB MA
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The problem of predicting the behavior of large-scale disturbances in the mean horizontal flow of the earths atmosphere, which is directly connected with the problem of predicting the day-to-day changes of surface weather conditions, has been studied from the standpoint of formulating and solving the hydrodynamical equations which govern the flow. Owing to the difficulty of solving the complete system of equations, it is convenient to develop a scale theory whereby the various possible types of atmospheric motion, each corresponding to a distinct type of solution, can be distinguished and classified. As it turns out, each type of motion is characterized by its phase speed and frequency. The large-scale disturbances, for example, are distinguished from all other types of motion by the fact that their characteristic phase speed is much less than that of sound waves and of high- speed internal gravity waves. By explicitly introducing this information into a mean vorticity equation for adiabatic flow, it is then possible to reduce the system to a single equation from which the extraneous solutions have been excluded and which is otherwise free of major difficulties. The resulting prognostic equation, which governs the largescale motions of a fictitious two- dimensional fluid whose velocity is a vertically integrated mean value of the horizontal component of velocity in the real three-dimensional atmosphere, forms the basis for a method of numerical prediction. An iterative scheme, based on the solutions of a succession of linear equations, has been proposed for solving the nonlinear prognostic equation.