Abstract
It is studied by means of sca l e analysis what sets of equations are to be applied to quasi-geostrophic disturbances in low latitudes. The vorticity equation becomes the barotropic equation in a first-order approximation, and it is used to prognose a stream-function field and not a geopotential field. The divergence equation is primarily modified to the so-called balance equation for long waves and altered to the expression of the geostrophic relation for ultra-long waves. These formulae each turn out to be the diagnostic equation used to seek a geopotential field from a given stream-function field in a contrary relation to middle latitudes. It is moreover concluded for ultra-long waves that the magnitude of zonal wind takes the order of 10 m⋅sec-1, that of meridional wind must be, at most, of the order of 1 m⋅sec-1 and the continuity equation is used to determine the magnitude of meridional wind. The thermal equation loses the prognostic property for thermal change and represents the diagnostic equation used to estimate the magnitude of vertical motion even if including the time-change term in it The vertical mortion is primarily contributed by a non-adiabatic heating effect only. So we need generally to give the two kinds of data of a stream-function field and a non-adiabatic heating effect as initial data to solve the obtained set of equations.
