Abstract
We shall express the atmospheric motion by means of the three variables of ψ=(ψ1+ψ3+ψ5)/3, Δψ=(ψ5-ψ1), and Δ2ψ=(ψ1+ψ5-2ψ3), rather than using the stream functions at the three isobaric levels ψ1,ψ3, and ψ5. After some manipulations the set of equations which describes the rate of change of ψ, Δψ, and Δ2ψ has been derived. The problem of finding the physical properties of disturbances has been studied as an initial value problem, in which the mathematical problem is to estimate the initial changes of the amplitude and phase of the respective variables. We have next examined what the present system implies with regard to the energy redistribution among various forms, each being associated with one of the variables ψ, Δψ, and Δ2ψ. It is found that (1) there is no direct conversion of potential energy into K(ψ), expressing the kinetic energy of the vertically averaged flow ψ,(2) the conversion of potential energy into K(ψ), which denotes the kinetic energy associated only with the mean vertical shear Licb, is usually one order of magnitude larger than that into K(Δ2ψ), being a component of kinetic energy related to Δ2ψ, (3) there is a supply of kinetic energy from both K(Δψ) and K(Δ2ψ) to K(ψ); the former supply is generally larger than the latter supply by about ten times.
