Convective equations for strong stratified medium
It seems the most obvious generalization of Bussinesk equations in the case of atmospheric flows with strong changes of thermodynamics parameters with height is presented in [1,2].
In presented paper a). A generalization of [1,2] in the case of arbitrary medium are given; b). The solvability condition of this equations is given; c). the question what is 'equlibrium' pressure in the deep convection equations is discussedый; d). It is shown, that Mach number M, in the validity condition M2<<1 can be estimated as
M2=a rT2/H2
Here rT is a characterian size of disturbance, H is a height of the atmosphere, a<1 is a parameter characterizing atmosphere stability. It is shown also, that it is necessary to assume the condition rT<<H to make the equations [1,2] correct. Moreover, the equations [1,2] can be derived by the parameter rT/H<<1 expansion. In this case the flow region can have a size in oder to H.
[1] Berezin Yu.A., Zhukov V.P // Mechanika Zhidkosti i gasa (Izvestia academii nauk) 1989. № 4. P. 3-9.
[2] Zatevahin M.A., Kuznetcov, A.E., Nikulin D.A., Streletc M.H.//Teplofizika vysokih temperatur. 1994. V. 32 № 1. P. 44.
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