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.
Abstracts file: | zhukov_Ya-2011.doc |
Full text file: | zhukov_rassh.doc |