Abstract
In this paper, from the relationship between nonextensive parameter and polytropic index, we deduce the nonextensive density distribution and Du's equation (Du J. L., Europhys. Lett., 67 (2004) 893), in one self-gravitational system. We propose that the adiabatic process should be the limit state of the polytropic process in one stationary system, so one inequality which can be regarded as the convection stability criterion is constructed. By applying it into the atmospheric convection of the Earth, one can find that when the vertical temperature gradient is higher than 1 °C per one hundred meters, which is called adiabatic lapse rate in aerography, convection or turbulence will take place. One important conclusion can also be drawn that a sunspot is a kind of turbulent temperature inversion phenomenon, just similar to the one in the aerography.
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