Atmospheric convection is an essential aspect of atmospheric movement, and it is a source of errors in Climate Models. Being able to generate approximate limit formulas and compare the estimations they produce, could give a way to reduce them. In this article, it is shown that it is enough to assume that the velocity's L 2 -norm is bounded, has locally integrable, L 1 loc , weak partial derivatives up to order two, and a negligible variation of its first velocity's coordinate in direction parallel to the surface, to obtain a 1 arXiv:1811.03237v1 [math.AP] 8 Nov 2018Reynolds' limit formula for a Dorodnitzyn's compressible gaseous Boundary Layer in atmospheric conditions. MSC 2010: 35Q30, 76N15, 76N20.