  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
Reynolds' limit formula for a Dorodnitzyn's compressible gaseous Boundary Layer
in atmospheric conditions.
