  In this paper, we rigorously derive the governed equations describing the
motion of stable stratified fluid, from the mathematical point of view.
Specially, we prove that the scaled Boussinesq equations strongly converge to
the viscous primitive equations with density stratification as the aspect
ration parameter goes to zero, and the rate of convergence is of the same order
as the aspect ratio parameter. Moreover, in order to obtain this convergence
result, we also establish the global well-posedness of strong solutions to the
viscous primitive equations with density stratification.
