The PDE polluted atmosphere model: a mathematical justification of a meteorological approach

In this thesis we have proved weak and strong convergence results for the solutions of the polluted atmosphere considered as a shallow domain. Specifically, we have given a rigorous mathematical proof that the 3D Navier-Stokes equations and the hydrostatic equations of the polluted atmosphere are not just formally connected to each other, but the velocity and concentration solutions of the first one converge to the respective solutions of the latter. We performed this analysis for the geophysical and downwind coordinate systems. Moreover we have verified an existence result for both for the weak and strong velocity-concentration solution of the limit model. We also approached the phenomena from the viewpoint of computational fluid dynamics --- we have developed a library of Python scripts using FEniCS that visualise this convergence result for the case of weak solutions.