“…This mathematical approach in the context of geophysical flows was initiated in BMN [4,6,10,11], Mahalov and Marcus [40]. In the context of symmetric hyperbolic systems (including weakly nonlinear geometric optics), related singular oscillating limits have been investigated by Joly, Metivier and Rauch [31,34], Schochet [45] (where the weakly compressible limit of 3D Euler equations was considered), Grenier [30], Embid and Majda [26]. For general "primitive" equations of geophysics, following methods for hyperbolic Euler-type systems of Bardos [17], Bourgeois and Beale [19] have demonstrated convergence to quasi-geostrophic limit equations for special classes of initial data (of infinite codimension).…”