On the zero-Rossby limit for the primitive equations of the atmosphere (Q2757160)

The authors consider primitive Boussinesq hydrostatic equations governing the atmospheric motions on a two-dimensional torus. It is proved that, if the initial data approximate data of geostrophic type, the corresponding solutions of simplified equations approximate the solutions of full quasigeostrophic equations with order Ro accuracy as the Rossby number Ro goes to zero (the zero-Rossby number limit). This result holds even when the Prandtl number is not one. Additionally, the authors prove that Ekman-type boundary layers do not occur in the considered initial-boundary value problem. The proofs are based on some estimates for Galerkin approximate solutions.