High-order approximation equations for the primitive equations of the atmosphere (Q1392612)

We present a family of models approximating the primitive equations of the atmosphere, which are known to be the fundamental equations of the atmosphere. The primitive equations of the atmosphere are used as a starting point, and asymptotic expansions with respect to the Rossby number are considered to derive the \(n\)th-order approximate equations of the primitive equations of the atmosphere. Simple global models of the atmosphere are obtained. These higher-order models are linear and of the same form (with different right-hand sides, depending on the lower-order approximations) as the (first-order) global quasi-geostrophic equations. The article is concluded by numerical simulations based on these models.