A view of the equations of meteorological dynamics and various approximations.

*(English)*Zbl 1036.86001
Norbury, John (ed.) et al., Large-scale atmosphere-ocean dynamics. Vol. 1: Analytical methods and numerical models. Cambridge: Cambridge University Press (ISBN 0-521-80681-X/hbk). 1-100 (2002).

The article gives a concise introduction to and an excellent description of the continuum mechanical concepts used in meteorology: in “steps” of 12 sections, the equations governing atmospheric flow and the approximate forms used by numerical modelers as well as theorists are presented starting from first principles.

After introducing fundamental concepts of fluid kinematics (sect. 2) and discussing conservation laws (sect. 3), the basic equations of meteorological dynamics are presented in sect. 4. To provide a basis for a numerical treatment of these equations, various approximation schemes (such as the hydrostatic approximation, the hydrostatic primitive equations and the shallow water equations) are treated in sect. 5. Sections 6 to 9 and 11 cover refined approximation methods (e.g. the geostrophic approximation and the approximation of Coriolis effects), discuss the occurrence of different types of waves and their (partial) removal from the models. The quasi-geostrophic model is treated in detail in sect. 10, and the concluding sect. 12 gives a brief survey of issues in numerical modeling for weather forecast and climate simulation.

The article, covering 100 pages, is excellent to read and appeals to beginners in the field as well to specialists. An extensive bibliography completes the article.

For the entire collection see [Zbl 0994.00019].

After introducing fundamental concepts of fluid kinematics (sect. 2) and discussing conservation laws (sect. 3), the basic equations of meteorological dynamics are presented in sect. 4. To provide a basis for a numerical treatment of these equations, various approximation schemes (such as the hydrostatic approximation, the hydrostatic primitive equations and the shallow water equations) are treated in sect. 5. Sections 6 to 9 and 11 cover refined approximation methods (e.g. the geostrophic approximation and the approximation of Coriolis effects), discuss the occurrence of different types of waves and their (partial) removal from the models. The quasi-geostrophic model is treated in detail in sect. 10, and the concluding sect. 12 gives a brief survey of issues in numerical modeling for weather forecast and climate simulation.

The article, covering 100 pages, is excellent to read and appeals to beginners in the field as well to specialists. An extensive bibliography completes the article.

For the entire collection see [Zbl 0994.00019].

Reviewer: Nina Kirchner (Kaiserslautern)