The General Circulation of the Atmosphere

Abstract

Large-scale processes in the atmosphere (synoptic and global processes) require an individual description. Since the large-scale movements are practically quasi-static and nondiverging, they can be described in an appropriate form by simplified equations of hydrodynamics (in which for the quasi-static approximation it is necessary to use the so-called “traditional approximation” for the Coriolis acceleration; in addition, since the heights z = r − a are small in comparison with the distance r from the Earth’s center, it is advisable everywhere to use the Earth’s radius a instead of r). The equation of hydrostatics is

$$\partial .p/\partial z = - g\varrho $$

where g is the free-fall acceleration, and z is the height above the surface of the geoid (often referred to as “sea level”). Using the complement of the latitude θ = π − ϕ and the longitude λ, and designating the velocity components as v _z , v_θ, and v_λ, we can write the continuity equation (the condition of nondivergence of the velocity field) as follows:

$${{\partial {\upsilon _z}} \over {\partial z}} + {1 \over {a\,\sin \,\theta }}\left( {{{\partial {\upsilon _\theta }\,\sin \,\theta } \over {\partial \theta }} + {{\partial {\upsilon _\lambda }} \over {\partial \lambda }}} \right) + 0$$

.