The Primitive Equations
Petros Katsafados, Elias Mavromatidis, Christos Spyrou · 2020
The primitive equations describing changes in the atmospheric motion and thermodynamics are based on the mathematical expressions of a complete set of conservation principles. This chapter discusses the three fundamental physical principles that govern the atmospheric motions: the conservation of momentum, the conservation of the dry air mass, and the conservation of heat. The conservation of momentum in the atmosphere comes from Newton's second law of motion. The mathematical expression of the conservation of mass is called the continuity equation. Therefore, the mass has neither sinks nor sources within the atmosphere. The thermodynamic processes that control the evolution of weather systems are represented by the first law of thermodynamics, which is an expression of the principle of conservation of energy. The moisture forecast equation indicates that in a parcel of air, the total amount of water is conserved as the parcel moves around.