Dynamics of Rotating Fluids

Abstract

The final target of this text is “geophysical fluids”, which are governed by both general fluid dynamic concepts and rotational effects. “Rotational effects” are introduced in the first instance when describing the fluid in a rotating system such as the Earth. In the beginning of this chapter, we derive the fundamental equation of rotating fluids by rearranging the fundamental equation introduced in Chap. 1, then, simplify the equation by introducing approximations commonly used in geophysical fluid dynamics, and derive steady-state and wave solutions to the fundamental equations. After introducing the rotating coordinate system and simplification of equations, steady field in the f-plane approximation is discussed, such as geostrophic flow, Taylor-Proudman theorem, Ekman’s drift current including Ekman transport and Ekman pumping. Time variation field in the f-plane is also discussed in the next section, such as inertial gravity waves, inertial oscillation, Kelvin waves and quasi-geostrophic component. Next, time variation field in $\beta$-plane approximation is explained in advance of steady field, describing quasi-geostrophic component in the $\beta$-plane and Rossby waves with various scales. Then, steady field in the $\beta$-plane is discussed, such as steady vorticity equation, western intensification, and Sverdrup transport. Finally, phenomena in the rotating stratified fluid are explained using two-layer fluid, then internal radius of deformation, and baroclinic Rossby waves are introduced. Additionally, as a brief explanation of general circulation of the ocean, thermohaline and wind-driven circulations are discussed.