This book develops a fundamental understanding of geophysical fluid dynamics based on a mathematical description of the flows of inhomogeneous fluids. It covers these topics:

1. development of the equations of motion for an inhomogeneous fluid
2. review of thermodynamics

3. thermodynamic and kinetic energy equations
4. equations of state for the atmosphere and the ocean, salt, and moisture effects

5. concepts of potential temperature and potential density

6. Boussinesq and quasi-geostrophic approximations
7. conservation equations for vorticity, mechanical and thermal energy instability theories, internal waves, mixing, convection, double-diffusion, stratified turbulence, fronts, intrusions, gravity currents

Graduate students will be able to learn and apply the basic theory of geophysical fluid dynamics of inhomogeneous fluids on a rotating earth, including:

1. derivation of the governing equations for a stratified fluid starting from basic principles of physics

2. review of thermodynamics, equations of state, isothermal, adiabatic, isentropic changes

3. scaling of the equations, Boussinesq approximation, applied to the ocean and the atmosphere

4. examples of stratified flows at geophysical scales, steady and unsteady motions, inertia-gravity internal waves, quasi-geostrophic theory

5. vorticity and energy conservation in stratified fluids

6.boundary layer convection in stratified containers and basins