Abstract
This chapter provides a brief survey of some of the most important concepts of fluid dynamics and moist thermodynamics relevant to understanding the dynamics of tropical cyclones and includes a set of references. The chapter introduces the equations for fluid motion applied to a rotating earth, the concepts of vorticity and potential vorticity as well as theorems relating to these quantities. It introduces the vorticity-streamfunction solution method for barotropic flow and describes the membrane analogy for interpreting solutions to the partial differential equations that arise. Discussed also are the equation of state for moist air, relevant thermodynamic equations and constraints, saturation and latent heat release, equivalent potential temperature, moist entropy, moist static energy, viscosity, diffusion, friction and turbulence and the concept of balanced flow evolution and potential vorticity inversion. A summary of important dynamical constraints stemming from the flux form of the potential vorticity and vertical vorticity equations is provided also as it relates to the vortical organization of tropical cyclones and other intense geophysical vortices.
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