We have investigated how a body may move and deform; this is kinematics, codified in the equation of conservation of mass. We also have investigated the distribution of stresses within a body which may cause it to deform; this is dynamics, codified in the equation of conservation of momentum. Versions of these conservation equations for elastic and fluid bodies are presented in § 4.7. We now turn our attention to the manner in which a body responds to the stresses; this is rheology. Commonly, rheology is taken to mean a change of body shape (called shear rheology), but it also encompasses the change of volume or density (without change of shape) induced by a change of pressure (called compression rheology). This latter response is determined by the equation of state, giving the density ρ in terms of appropriate independent thermodynamic variables. Generally, the equation of state is presented in differential form (as in § 5.2), but for an ideal gas, it is a simple algebraic equation.

As explained in Appendix E.5, in a system composed of one constituent the density is a function of two independent thermodynamic variables, with some freedom in the choice of those variables. Two useful choices of independent variables are temperature T and pressure p, or pressure and specific entropy s. It should be noted that the density and pressure are unique variables, in that they play leading roles in both thermodynamics and dynamics. The differential form of the equation of state for density is presented in § 5.2, following a discussion in the next section of some new adjectives that we encounter while delving into the dynamics and thermodynamics of geophysical fluids. The thermodynamic presentation in this chapter is rather abbreviated; for more detail, refer to Appendix E.

New Adjectives

In our study of geophysical fluids, we will encounter a number of new adjectives. It may be helpful to define these clearly at this point, before plunging into the dynamic and thermodynamic details. These adjectives include: