The entropic energy of geophysical fluid systems. Tellus

The main objective of this work is to develop an integral theory for a wide class of fluid systems that not only includes the concepts of balance of mass, momentum, and energy, but also of entropy and the second law of thermodynamics. This theory provides an explicit relationship between the integrals of kinetic energy and of entropy in terms of a new energy form, the entropic energy. Linearly viscous fluids whose entropy functions are strictly concave are defined as equilibrium regular fluids. A fluid system consists of an equilibrium regular fluid of fixed mass M, whose body force is a consequence of a steady, positive, monotonic potential field, and whose bounds satisfy certain specified conditions. Geophysical fluid systems are a non-degenerate set of fluid systems. In geophysical fluid systems there exists a unique state for given values of system mass and system total energy E, called the associated equilibrium state, that is motion-less, hydrostatic, and isothermal (Theorem 2.1). The product of the temperature To of this state and the difference So- S in system entropies between it and a natura