Title: A variational derivation of the nonequilibrium thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation,
Abstract: Irreversible processes play a major role in the description and prediction of
atmospheric dynamics. In this paper, we present a variational derivation of the
evolution equations for a moist atmosphere with rain process and subject to the
irreversible processes of viscosity, heat conduction, diffusion, and phase
transition. This derivation is based on a general variational formalism for
nonequilibrium thermodynamics which extends Hamilton's principle to
incorporates irreversible processes. It is valid for any state equation and
thus also covers the case of the atmosphere of other planets. In this approach,
the second law of thermodynamics is understood as a nonlinear constraint
formulated with the help of new variables, called thermodynamic displacements,
whose time derivative coincides with the thermodynamic force of the
irreversible process. The formulation is written both in the Lagrangian and
Eulerian descriptions and can be directly adapted to oceanic dynamics. We
illustrate the efficiency of our variational formulation as a modeling tool in
atmospheric thermodynamics, by deriving a pseudoincompressible model for moist
atmospheric thermodynamics with general equations of state and subject to the
irreversible processes of viscosity, heat conduction, diffusion, and phase
transition.