Energetics of deep moist convection

Margules (1905) articulated that, of the large reservoirs of internal and potential energies in the atmosphere, only a small portion is transformed into the kinetic energy of atmospheric motions. Thus, only part of the energy reservoir is available for transformation. Building on this idea, Lorenz (1955) introduced the concept of available potential energy as the maximum kinetic energy attainable by an adiabatic redistribution of the mass of a hydrostatic atmosphere. He formulated a global theory of available potential energy for a hydrostatic atmosphere that has become a cornerstone for describing the general circulation of the atmosphere.

In this study, an Eulerian formulation of local available energetics (sometimes called exergetics) is presented that is valid for compressible, multi-component, nonhydrostatic flows that allow for frictional, diabatic, and chemical (e.g., phase changes) processes. This formulation is shown to be the nonlinear extension of linear available energetics. The exergy is defined relative to an arbitrary isothermal atmosphere in hydrostatic balance with uniform chemical potentials. It is shown that the potential exergy can be divided into potential, elastic, and chemical exergies. Each is shown to be positive definite. The general formulation is applied to the specific case of an idealized, moist, atmospheric sounding with liquid water and ice. The exergy is dominated by potential exergy in the troposphere but elastic exergy dominates in the upper stratosphere. The chemical exergy is significant in the lower troposphere where it dominates the elastic exergy. The total exergy increases with increasing water content.

This formulation will be applied to numerical simulations of deep moist convection.