Incorporating Non-Hydrostatic Pressure Work in Thermal Energy Conservation—Implication of Thermal and Kinetic Energy Exchange

Energy conservation and the kinetic and thermal energy exchange in the atmosphere are revisited. Total energy conservation describes the balance between the net change of total energy within a system and the net change of external mechanical and thermal work done to the system, which constrains the sum of kinetic and thermal energy changes. Because the external thermal work can induce a non-hydrostatic vertical pressure gradient inside the system, part of the kinetic energy change is contributed by the work done through this internally-generated non-hydrostatic vertical pressure gradient. Constrained by total energy conservation, the energy available for the internal energy change has to be compensated for the amount of the external thermal work done to the kinetic energy change. This thermal and kinetic energy exchange is included in kinetic energy conservation derived from momentum conservation, however, is missed in the traditional thermal energy conservation equation. Observations in the atmospheric boundary layer confirm the role of this extra term in the thermal energy conservation equation in order to explain observed temporal variations of air temperature. The new understanding may have important impacts on simulating flow motions and thermal structures in the atmosphere and the oceans.