On the Dynamic Interpretation of the Virtual Temperature

Abstract

The concept of virtual temperature is reviewed and extended into the definition of the dynamic virtual temperature, which is the temperature that a parcel of dry air should have in order to experience the same acceleration as a parcel of cloud air. It is obtained from the equations of motion and depends on the water content in the three thermodynamic states: vapor, liquid, and solid. The scale analysis of the equation of the dynamic virtual temperature shows that the terms due to the acceleration and phase transitions of the particles are negligible with respect to the terms depending on gravity. Therefore, even though conceptually more adequate, the approximate mathematical expression of the dynamic virtual temperature is practically identical to the conventional definition of virtual temperature accounting for water loading.