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.

On the relative density of clouds

“…We will show that the osmotic pressure exerted by the hydrometeors is negligible and the procedures commonly presented in the above references can be justified if one considers hydrometeors as a pseudo-gas. This was pointed out by Monteiro and Torlaschi (2007). The concept of osmotic pressure is common in physics (e.g.…”

“…For cloud droplet sizes greater than 1 μ m, the individual bombardment by microscopic gas molecules will have little effect and Brownian forces become insignificant (Brady, ; Seinfeld and Pandis, ) and a new definition of density temperature should come from hydrodynamic considerations. Monteiro and Torlaschi () redefined density temperature from a dynamical point of view, showing that a more adequate definition of virtual temperature is the temperature that a parcel of dry air should have in order to experience the same acceleration as a parcel of cloud air and not in terms of its densities, as is usually done in the literature. They started from the dynamical equations for moist air from Bannon () and, performing a scale analysis, they showed that the contributions due to the acceleration and phase transitions of the condensate particles are negligible with respect to the contributions of gravity.…”

“…When the hydrometeor size is higher than 1 μ m, hydrodynamic forces prevail over Brownian forces and the hydrometeors cannot be considered in suspension. Under those conditions, a dynamical definition of density temperature is needed such as the one proposed by Monteiro and Torlaschi ().…”

“…When the hydrometeor size is higher than 1 μm, hydrodynamic forces prevail over Brownian forces and the hydrometeors cannot be considered in suspension. Under those conditions, a dynamical definition of density temperature is needed such as the one proposed by Monteiro and Torlaschi (2007). Using standard notation from textbooks such as Emanuel (1994), we present a simpler but general expression to compare cloud densities and we test this approach comparing our conclusions with those of PF11.…”

The equations of motion for moist atmospheric air

“…(As another example, consider a block of ice melting on a Cotton et al [2011], the formulation of B02 obeys momentum conservation, does the contrasting formulation of O01, used in global atmospheric models [Satoh, 2014], violate it? While some authors have argued that the reactive motion term in equation (14) is usually small [Monteiro and Torlaschi, 2007], Cotton et al [2011] concluded that this term warranted further study. Irrespective of its magnitude, resolving the discrepancy between the formulations of O01 and B02 is necessary for correct 10.1002/2017JD026773 employment of the fundamental equations of momentum conservation to a moist atmosphere.…”