On the role of thermal expansion and compression in large scale
atmospheric energy and mass transports
Authors: Nicholls Melville E. , Pielke Sr. Roger A. 
Published: April 2018

Abstract. There are currently two views of how atmospheric total energy transport is accomplished. One view considers total energy as a quantity that is transported in an advective-like manner by the wind. The other considers that thermal expansion and the resultant compression of the surrounding air causes a transport of total energy in a wave-like manner at the speed of sound. This latter view emerged as the result of detailed analysis of fully compressible mesoscale model simulations that demonstrated considerable transfer of internal and gravitational potential energy at the speed of sound by Lamb waves. In this study, results are presented of idealized experiments with a fully compressible model designed to examine the large-scale transfers of total energy and mass when local heat sources are prescribed. For simplicity a Cartesian grid was used, there was a horizontally homogeneous basic state, and the simulations did not include moisture. Three main experimental designs were employed: The first has a convective storm scale heat source. This experiment illustrates the basic process of expansion in the heated region leading to compression of the adjacent air and the subsequent formation of a Lamb wave that propagates laterally at the speed of sound. The second experiment has a continent scale heat source prescribed near the surface to represent surface heating and which includes a constant Coriolis parameter. Results indicate that after several hours considerable amounts of total energy and mass are transferred offshore at the speed of sound. This simulation is compared to one with the term in the governing equations responsible for forcing thermal compression waves omitted. There is a fairly small but nevertheless significant difference of the wind field compared to the fully compressible results. A comparison of the fully compressible simulation with a simulation without the Coriolis force illustrates the role of geostrophic adjustment in significantly influencing the total energy distribution. The third experiment has a cloud cluster scale heat source prescribed at the equator and which includes a latitude dependent Coriolis parameter. Results show considerable amounts of meridional total energy and mass transfer at the speed of the sound. This study suggests that the current understanding of large scale total energy transfer that assumes it is accomplished solely in an advective-like manner by the winds is not correct. If so the current theory would be incomplete, and since some of the transfer might be occurring at the speed of sound this could bring into question the methodology commonly used to attribute the total energy transports to transient eddy, stationary eddy, and mean meridional circulations. Based on these results the conceptual differences between the terms total energy transport and heat transport in a fluid are discussed. Fast moving compression waves are unlikely to be accurately simulated by most climate models since they utilize semi-implicit time differencing techniques, and this could potentially be a source of error that has yet to be evaluated.