A Theory for the Spurious Pressure Waves in Compressible Large Eddy Simulations of Shallow Cumulus Clouds

Abstract Large‐eddy simulation (LES) has been an indispensable modeling tool for the study of shallow cumulus (ShCu) clouds. However, a recent study uncovered omnipresent spurious pressure waves around simulated ShCu clouds by three compressible community LES models, suggesting a potentially common issue. These waves degrade the simulation of pressure‐related variables and lead to unclosed turbulence flux budgets. An analytic theory is proposed to explain pressure wave generation by latent heating. Specifically, the solution to the linearized pressure equation with a diabatic source contains a singularity condition when the time rate of heating equals the time interval of a sound wave propagating through a cloud. The former is tied to the model time step in most bulk microphysics schemes that adopt saturation adjustment to parameterize cloud water condensation. The theory suggests that wave stabilization requires more frequent microphysics updates than is currently done, and is supported by LES results.