Quantifying Numerical Energy Dissipation in Implicit Large Eddy Simulations

Abstract

A novel methodology, using energy tracers, is introduced with the aim of diagnosing numerical energy dissipation, both globally and locally, in numerical models of the atmosphere. Energy dissipation might correspond to some physical process, such as the cascade of kinetic energy to unresolved scales if that energy is not restored as heat. Energy dissipation might also arise as an artifact of the numerical methods used; for example, in the current study the model used conservatively transports entropy, neglecting entropy sources due to mixing, resulting in a spurious energy loss. The energy tracer methodology is applied to Implicit Large Eddy Simulation of several canonical atmospheric boundary layer flows. The method is found to produce plausible local estimates of kinetic energy dissipation that are correlated with the local rate of strain. However, it does not yield useful estimates of the local spurious internal energy loss due to numerical mixing; possible reasons are discussed. The energy tracer method does produce useful estimates of the global kinetic energy dissipation and internal energy loss. For simple cases, the global internal energy loss estimates are confirmed by an independent method based on changes in the pdf of specific entropy or total specific humidity. The spurious global internal energy loss can be reduced by conservatively transporting, instead of entropy, a thermodynamic variable that is more nearly linearly mixing. This idea is analyzed theoretically, and is demonstrated in simulations that transport a quantity approximating the ice‐liquid water potential temperature.