Inherent Dissipation of Upwind‐Biased Potential Temperature Advection and its Feedback on Model Dynamics. (19th March 2021) - Gassmann, A.
Abstract: Higher order upwind‐biased advection schemes are often used for potential temperature advection in dynamical cores of atmospheric models. The inherent diffusive and antidiffusive fluxes are interpreted here as the effect of irreversible sub‐gridscale dynamics. For those, total energy conservation and positive internal entropy production must be guaranteed. As a consequence of energy conservation, the pressure gradient term should be formulated in Exner pressure form. The presence of local antidiffusive fluxes in potential temperature advection schemes foils the validity of the second law of thermodynamics. Due to this failure, a spurious wind acceleration into the wrong direction is locally induced via the pressure gradient term. When correcting the advection scheme to be more entropically consistent, the spurious acceleration is avoided, but two side effects come to the fore: (i) the overall accuracy of the advection scheme decreases and (ii) the now purely diffusive fluxes become more discontinuous compared to the original ones, which leads to more sudden body forces in the momentum equation. Therefore, the amplitudes of excited gravity waves from jets and fronts increase compared to the original formulation with inherent local antidiffusive fluxes. The means used for supporting the argumentation line are theoretical arguments concerning total energy conservation and internal entropy production, pure advection tests, one‐dimensional advection‐dynamics interaction tests and evaluation of runs with a global atmospheric dry dynamical core. Plain Language Summary: For ease of calculation, an alternative to using the internal energy equation is to consider the movement of an air parcel which maintains a constant value related to temperature and pressure (potential temperature). The pressure gradient converts the energy from internal to kinetic or vice versa, thereby influencing the direction and speed of wind. Hence, in the total energy conservation law, the pressure gradient force and the potential temperature transport equation are interdependent. Equations that simulate the movement the air parcels and its properties (advection equations) have been developed to provide accurate and consistent results. This article reviews whether contemporary advection methods for potential temperature are consistent. This means ensuring the underlying physical laws are met, in particular, the second law of thermodynamics, stating that field variables need to be diffused. However, most numerical advection methods can occasionally act in an antidiffusive way. The pressure inherits this antidiffusion from the potential temperature, if the density is held constant. Due to antidiffusion, the modeled wind direction may be incorrect. Avoiding antidiffusion prevents this effect, but leads to sudden pressure forces. These forces lead to higher gravity wave crests generated at the fronts of weather systems. Key Points: The local antidiffusion within upwind potential temperature advection schemes leads to negative dissipation This antidiffusion induces spurious accelerations in the wind field in one‐dimensional and full model runs Entropically consistent schemes are less accurate and exhibit higher amplitudes of front‐generated gravity waves