Statistical mechanics for conservative discretizations of two-dimensional incompressible flow
Sommer, Matthias; Brazda, Katharina; Hantel, Michael
In this article two conceptually different approaches to incompressible two-dimensional fluid mechanics are discussed and compared. The first is the statistical description of the equilibrium potential vorticity field satisfying conservation constraints for energy and the generalized potential enstrophies. The second one is the numerical description of the barotropic quasigeostrophic potential vorticity equation taking into account the same conservation laws. Both approaches continue previous works in these fields. By analyzing the statistical properties of the numerical output it is possible to validate the assumptions of the statistical theories. This is not only a proposal for the use of general conservative discretization schemes but also for the consideration of principles from statistical mechanics in numerical analysis. Specially when thinking about long-term simulation of the atmosphere in climate research, statistical properties of a numerical discretization scheme may have a strong impact on the results.