Numerical Simulation of the Neutral Boundary Layer: a Comparison of Enstrophy Conserving with Momentum Conserving Finite Difference Schemes

The application of integral constraints to a numerically integrated system of dynamical equations is a method by which one can insure that a chaotic flow maintains its integrity. Such constraints have been a mainstay of climate models, largely out of necessity to eliminate unrealistic long term trends in such quantities as enstrophy, entropy, mass, momentum, energy, moisture and so on. It is interesting that although large eddy simulations (LESs) deal with a similar long-term integration problem (i.e. simulations over many eddy lifetimes), there has been little attention paid to the integrity of the conservation properties of the underlying dynamics schemes. This may in part be due to the strong emphasis that has been placed upon the subgrid scale diffusion schemes that are typically used to complement the dynamics schemes and in effect compensate for many of their flaws, in addition to acting as a physical representation of subgrid scale turbulence.