subgrid

Comp. article by Browning and Kreiss cited earlier (that you obviously have not done), you will see very clearly that the only way to run the NS equations without the correct small physical dissipation (kinematic viscosity) is by using a larger unphysical viscosity (what you call a subgrid scale sink of energy) and this alters the spatial spectrum of the solution as clearly shown in the Math.

Exponential Growth in Physical Systems « Climate Audit 2007

There one can see that these fitered equations contain a so-called subgrid-scale stress/dissipation term.

Exponential Growth in Physical Systems « Climate Audit 2007

In addition to the explicitly resolved scales of motions, the models also contain parametrization schemes representing the so-called subgrid-scale processes, such as radiative transfer, turbulent mixing, boundary layer processes, cumulus convection, precipitation, and gravity wave drag.

GCMs and the Navier-Stokes Equations « Climate Audit 2005

But not including some kind of subgrid model or eddy mixing parameter is not correct either.

Exponential Growth in Physical Systems « Climate Audit 2007

But not including some kind of subgrid model or eddy mixing parameter is not correct either.

Exponential Growth in Physical Systems « Climate Audit 2007

So, I think also for these class of problems it should be possible to develop some kind of subgrid models.

Exponential Growth in Physical Systems #2 « Climate Audit 2007

So let us assume we have a spatial filter (I will denote it by .) which doesn’t touch the large scales (larger than the grid size) but takes an average over the small unresolved scales (the so called subgrid scales).

Exponential Growth in Physical Systems #2 « Climate Audit 2007

The importance of small/subgrid-scale processes on large-scale behavior should also be emphasized.

Sea ice in the Arctic 2009

Recent advances in stand-alone sea-ice modeling, including those in modeling sea-ice thermodynamics (e.g., introducing the effects of subgrid-scale parameterizations with multiple thickness categories – the so-called "ice-thickness distribution"), are now being incorporated into AOGCMs.

Global coupled atmosphere-ocean general circulation models 2009

If none of those 4 ways can lead to a viable solution, then we know fer sure that a 3x3 sudoku subgrid can never sum to 1000.

The Volokh Conspiracy » Math Puzzle: 2009