That is very interesting. Thank you for your reply.

I am curious about this DNS approach for such a large scale problem. How fine is the grid to solve all flow scales?

k-epsilon

It will depends on the problem. A more accurate for general purposes I think is SST, but k-e and k-w can deal with a lot of problems. They variants are good as well e.g. RNG approach. DES and LES are good if  the flow structures are important on the analyses. Transitional models are good if the flow is able to pass from laminar to turbulent regime. DNS is the best choice if the turbulence itself is the key interest (or other applications such as combustion). Reynolds Stress, or second moment closures are other elegant and precise formulation. But some of them have a hard computational cost (SMC, LES, DNS, etc) . Some times I use none turbulence model once the Navier-Stokes equatiom does not is dependent of one. Of course, the mesh will  have a determined frequency that can be solved and the solver need to be able to deal with the 'more dynamic' behavior  without a effective viscosity to dissipate the energy such is done in RANS modeling. 

It depends on the problem. Effectively I most often end with RANS models as a standard solution. Somehow my problems often contain both laminar, transition and turbulent flow and then I prefer k-w-SST.

I believe that Large Eddy Simulation is the best tool we have for atmospheric turbulence. I wish some day in the future to see Direct Numerical Simulation for high Reynolds numbers.