Similar topics posted on RG:

https://www.researchgate.net/post/Can_DNS_simulates_turbulent_flows

https://www.researchgate.net/post/Is_a_complete_mathematical_description_of_turbulence_possible

https://www.researchgate.net/post/Why_not_take_DNS_results_for_validating_turbulence_models_in_fluid_mechanics

Dear distinguish Professor Filippo Maria Denaro

What i mean is to develop Navier Stokes equation that includes mathematical terms(formulations) describing New Navier stokes equation with no need to use turbulence models.

Best Regards

Dear Ahmed Abdelhameed

you will find in the posts above some discussions about that. Both about the suitability of the standard NSE and possible implementation of different closures in the Newtonian model.

Dear Ahmet,

The NS by itself provide a full desveiption of fluid flows, regardless the regime and type of flow. The problem is more nunerical than physical. Having said that, I dont think we are going to see a “new NS” with or with new terms that resembles turbulence. However, professor Denaro suggested another post where younwill find different opinions and you will see that your question is answered there too. Now, here is my two cents, I strongly bekieve that unresolved flows are gaining mometum in the turbulence field. However, you will see other group who dont like that idea. I suggest you to read professor Pruett papers. Although he devoted years of research in the temporal filtering LES you will se a completly different perspective. I believe that under-resolved turbukent flows or ILES are an interesting idea and they are relates to your question. Again, that is my humble opinion!

If for a particular flow you can overcome the closure problem for solving NS equations your are done with it.

DNS for Navier Stokes can be gray area if not properly explained.

For incompressible flows, the smallest scales where the peak of the dissipation occurs decreases in size compared to the largest integral length scales as a power law of Reynolds number. Hence for very large Reynolds number practical DNS is most reliable but May be beyond our reach because of computational bottleneck. Consider for example, Atmospheric flows. DNS is impossible to do, because Reynolds number is 100,000,00,000 or more.

Another example, to consider is turbulent combustion. The Navier Stokes term does give the full description of the flow and ideally one would do DNS with no models and should be done. But there are chemical kinetics of 100's of species and many assumptions have to be made on the reaction kinetics which are sometimes serious simplifications.

So from these examples I wanted to show that in many practical problems DNS may be the "best" outcome, but may not be feasible either because resolving all scales are impossible now or even when flow terms are completely well described and grid resolved, the chemistry for example might be hard to model (the reaction rates). Thus the flow which is coupled with the chemistry is not fully described as well.