BTW, I know it might be impossible because the total grid number I need is approximately Re^(9/4). But I want to use a finer mesh to try LES simulation. But I cannot find a criterion about mesh size used in LES, maybe delta x and delta z? But I think if I could draw a mesh which could be close to kolmogrove scale, it would be great.

I'm I'm pretty sure that in your case L is either related to the cylinder dimensions (most likely diameter) or to how you assigned the inlet/initial turbulent fluctuations. However I expect the cylinder dimensions to eventually dominate the spectral content

OK. That's almost blow my brain. It's not possible in my question to use DNS:). So I turn up to LES, but do you know what about the mesh resolution in a LES simulation? I remember there is a concept called delta x, delta z, but I cannot find any exact support material and the calculation method of delta x and delta z. Any suggestions?

Best,
Gang

As Paolo wrote, you can assume that the integral length scale is of the order of the diameter. Your domain must be enough long and large to allow a physical correlation of the structures at such length. I suppose you assume periodic condition in spanwise direction and the extension must be enough wide.
In case of a DNS you need of a grid that must be refined in the BL in such a way that at least 3-4 nodes are at y+<1 (y+ is nothing but the local Re number measured in direction normal to the wall). This constraint is valid also for a resolved LES. In the latter case you can use a larger grid size in spanwise direction.

Yes, my yplus around the structures is averaged 0.5. Yes, I know i couod use a little bit larger mesh in the spanwise direction. I think it should also be refined, to achieve my resolved part of TKE, or resolved Reynolds stress could take 80% of the total TKE , or total Reynolds stress. But I cannot find the reference about how fine should I apply on the spanwise and close-to-structured mesh. Do you have any reference about this?

Best,
Gang

while close to a wall you need to resolve the BL profile, that means you need more nodes in the viscous sublayer, the spanwise direction can be discretized in LES using dz+ =20-30.
There are references in the textbook of Sagaut as well as papers published. For example have a look here https://www.researchgate.net/publica...ates_revisited