I am reading something about LES. One thing confusing me is that LES is independent of Reynolds number. What does it mean?

Many thanks, Thomas

The SGS contribution does change with Reynolds number.

if the molecular viscosity doesn't appear in the filtered NS equation for turbulent flow, then what is Reynolds number? infinte?

The molecular viscosity does appear in the filtered equation. The sub grid viscosity (the sub-grid contribution) is added to this to give a new viscosity which acts on the flow.

As Reynolds number increases (infinite), the viscous stress reduces (goes to zero), but the SGS contibution increases to provide dissipation

Can we ignore the molecular viscosity at all in the first place when we derive the filtered NS equation?

Regarding the SGS dissipation, on what range of spectrum tubulent energy is dissipated by it. If the SGS contribution can be divided into two parts when molecular viscosity is set as non-zero, what is the difference between the two parts that are contributing to the total stress? -thanks.

1) Molecular viscosity cannot be neglected if a solid boundary is involved. The (LES) SGS terms go to zero near a solid boundary (Dynamic model). Otherwise, a damping function (Van Driest) is used to smoothly force it to zero.

2) The principle of LES is that since you are not resolving all scales (as in DNS), you have to find some way to dissipate the energy (which is subgrid in LES because you are resolving large scales) to mimic the energy cascade as we know from Kolmogorov theory.

3) The range of spectrum for SGS dissipation is really decided by the flow energy (Reynolds number), but is at the smallest scales (Kolmogorov). You will have to read books/literature to know more.