time step size requirement

turb

Dear CFDers, Stupid question: is there any number (analog to CFL condition) dictating numerical sustaining of turbulence?

What I mean is: suppose I dont use any Subgrid model in LES and try to run some simulation in a let's say coarse mesh. In this case, one would be able to run with time step size bigger than the one associated with the highest "physical" frequency present, but still respecting CFL condition. Altough this would (pehaps) have no physical meaning, from the numerical point of view, is there any theorem about wether it is possible to get "oscilatory" solutions (just like turbulence)? And some criteria on how big can this time step be in order to still have this oscilatory, but unreal solution?

(Suppose we are using a non dissipative numerical scheme)

Any ideas/references?