Does the fluctuating velocity also lead to fluctuating pressure distribution? In RANS, there was no fluactating of pressure, is it only a simplification assumption to neglect the pressure fluctuation?

Yes, of course it does. In fact, in RANS there is fluctuating pressure. The pressure solves in the momentum equation and in the energy equation is the mean pressure, but since the pressure terms are linear the fluctuating part automatically vanish throught the average processus.

On the other side, the non-local mixing effect of the fluctuating pressure over the fluctuating velocity (grad(pu)) that appears in the turbulent kinetic energy is modelised together with the triple correlation term (uuu) throught the turbulence viscous term. That's why they don't clearly appears inthe k-eps equation.

For Reynolds Tensors RANS equation closure, this modelisation is less obvious since the (grad(pu)) terms are anistrope and play a major role in shear layer by damping the anisotropie of the Reynolds Tensor.

Hope that help,

Sylvain