(u_mean + u') * (u_mean + u') * = u_mean*u_mean + 2*u_mean*u' + u'*u' The assumption here is that the turbulent scaled is veri smol, so that when averaging that, avg(u') = 0, so avg(2*u_mean*u') = 0 also. This is a reason why by taking delta_t --> 0 for URANS solution, you will never converge to DNS results