Hidden intermittency and a DNS of a turbulent round jet at a high Reynolds number

In experiments and simulations of turbulent round jets, similarity is observed primarily for the mean velocity. Using symmetry methods, we calculate similarity-type scaling laws for arbitrarily high moments of velocity from the infinite set of moment equations. Most centrally, symmetry theory provides moment-based scaling on instantaneous rather than fluctuation velocities. To prove its validity, a large-scale direct numerical simulation (DNS) of a turbulent jet flow was conducted at Re=3500 and a box length of z/D=75. As an inlet, a fully turbulent pipe flow is utilized to obtain similarity at small z. Nearly perfect similarity is observed in the z/D=25−65 range and this is especially true for U_z-moments up to order n=10. In matching theory and DNS data, we found that U_z-moments show Gaussian-like curves that get increasingly narrower with n, and this n-dependence is non-linear. The two statistical symmetries describing non-Gaussianity and intermittency, which were central for high-order moments in near-wall turbulence, are broken for turbulent jets. Instead, we find a new statistical symmetry, which, like the other two, is also based on the linearity of the moment equation.