Symmetry Theory and Turbulent Jet Scaling Laws of a Spatially Evolving Turbulent Round Jet

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 a Reynolds number \({ R e}=3500\) based on the jet diameter D and jet-inlet bulk velocity \(U_\text {b}\) in a box with the length of \(z/D=75\) . Almost 200 washouts are calculated for a very good statistical convergence. Virtually perfect similarity is observed in the \(z/D=25-65\) range and this is especially true for \(U_z\) -moments up to order \(n=10\) . Integration constants in the prefactor of the scaling laws are independent of the moment order n and therefore universal. Further, in matching theory and DNS data, we found that the \(U_z\) -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.