Similarity in the far field of a turbulent round jet

In this paper, we test the idea of equilibrium similarity, for which all scales evolve in a similar way in a turbulent round jet, for a prescribed set of initial conditions. Similarity requirements of the mean momentum and turbulent energy equations are reviewed briefly but the main focus is on the velocity structure function equation, which represents an energy budget at any particular scale. For similarity of the structure function equation along the jet axis, it is found that the Taylor microscale lambda is the relevant characteristic length scale. Energy structure functions and spectra, measured at a number of locations along the axis of the jet, support this finding reasonably well, i.e., they collapse over a significant range of scales when normalized by lambda and the mean turbulent energy <q(2)>. Since the Taylor microscale Reynolds number R-lambda is approximately constant (similar or equal to450) along the jet axis, the structure functions and spectra also collapse approximately when the normalization uses either the Kolmogorov or integral length scales. Over the dissipative range, the best collapse occurs when Kolmogorov variables are used. The use of <q(2)> and the integral length scale L provides the best collapse at large separations. A measure of the quality of collapse is given. (C) 2005 American Institute of Physics