Two-point similarity in turbulent planar jet flows

A similarity analysis was performed using the governing equations for the two-point velocity correlations and for the second order structures functions in the far field of a turbulent planar jet. The equilibrium of the large- and small-scale motions was ensured by requiring that the turbulent transfer terms are in equilibrium throughout the flow. The results show that the equations for the two-point velocity correlations at large separation distances admit similarity solutions where the dissipation rate is proportional to uo3/lo when the growth rate of the flow is constant and proportional to Uouo2/δ or uo3/lo(dδ/dx1)−12 when the growth rate decreases as the flow evolves. The turbulent normal stresses decay at x1−1 in all solutions suggesting that the change in dissipation rate is associated with a change in the development of the mean flow. The analysis for the structure functions show that these equations admit similarity solutions for the inertial range with a length scale proportional to the Taylor microscale λ. The scale for the third order structures function is proportional to ϵλ or uo3/Reλ in all cases, but the velocity scale for the second order structure functions is proportional to uoReλ−(1−ns)/(3−ns) where ns ≤ 1. The velocity scale is uo when ns is 1 but previous measurements in high Reynolds number planar jets (Pearson and Antonia, 2001, J. of Fluid Mech., 444, 343-382), indicate that ns ≲ 0.