An empirical expression for εθ on the axis of a slightly heated turbulent round jet

Self-preservation analyses of the equations for the mean temperature and the second-order temperature structure function on the axis of a slightly heated turbulent round jet are exploited in an attempt to develop an analytical expression for epsilon(theta), the mean dissipation rate of (theta(2)) over bar /2, where (theta(2)) over bar is the temperature variance. The analytical approach follows that of Thiesset et al. (J. Fluid Mech., vol. 748, 2014, R2) who developed an expression for epsilon(k), the mean turbulent kinetic energy dissipation rate, using the transport equation for (delta u) over bar (2), the second-order velocity structure function. Experimental data show that complete self-preservation for all scales of motion is very well satisfied along the jet axis for streamwise distances larger than approximately 30 times the nozzle diameter. This validation of the analytical results is of particular interest as it provides justification and confidence in the analytical derivation of power laws representing the streamwise evolution of different physical quantities along the axis, such as: eta, lambda, lambda(theta), R-U, R-Theta (all representing characteristic length scales), the mean temperature excess Theta(0), the mixed velocity-temperature moments (u theta(2)) over bar, (v theta(2)) over bar and (theta(2)) over bar and epsilon(theta). Simple models are proposed for (u-theta(2)) over bar and (v theta(2)) over bar in order to derive an analytical expression for A(epsilon theta), the prefactor of the power law describing the streamwise evolution of epsilon(theta). Further, expressions are also derived for the turbulent Peclet number and the thermal-to-mechanical time scale ratio. These expressions involve global parameters that are most likely to be influenced by the initial and/or boundary conditions and are therefore expected to be flow dependent.