Dynamics of Passive Scalar in Swirling Turbulent Far Wakes

The dynamics of passive scalar in swirling turbulent far wakes with varied values of the total excess momentum and angular momentum are described within a second-order mathematical model. The model includes averaged equations of momenta, turbulence energy balance, dissipation rate transfer, averaged concentration, and dispersion of its turbulent fluctuations in the far wake approximation. The closure of the mathematical model is based on Rodi’s algebraic model of the Reynolds stresses. At large distances, a self-similar solution based on numerical experiments is obtained for problems of the dynamics of passive scalar in turbulent wakes behind a self-propelled body and in a momentumless swirling turbulent wake. The group-theoretical analysis of the mathematical model under study is carried out. The model is reduced to a system of ordinary differential equations, which is solved numerically by the shooting method. The resulting solution is compared with the self-similar solution found by direct numerical integration of the differential equations of the model at large distances from the body. Good agreement is obtained. The problem of asymptotic behavior of characteristics of passive admixture in a swirling turbulent wake behind a sphere with nonzero values of the total excess momentum and angular momentum is also considered. With application of the group-theoretical analysis, it is shown that there is no physically meaningful self-similar solution to the equations of passive admixture dynamics.