Lagrangian transport equations and an iterative solution method for turbulent jet flows

Turbulent jet flows exhibit Kelvin–Helmholtz type of instabilities at its onset. Using a Galilean transform, the Navier–Stokes equation leads to an explicit, solvable expression for the Reynolds stress gradient, which is verified through comparison with DNS (direct numerical simulation) and experimental data for canonical flows. The Reynolds stress budget shows that the momentum balance of u’², pressure, and viscous forces forms a triad of forces to generate the Reynolds stress. For jet flows, an additional Lagrangian transport equation for u’², also confirmed using data, constitutes a closure method, which is demonstrated and compared with experimental data and turbulence models. Similar approach is being tested in other turbulent flows.