Direct simulation of a self-similar turbulent mixing layer

Abstract

Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart [J. Fluid Mech. 187, 61 (1988)]. In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the ‘‘braid’’ regions, and scalar mixing that is characterized by ‘‘marching’’ probability density functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are ‘‘nonmarching.’’ It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings. .