Effect of scalar-field initial conditions on the evolution of the scalar dissipation rate budget in turbulent channel flow*

Direct numerical simulations were performed to investigate the dependence of scalar mixing within turbulent channel flow on the initial conditions of the scalar field itself.  Three distinct initial fields are mixed by identical hydrodynamic fields.  The equations of conservation of mass and momentum were solved by way of a spectral method using a code entitled CHANNELFLOW (Gibson et al., 2008; Gibson, 2010; http://channelflow.org/), and the advection-diffusion equation was solved using a flux integral method entitled 3DFLUX (Germaine et al., J. Fluid Mech., 2013).  The three flows depict distinct differences in the scalar-field evolutions, and thus exhibit clear dependencies on the initial conditions.  These differences, which are also reflected in the evolutions of the unmixedness and the mix-norm, are explained by investigating the evolutions of the different terms in the scalar dissipation rate budget. To enhance mixing in such a flow, it is recommended that initial interfaces of the scalar field be aligned normal to the mean velocity vector.