Direct numerical simulations of a statistically stationary and streamwise periodic turbulent mixing layer

Turbulent mixing layers are one of the most studied turbulent free shear flows and are found in combustion, aerodynamics, and atmospheric applications. Most turbulent mixing layer simulations are computationally inefficient. In temporally evolving (spatially homogeneous) mixing layers, the thickness continuously grows in time and most of the simulation time is wasted resolving the transient behavior. Spatially evolving (temporally stationary) mixing layers grow in space and require a long streamwise domain to develop the desired Reynolds number. To combat these limitations, we propose a method utilizing direct numerical simulation (DNS) of incompressible turbulent mixing layers that normalize the coordinate system under which the Navier-Stokes equations (NS) are solved. Anticipated self-similarity is used to develop this scaling and introduces additional unclosed source terms involving the mixing layer growth rate which are resolved on the fly using the simulation data. This approach is an extension of Ruan (2021) where this technique was originally applied to turbulent flat-plate boundary layers. To validate our approach, we compare mean, extracted growth rates, rms, and Reynolds shear stress profiles with other DNS calculations of turbulent mixing layers.