Large-Eddy Simulation of a Three-Dimensional Mixing Layer
With the aid of an appropriate parameterization, we simulate numerically a three-dimensional turbulent mixing layer at high Reynolds number. Results are compared with corresponding direct simulations performed with the same pseudo-spectral numerical code. Periodicity is assumed in streamwise and spanwise directions. The evolution of a passive temperature is calculated simultaneously.
Both two- and three-dimensional instabilities grow naturally from a small amplitude three-dimensional random perturbation superimposed upon the basic hyperbolic tangent velocity profile.
Kelvin-Helmholtz billows, greatly distorted three-dimensionally, are found in both cases. We discuss the comparative growth of three-dimensional spanwise modes and two-dimensional instabilities.
Spatially-organized longitudinal structures appear, carrying streamwise vorticity which grows rapidly and levels off at about 2.5 times the initial vorticity brought by the inflexional shear. The spanwise spacing between these streamwise vortices is found and is in good agreement with recent high Reynolds number experiments.
Both in large-eddy and direct simulations, the growth rate of the vorticity thickness and the variance of the velocity fluctuations, obtained after streamwise and spanwise averaging, are also in good agreement with their experimental counterparts.
Spectra of kinetic energy and temperature fluctuations variance, obtained from large-eddy simulation, are both found to cascade with a slope of about −2. Calculations with a larger spatial resolution and a different spectral eddy-viscosity will soon be made.
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