Towards practical large-eddy simulations of complex turbulent flows

Turbulence that occurs in nature, or in engineering flows, is usually not, even approximatively, homogeneous. There are frequent variations of the mean velocity with position. By explicating the scale-by-scale energy budget of nonhomogeneous turbulence, it has been argued that the subgrid-scale (SGS) stress tensor should encompass two types of interactions [1, 2]: (i) between the mean velocity and the resolved fluctuating velocities (the rapid part of the SGS stress) and (ii) among the resolved fluctuating velocities themselves (the slow part of the SGS stress). The rapid part is related to the large-scale distortion, while the slow part is associated with the Kolmogorov’s energy cascade [3]. Interestingly, these developments end up with a shear-improved Smagorinsky model (SISM) [1], for which the SGS viscosity writes