The sensitivity of shallow mixing layers to upstream perturbations and its implication to numerical code validation

Abstract

Unsteady numerical simulations (Unsteady RANS or Large-eddy simulation) of shallow mixing layers are gaining attention in researches. However, the fact that the development of shallow mixing layers is sensitive to upstream perturbations poses a challenge to the validation of numerical results against experiments. A valid question is that whether upstream perturbations should be simulated in detail so as to obtain numerical results directly comparable to experiments. In an attempt to answer the question, the paper studies the sensitivity of the downstream dynamics of shallow mixing layers to upstream perturbations. Simulations of temporal shallow mixing layers are performed with different types of initial perturbations, noting that initial perturbations in temporal simulations correspond to upstream perturbations in spatial simulations. Results suggest that although the initial development of vortices is known to be sensitive to initial perturbations, agreement is obtained for the energy spectra at large times when the difference in the perturbation forms is at large wavenumbers, because of the dissipation by both the bottom friction and the sub-depth scale eddy-viscosity. When the difference in the perturbation forms is at small wavenumbers, the difference in the initial development of large scale coherent structures is kept in the energy spectra at large times as the bottom friction causes the mixing layer stable after a certain time. It may imply that numerically simulated energy spectra at the downstream are comparable to experiments without simulating precisely the high wavenumber upstream perturbations, but low wavenumber perturbations should be well incorporated in modeling so as to obtain the correct dynamics of the large-scale coherent structures.