Development of similarity relationships for energy dissipation rate and temperature structure parameter in stably stratified flows: a direct numerical simulation approach

摘要

In this study, a newly developed direct numerical simulation (DNS) solver is utilized for the simulations of numerous stably stratified open-channel flows with bulk Reynolds number (Re-b) spanning 3400-16,900. Overall, the simulated bulk Richardson number (Rib) ranges from 0.08 (weakly stable) to 0.49 (very stable). Thus, both continuously turbulent and (globally) intermittently turbulent cases are represented in the DNS database. Using this comprehensive database, various flux-based and gradient-based similarity relationships for energy dissipation rate (epsilon) and temperature structure parameter (C-T(2)) are developed. Interestingly, these relationships exhibit only minor dependency on Re-b. In order to further probe into this Re-b-effect, similarity relationships are also estimated from a large-eddy simulation (LES) run of an idealized atmospheric boundary layer (very high Re-b) case study. Despite the fundamental differences in the estimation of epsilon and C-T(2) from the DNS- and the LES-generated data, the resulting similarity relationships, especially the gradient-based ones, from these numerical approaches are found to be remarkably similar. More importantly, these simulated relationships are also comparable, at least qualitatively, to the traditional observational data-based ones. Since these simulated similarity relationships do not require Taylor's hypothesis and do not suffer from mesoscale disturbances and/or measurement noise, they have the potential to complement the existing similarity relationships.