HERCULES

A high order finite difference solver for massively parallel simulations of stably stratified turbulent channel flows. Investigation of stably stratified turbulent flows in the atmosphere is challenging owing to its nonstationarity and heterogeneity, especially in very stable conditions. In recent years, numerical simulation has become a powerful tool to complement the understanding of fundamental characteristics of strongly stratified flows. Owing to its highly accurate representation of small-scale turbulence structures, direct numerical simulation (DNS) is shown to be the most effective numerical approach for strongly stratified flows. However, due to the limitation of the traditional parallel strategy, existing DNS studies on stratified channel flows are limited to relatively low Reynolds numbers. In order to make the DNS studies more relevant to the atmospheric boundary layer flows, in this paper, a high-order finite-difference DNS solver is developed for simulating stably stratified turbulent channel flows at relatively high Reynolds numbers. Utilizing the advanced two dimensional domain decomposition technique, the DNS solver is shown to be competent for petascale simulations with excellent scalability tested up to 32,768 CPU cores. Using this newly developed solver, two stably stratified open-channel simulations are conducted with the highest Reynolds number being approximately $10^{5}$. The fundamental characteristics of strongly stratified turbulent flows, e.g., spatio-temporal variation of global intermittency, are compared with those previously reported at relatively low Reynolds numbers, and their similarities and discrepancies are also discussed. In addition, the DNS-based Monin-Obukhov similarity relationships are compared with those proposed based on observational data to evaluate their relevance to atmospheric flows. The source code and the simulation results are available at url{http://sites.google.com/site/scdnscode/}.