Constructing Flux- and Gradient-based Similarity Relationships for Stably Stratified Flows using Direct Numerical Simulation

In this work, we evaluate the feasibility of constructing similarity relationships for stably stratified flows using direct numerical simulation (DNS). A DNS dataset is created including numerous simulations of stably stratified channel flows with a wide range of Reynolds numbers and Richardson numbers. Utilizing this comprehensive DNS dataset, various flux- and gradient-based similarity relationships are constructed. These numerically generated similarity relationships are then compared with the existing similarity relationships proposed based on observational data. Despite the relatively low Reynolds number in the DNS runs, the simulated similarity relationships are comparable, at least qualitatively, to the traditional observational data-based ones. Since these simulated similarity relationships do not suffer from mesoscale disturbances and/or measurement noise, their uncertainty is much less compared with the observationally-based ones. Therefore, the DNS approach is shown to have the potential to complement the existing similarity relationships.