Flux Richardson Number and Turbulent Prandtl Number in a Developing Stable Boundary Layer

Abstract

Wind tunnel experiments and large-eddy simulations for stable stratification are performed to specify flux Richardson number Rf and turbulent Prandtl number Pr as a function of gradient Richardson number Ri. We attempted to avoid self-correlation by using independent samples for the variables commonly contained in these nondimensional numbers and confirmed the dependence of Rf and Pr on Ri for 10 −3 < Ri < 5. We found that Rf could exceed unity in a stable boundary layer under a developing stage, while the assumption of local energy balance violates for Rf > 1, which corresponds to negative production of turbulent kinetic energy. Nevertheless, the analysis of the TKE budget shows that the third-order term in the prognostic equation of TKE, which plays a role in the TKE transfer, can contribute to increase TKE despite negative TKE production. Therefore, TKE cannot be determined locally and the effects of TKE transfer must be taken into account in the region satisfying Rf > 1.

Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

“…(1). However, it is consistent with the findings reported by [35] based on wind tunnel experiments and large-eddy simulations; refer to their Fig. 3.…”