Abstract
We use a database of direct numerical simulations to evaluate parametrizations for energy dissipation rate in stably stratified flows. We show that shear-based formulations are more appropriate for stable boundary layers than commonly used buoyancy-based formulations. As part of the derivations, we explore several length scales of turbulence and investigate their dependence on local stability.
Highlights
Energy dissipation rate is a key variable for characterizing turbulence (Vassilicos 2015)
Since L H is proportional to κz in the surface layer, it can be directly compared with the so-called master length scale (L M ) of Mellor and Yamada (1982)
Our direct numerical simulation (DNS)-based results suggest that shear-based parametrizations are more appropriate for regions of the stable boundary layer where Rig does not exceed 0.2
Summary
Energy dissipation rate is a key variable for characterizing turbulence (Vassilicos 2015). A few years later, Weinstock (1981) revisited the work of Chen (1974) and again made use of Eq 2, albeit with different assumptions (see Appendix 2 for details) He arrived at the following equation ε ≈ σw N ,. We quantify the relationship between ε and e (as well as between ε and σw) by using turbulence data generated by direct numerical simulation (DNS). To this end, we first compute several well-known “outer” length scales (e.g., buoyancy length scale and Ozmidov scale), normalize them appropriately, and explore their dependence on height-dependent stability.
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