imulations (please refer to their Fig. 1).

In summary, neither $\overline{\varepsilon} = \overline{e} N$ nor $\overline{\varepsilon} = \sigma_w^2 N$ are appropriate parameterizations for weakly or moderately stratified conditions; they may provide reasonable predictions for very stable conditions. In contrast, the shear-based parameterizations should be applicable from a wide range of stability conditions, from near-neutral to at least $Ri_g \approx 0.2$. Since within the stable boundary layer, $Ri_g$ rarely exceeds 0.2 [see @nieuwstadt84], we believe Eq. \[EDR1\] or Eq. \[EDR2\] will suffice for most practical boundary layer applications. However, for free atmosphere, where $Ri_g$ can exceed O(1), Deardorff’s parameterization (i.e., $\overline{\varepsilon} = 0.25 \overline{e} N$) might be a more viable option. Unfortunately, we cannot verify this speculation using our existing DNS dataset.

Concluding Remarks
==================

The boundary-layer community almost always utilizes buoyancy-based energy dissipation rate parameterizations for numerical modeling studies. Only a few studies [e.g., @grisogono08; @rodier17] have explored the possibilities of combining buoyancy-based and shear-based parameterizations. In this paper, we demonstrated that shear-based parameterizations are much more appropriate for stable boundary layer flows as long as $Ri_g$ does not exceed 0.2. Our DNS-based results are in complete agreement with the theoretical work (supported by numerical results) of Hunt et al. [@hunt88]. They concluded:

> “...when the Richardson number is less than half, it is the mean shear ... (rather than the buoyancy forces) which is the dominant factor that determines the spatial velocity correlation functions and hence the length scales which determine the energy dissipation or rate of energy transfer from large to small scales.”

We sincerely hope that our community will begin to appreciate this incredible insight of Hunt and his co-workers in future modeling studies (including large-eddy simulati