Boundary layer entrainment for different capping conditions

Using large-eddy simulations, we consider the rate of entrainment across the top of quasi-steady convective boundary layers for a wide range of capping conditions. These conditions include both large and small temperature jumps and wind shear, cases with a rigid lid and an imposed downward heat flux, and cases with a second buoyantly driven layer above the primary one. In order to compare the entrainment rates for different conditions, it is necessary to properly non-dimensionalize the results. For dry convective boundary layers this is usually done in terms of the surface heat flux and the height of the mixed layer. For the wide range of capping conditions we consider, however, the horizontal mean profiles of temperature, heat flux, etc., can be radically different near the inversion region, making it problematic to find a universally applicable definition of the mixed layer height based on local inversion properties. In previous work (JAS 1998, p2645) we argued that for at least some conditions the entrainment rate is set by the boundary-layer-scale eddy dynamics and is therefore insensitive to the details of the near inversion properties. Consistent with this philosophy, we use properties of the boundary layer as a whole (such as the rate of temperature increase within the boundary layer) to scale our LES results, in place of a height defined using some inversion feature (though the two agree when the latter can be unambiguously defined). Comparing our results in this way, we find that the entrainment efficiency is, to a good approximation, independent of the capping conditions.

The cases where the shear production becomes significant warrant more attention because the inversion gradients can change significantly over time, and the shear dynamics can exhibit a strong intermittency. The boundary-layer convection driven entrainment sharpens the inversion temperature and velocity gradients. This increases the level of shear instability locally in some regions, touching off short periods of intense shear production. The resultant mixing reduces the gradients, whereupon the cycle may repeat. Assuming that the entrainment into the mixed layer itself is governed by the buoyantly driven boundary-layer-scale eddies in the same way as in the absence of large shear, we can infer what portion of the negative entrainment buoyancy flux is a result of the shear production. The ratio of this to the shear production itself (i.e., the appropriately defined flux Richardson number) we find to be fairly constant with a value near .25 for different shear cases, as well as for different time periods within a given case (following the intermittency). This is for shear production within the inversion region; we find shear production within the boundary layer or near the surface to be far less efficient in driving entrainment.

We may also add results from more recent LES entrainment experiments and discuss the nature of the large eddy dynamics which may be responsible for setting the entrainment rate.