The convective boundary layer - Turbulence in the Atmosphere - page 263

11.8 Explain what is meant by top-down and bottom-up diffusion. Why can the
first exist alone, but not the second?
11.9 Explain the physical meaning of the finding that the correlation coefficient of
top-down and bottom-up scalar fields is negative when both boundary fluxes
are into the CBL.
11.10 Explain why the CBL is often “well mixed” in but not in Q .
11.11 Explain the concept of entrainment velocity .
11.12 Explain physically why the entrainment velocity is typically much smaller
than the turbulence velocity scale u .
11.13 Explain why the ABL is apt to be baroclinic. Why is this not true of
engineering boundary layers?
11.14 Explain physically why the vertical flux of temperature is a source of TKE
in unstable stratification and a sink in stable stratification.

Problems
11.1 Explain why the concept of mixed-layer similarity is consistent with that of
local free convection.
11.2 Develop a criterion for the negligibility of the effects of horizontal inhomo-
geneity and time changes on mixed-layer similarity.
11.3 Discuss the averaging-time requirement for stress measurements in the CBL.
Does it explain why we know so little about stress profiles there?
11.4 Discuss the failure of mixed-layer similarity for scalars in the context of the
right panel of Figure 11.2 . What does that figure suggest also about the M-O
similarity of scalars?
11.5 Examine the potential importance of the term that horizontal advection of
mean momentum produces in the mean-shear equation. Is it likely to be as
important as baroclinity?
11.6 Interpret physically the reason why the correlation coefficient r tb in
Eq. (11.29) is nonzero. What sign do you expect it to have?
11.7 Generalize Eq. (11.42) to the more realistic case of finite depth of the
interfacial layer. Does it have an appreciable effect on the result?
11.8 Interpret in the context of the mixing-length model the failure of the eddy-
diffusivity model for diffusion of a conserved scalar in the CBL.
11.9 Stress measurements in the CBL are plagued by scatter, as Figure 11.8
indicates. How would area averaging help this? Use the expression for
convergence of a spatial average to the ens emble average.
11.10 Derive the conservation equation for w 3 in a CBL. Simplify it as mu ch
as possible. What is its principal source term? Does it explain why w 3 is

positive?