The convective boundary layer - Turbulence in the Atmosphere - page 264

11.11 Derive the conservation equation for θ 3 in a CBL. Simplify it as muc h a s
possible. What is its principal source term? Use it to predict the sign of θ 3 .
11.12 What do the results of Section 11.3 imply about the vertical diffusion of trace
species in cloud layers?
11.13 Discuss the influence of the parameter m = fz i /w ∗ on themeanwind profile
in a baroclinic CBL. Can you interpret m physically?
11.14 Use Eq. (11.19) to show that the scalar flux profile is linear in a quasi-steady,
horizontally homogeneous ABL.
11.15 Derive the Poisson equation for pressure by taking the divergence of the
Navier-Stokes equation. How does it indicate that the pressure field in the
ABL is fundamentally different from that in a constant-density engineering
flow?
11.16 Using the approach in Eqs. (11.27) and (11.28) ,derive Eqs. (11.31) and
(11.32) . Assume that any two c t ,andanytwo c b , are perfectly correlated.
(Is that a reasonable assumption? Discuss.)
11.17 Derive Deardorff's expression for γ θ in Eq. (11.33) . Use the scalar flux con-
servation equation (10.48), assume the turbulent transport term is negligible,
and model the pressure-destruction term with a Rotta time scale.
11.18 Show that if τ u τU the time-change and horizontal advection

terms in the stress budgets Eqs. (11.14) and (11.15) are negligible.
11.19 Develop a criterion for the negligibility of the time-change term in the mean-
momentum balance (11.3) . Then show that this criterion can be difficult to
meet in practice.
11.20 Show that Eq. (8.69) does yield the TKE budget (11.2) for a horizontally
homogeneous ABL. Why does the Coriolis term vanish?
11.21 Explain why R ∗ , Eq. (11.47) , is characteristic of CBL structure.

τ and L x

References
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Van Dop, Eds., Dordrecht: Reidel, pp. 107-158.
Deardorff, J. W., 1966: The counter-gradient heat flux in the atmosphere and in the
laboratory. J. Atmos. Sci. , 23 , 503-506.
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