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4.2 Explain how the averaging process allows us to write the mean flux in the
averaged form of the scalar conservation equation (1.29) as the sum of mean-
mean, turbulent, and molecular diffusion parts.
4.3 In equation terms, why does the mean temperature outside in the morning
increase predictably on sunny days?What is the physical mechanism causing
this increase?
4.4 What is the physical mechanism underlying the diffusion of a plume from a
point source in laminar flow? In turbulent flow? By what ratio do the effective
diffusivities differ?
4.5
Explain how we can often diagnose the turbulent flux profiles in turbulent
flow. Illustrate with an example.
4.6
Explain the essence of the “mixing-length” idea.
4.7
Interpret
the physical origins of the horizontal
turbulent flux term in
Eq. (4.11) .
4.8 Interpret Eq. (4.11) through a mean mass balance for a control volume down-
stream of a line source in the cross-stream direction. Explain physically why
each of its terms is nonzero.
4.9 Explain why the entrainment flux at the top of the convective boundary layer,
Figure 4.1 , is negative.
4.10 Explain physically why we expect the Lagrangian autcorrelation function to
be nonzero for some initial time period.
4.11 In an Eulerian frame the Taylor problem of Subsection 4.3.2 is stationary.
Why is it nonstationary in a Lagrangian frame? In what problem would it
also be stationary in a Lagrangian frame?
Problems
4.1
A reactive trace constituent having the evolution equation
D
c
Dt =
˜
c
τ ,
˜
2
γ
c
˜
with τ a decay time scale, diffuses in a turbulent flow. Assume that in this
flow a conserved constituent has an eddy diffusivity. Using the mixing-
length ideas, discuss under what conditions you would and would not
expect this reactive constituent to have the eddy diffusivity of a conserved
constituent.
4.2 Why might the horizontal turbulent temperature flux be of little practical
consequence in a boundary layer, even though it can be larger than the vertical
flux?
 
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