Turbulent fluxes - Turbulence in the Atmosphere - page 87

4.3 Have you seen chimney plumes that do not diffuse? Under what atmospheric
conditions have you seen them? Sketch what you have seen. What causes
this behavior?
4.4 What is the physical origin of the flux-gradient relation in molecular dif-
fusion? What averaging process is involved? Such a flux-gradient relation
need not apply to turbulent diffusion. What difference in the two processes
could account for this?
4.5 Prove that Eq. (4.8) , with its parameters defined as in Eq. (4.9) , is a solution
of Eq. (4.7) .
4.6 Flowbetween oppositelymoving parallel planes is calledCouette flow.When
is it laminar? Turbulent? Calculate the stress profile and the velocity profile
in laminar Couette flow. Why is the pressure gradient zero?
4.7 Calculate the stress profile in turbulent Couette flow. Sketch the mean veloc-
ity profile, contrasting it with the laminar case. Sketch the corresponding
profile of eddy diffusivity.
4.8 In a turbulent Couette flow one plane is held at temperature T 1 and the other
at T 2 . Write the mean temperature equation for this problem. Sketch the
vertical profile of turbulent temperature flux.
4.9 Water vapor enters a horizontally homogeneous atmospheric boundary
layer by evaporation from the underlying surface. The boundary layer is
deepening with time by entrainment of the overlying air, which is drier than
that in the boundary layer. The mean water vapor concentration does not
change with time.
(a) Write the mean water vapor concentration equation for this problem.
(b) Sketch and explain the profile of the vertical turbulent flux of water
vapor.
References
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Oxford University Press.
Corrsin, S., 1963: Estimates of the relations between Eulerian and Lagrangian scales in
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Csanady, G. T., 1973: Turbulent Diffusion in the Environment. Dordrecht: Reidel.
Lumley, J. L., 1962: The mathematical nature of the problem of relating Lagrangian and
Eulerian statistical functions in turbulence. Mécanique de la Turbulence ,Paris:
CNRS, pp. 17-26.
Lumley, J. L., 1989: The state of turbulence research. Advances in Turbulence ,
W. K. George and R. Arndt, Eds., New York: Hemisphere, pp. 1-10.
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