Geoscience Reference
In-Depth Information
We l abe l i t
χ
u
i
c
because it has the form of a molecular destruction term. But under
local isotropy it vanishes (
Part III
), and the measurements of
Mydlarski
(
2003
)
confirm that; thus we shall neglect it.
Parallel arguments hold for the molecular terms in the stress budgets, so we
neglect them as well.
Questions on key concepts
5.1 Explain the physical meaning of the turbulent-flux conservation equations.
Why are they needed? In what applications are they used?
5.2 How can the equations give indications of whether a given second moment
is zero or nonzero?
5.3 How can the equations give indications that energy-containing-range fluctu-
ating variables have an
O(
1
)
correlation coefficient, as scaling guideline 2
indicates?
5.4 Explain scaling guideline 4 physically.
5.5 Explain the physical meaning of a “mixed-scale” covariance. Why is it
difficult to scale?
5.6 Explain physically why a spatial derivative of a covariance of turbulent vari-
ables scales differently than a covariance of a spatial derivative of turbulent
variables. What is their ratio?
5.7 Explain physically why the time-change and mean-advection terms in a
second-moment budget can involve external scales. Explain how this can
lead to a quasi-steady, locally homogeneous state. Give an example.
5.8 Which term in the velocity-velocity and velocity-scalar second-moment
equations do you find most difficult to interpret physically? Explain.
5.9 Interpret physically each term in the conservation equation for fluctuation
c
. Which term can be interpreted as a rigorous statement of mixing-length
ideas? Explain.
5.10 Discuss the range of scales involved in a variance conservation equation.
5.11 Discuss how the sign of a covariance can be diagnosed from its conservation
equation.
5.12 Discuss how the conservation equation for the flux of a conserved scalar can
reduce to an eddy-diffusivity model. Show that the vertical flux equation
is consistent with a scalar eddy diffusivity, but the horizontal flux equation
shows it to be a second-order tensor.
5.13 Explain why pressure fluctuations (scaling guideline 1,
Subsection 5.3.2
)
do not scale with
ρUu
, which is much larger than
ρu
2
. (Hint: consider a
Galilean transformation of the coordinate system.)
5.14 Explain why the pressure covariance term in the turbulent flux budget can
be interpreted as a rate of production of opposite-signed flux.
