Geoscience Reference
In-Depth Information
Questions on key concepts
(Unless stated otherwise these refer to three-dimensional turbulence.)
7.1 What is the inertial subrange? What is required in order that a turbulent flow
have one? Describe its basic physics.
7.2
Discuss the energetics of the inertial subrange in turbulence.What determines
the eddy scale at which it begins? Ends?
7.3
Explain why the viscous dissipation rate is independent of the value of the
fluid viscosity.
7.4
Explain where, how, and why the scalar spectrum departs from the velocity
spectrum when the Prandtl or Schmidt number
1.
7.5 Explain how temperature and velocity signals differ qualitatively from their
derivative signals. How does this difference evolve as
R
t
increases?
7.6 What is dissipation intermittency? In what types of problems might it be
important?
7.7 How does the observed behavior of turbulent fine structure violate Kol-
mogorov's universal equilibrium hypothesis?
7.8 Give an example of a process in the lower atmosphere that might be
strongly impacted by dissipation intermittency.
7.9 Discuss the analogy between the inertial ranges of two- and three-
dimensional turbulence.
7.10 Explain the analogy between the vorticity variance budget in 2-D turbulence
and the scalar variance budget in 3-D turbulence.
7.11 Turbulence was studied for many years before Kolmogorov proposed his
unifying hypotheses for its small-scale structure. Why do you think it took
so long for these hypotheses to emerge? What was the key to his discovery?
7.12 Explain the physical essence of the Kolmogorov-Obukhov revision of the
Kolmogorov
(
1941
) ideas. Can you argue physically that it is plausible that
local fine structure scales with local rather than global parameters? Can you
think of problems in other fields where this would seem to be the case?
7.13 Explain qualitatively the difference between the finest-scale structure of low-
R
t
laboratory turbulence and that in a cumulus cloud, and how it can impact
droplet physics in the two flows.
7.14 Explain how the Kolmogorov ideas of the global dynamics of 3-D turbulence
apply to 2-D turbulence. How and why do they differ in detail?
=
Problems
7.1
Explain why for separations
r
in the inertial range of scales the dominant
contributions to structure functions come from eddies of scale
r
.
