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whose quasi-steady solution is
C
PT
. Using the analogy with monetary budgets,
Launder
(
1996
) calls this the WET (
Wealth = Earnings times Time
) model. It has
useful diagnostic value
(Problem 5.4)
.
Beginning in the late 1960s, when growth in the size and speed of computers
made it feasible to solve such sets of partial differential equations numerically, the
turbulence community has used approximate versions of these covariance equations
as “second-moment” turbulence models. We now have nearly 40 years' experience
with such models in both engineering and geophysical flows.
5.6.2 History, status, and outlook
The use of second-moment turbulence models grew rapidly in the early 1970s. In
this period the modeling technique now called
large-eddy simulation
, or LES -
which as we'll discuss in
Chapter 6
is the time-dependent numerical calculation
of turbulent flow on a three-dimensional grid fine enough to resolve the energy-
containing eddies - also appeared (
Deardorff
,
1970
). LES attracted great interest,
but because it is vastly more demanding of computer resources it was not initially
competitive with second-moment modeling.
In a review paper on turbulence
Liepmann
(
1979
) criticized much of this early
second-moment modeling:
Problems of technological importance are always approached by approximate methods, and
a large body of turbulence modeling has been established under prodding from industrial
users. The Reynolds-averaged equations are almost always applied in such work, and the
hierarchy of equations is closed by semi-empirical arguments which range from very simple
guesses
...
to much more sophisticated hierarchies
...
.
I am convinced that much of this huge effort will be of passing interest only. Except
for rare critical appraisals such as the 1968 Stanford contest for computation of turbulent
boundary layers, much of this work is never subjected to any kind of critical or compar-
ative judgment. The only encouraging prospect is that current progress in understanding
turbulence will
...
guide these efforts to a more reliable discipline.
There were some early, in-depth assessments of the performance of second-
moment turbulence models, mainly in engineering but in geophysical applications
as well. The need was more pressing in engineering, and the requisite data were
much more accessible there. In time the salient features of these models became
evident. One is their lack of
universality
- their tendency to unreliability in flows
different from those used to develop them. In acknowledging this attribute
Lumley
(
1983
) cautioned that one should not expect too much from these models, which he
termed “calibrated surrogates for turbulence.” He felt they should “work satisfac-
torily in situations not too far removed geometrically, or in parameter values, from
the benchmark situations used to calibrate them.” He went on to write:
