Geoscience Reference
In-Depth Information
Many of the initial successes of the models
...
have been in flows
...
where details of
the models are irrelevant. Thus emboldened, the modelers have been over enthusiastic
in promoting their models
...
often without considering in depth the difficult questions that
arise. Consequently, there is some disillusionment with the models
...
This reaction is prob-
ably justified, but it would be a shame if it resulted in a cessation of efforts to put a little
more physics and mathematics into the models.
By the mid-1980s LES was being widely used in research applications in both
geophysical and engineering flows. It showed a universality lacking in second-
moment turbulence models. A decade later,
Bradshaw
(
1994
)wrote:
...
even if one makes generous estimates of required engineering accuracy and requires
predictions only of the Reynolds stresses, the likelihood is that a simplified model of tur-
bulence will be significantly less accurate, or significantly less widely applicable, than the
Navier-Stokes equations themselves - i.e., it will not be “universal”.
...
Irrespective of the use to which a Reynolds-stress model will be put, lack of univer-
sality may interfere with its calibration. For example, it is customary to fix one of the
coefficients
...
so that the model reproduces the decay of grid turbulence accurately. This
involves the assumption that the model is valid for grid turbulence as well as in the flows for
which it is intended - presumably shear layers, which have a very different structure from
grid turbulence.
...
It is becoming more and more probable that really reliable turbulence
models are likely to be so long in development that large eddy simulations (from which, of
course, all required statistics can be derived) will arrive at their maturity first.
In a later meeting
Bradshaw
(
1999
) summarized:
Perhaps the most important defect of current engineering turbulence models
...
is that their
non-universality
(the boundaries of their range of acceptable engineering accuracy) cannot
be estimated at all usefully a priori.
...
very few codes output warning messages when the
model is leaving its region of proven reliability.
The 20 years spanned by these comments saw Liepmann's pessimism about
turbulence modeling, then Lumley's appeal for broader understanding of its nature
and more patience with the model-development process, next Bradshaw's tacit
acceptance that before turbulence models become adequately reliable they may
be replaced by LES, and finally Bradshaw's doubts that we know enough about
turbulence-model reliability. The turn to LES is evident in geophysical applications,
where it has been used since the 1970s to generate surrogate “databases” for research
and more recently to evaluate turbulence models and parameterizations (
Ayotte
et al
.
,
1996
).
As we shall see in
Part II
, because of their larger scales and smaller speeds
geophysical flows tend to be much more strongly influenced by buoyancy. Because
of the tendency of turbulence models to nonuniversality, those for geophysical
applications need their own development and assessment process. The geophysical
community has recently pointed to the need to recognize, accommodate, and foster
