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Unformatted text preview: iment
mentioned in previous lectures, see figure in the next slide). This
corresponds to scales more than three times smaller than η. Field experiment in Sils
Maria, Switzerland, 2004
Reλ= 7⋅103 Thus, because it is not possible to separate eddies
into clearly defined classes according to the source
of their energy (decompositions?); and as there is no object,
for present purposes, in making a distinction based
on size between cumulus eddies and eddies a few
metres in diameter (since both are small compared
with our coordinate chequer), therefore a single
coefficient is used to represent the effect produced by
eddies of all sizes and descriptions. (eddy viscosity).
RICHARDSON 1922.. Decompositions, locality, in general, and of
cascade, energy (or whatever) flux, in particular.
Any decomposition results in a nontrivial bidirectional relation between small and
the large scales (whatever this means) which is non-local (functional) both in
space and time (i.e. history-dependent). Hence there is little chance that this
dependence can be local (in several meanings) as is insisted for quite a period of
time. Today – also in view of accumulating evidence - its is becoming clear that
locality is at best an extremely crude approximation which in many cases is good
for empirical purposes, but not as a basis for studying the physics of turbulence.
All the attempts to find a ‘good' decomposition are related to what Betchov called
the ‘dream of linearized physicists', i.e. a superposition of some, desirably simple
elements. The dream is, of course, to find sets consisting of small number of
weakly interacting elements/objects adequately representing the turbulent field. The dream is, of course, to find sets consisting of small number of weakly interacting
elements/objects adequately representing the turbulent field. Those known so far are
interacting strongly and mostly nonlocally*. This is a reflection of one of the central
difficulties in 'solving the turbulence problem' as a whole, in general, and the
‘closure problem' such as LES...
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- Spring '11
- The Land