Fig.I-29
Turbulence may be viewed upon as a process which makes possible faster dissipation of fluid motion at high Reynolds numbers, where otherwise the viscous damping would not be effective.

Statistical approach

Solution of turbulent flows is very difficult as a result of the chaotic character of vortical motions. Direct calculation of all vortices is out of question even for the most powerful present-day computers (Fig. I-31) since it would be necessary to compute all motions down to the tiny Kolmogorov microscale, which is of the order of hundredth to thousandth of a millimetre. These computations would be, as a matter of fact, extremely wasteful because they would
Fig.I-31 Com-
puter speed
(in FLOPS ... floating-
-point operations per
second) and RAM
memory requirements
for numericl solution
of turbulent flows.
Reynolds equations
(based upon statistical
approach) are at the
limit of what is
possible in practical
engineering problems.
DNS is still more
or less a dream -
several extremely laborious compu-
tations performed so far are still only
for Reynolds numbers well below
realistic values.
evaluate, at great expense, information not actually needed, at least for engineering purposes. What an engineer needs are statistical means - such as time-mean force action of air on
Fig.I-32
a moving car body. This fact has been at the foundation of the statistical approach to turbulence. basically, it is concerned in finding the most probable quantities in sufficiently great number of realisations of a particular process - as shown in the example of histories of velocity component in repeated unsteady flows in Fig.I-32 or in Fig.I-33. In the latter case the organised unsteady component is periodic (either as a result of periodic operation of some - e.g. reciprocating - machine, or resultant from cogerent vortices existing in turbulence). In the classical statistically stationary flow case,
Fig.I-33
we discriminate only between the the time-mean value and deviations from it, which are considered stochastic (in spite of possible contents of coherent motions). This approach originated already towards the end of the last century (Reynolds, 1893). Unfortunately, it did not fulfill the hopes originally laid into it. Because of the quadratic nonlinearity of governing equations, the introduction of time mean and fluctuating components generate additional variables - more of them, actually, than the number of available equations. To make the problem solvable, it is necessary to introduce some (unfortunately, more or less speculatrive) additional relations.


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This is page Nr. I09 from textbook Vaclav TESAR : "BASIC FLUID MECHANICS"
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