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Since the small-scale motion is determined by only two

parameters: dissipation rate and viscosity, there are

unique length, velocity and time scales that can be

formed using dimensional analysis

( )( )

( ) 21

41

413

/

/

u

which are called the Kolmogorov scales

There are two identities stemming from definition of theKolmogorov scales:

1Re ==

u- Kolmogorov scale is small enough for

dissipation to be effective

( ) 22

== u - showing that

1=u provides a

consistent characterization of the velocitygradients of the dissipative eddies

The ratios of the smallest eddies to largest scales are readily

determined from the definition of the Kolmogorov scales

and from the scaling introduced earlier 03

0lu

21

0

41

0

43

0

Re,Re,Re

u

u

l

Evidently, at high Reynolds number, the scales of smallest

eddies are small compared to those of larges eddies

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At sufficiently large Reynolds number the ratio 0l is so

small that there is a range of scales l that are very smallcompared to l0 , and yet very large compared with

0ll

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