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Reynolds number
A measure of the non-linearity of Navier-Stokes equations is given by the
Reynolds number
 |
(1.7) |
where
and
are respectively the typical length scale
and velocity of the fluid, e.g. in a pipe flow
is the diameter
of the pipe and
the mean velocity.
It was introduced by Osborne Reynolds, who showed that a transition
between laminar and turbulent flow occurs when the
number reaches
a critical value. Different geometries of the flow may change
the critical
number, but the transition is
universally controlled by this adimensional parameter.
The Reynolds number plays a fundamental role in turbulence, since it
gives a dimensional estimate of the relative weight between the
inertial term
and the viscous term
:
![\begin{displaymath}
{[{\mbox{\boldmath$u$}} \cdot \nabla {\mbox{\boldmath$u$}}] \over [\nu \Delta {\mbox{\boldmath$u$}}]}
\sim \frac{UL}{\nu}
\end{displaymath}](img91.png) |
(1.8) |
Because of its definition, the limit
in which
fully developed turbulence is achieved, can be rephrased as
the zero-viscosity limit
.
Next: Energy balance
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Previous: Navier-Stokes equation
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Stefano Musacchio
2004-01-09