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Reynolds number

A measure of the non-linearity of Navier-Stokes equations is given by the Reynolds number

where $L$ and $U$ are respectively the typical length scale and velocity of the fluid, e.g. in a pipe flow $L$ is the diameter of the pipe and $U$ the mean velocity. It was introduced by Osborne Reynolds, who showed that a transition between laminar and turbulent flow occurs when the $Re$ number reaches a critical value. Different geometries of the flow may change the critical $Re$ 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 ${\bf u} \cdot \nabla {\bf u}$ and the viscous term $\nu \Delta {\bf u}$:
Because of its definition, the limit $Re \to \infty$ in which fully developed turbulence is achieved, can be rephrased as the zero-viscosity limit $\nu \to 0$.

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next up previous contents
Next: Energy balance Up: Navier-Stokes equation Previous: Navier-Stokes equation   Contents

Stefano Musacchio 2004年01月09日