### Reynolds number

**(Re, kinetic Reynolds number)**
(measure reflecting a fluid system's propensity to turbulence)

A **Reynolds number** (**Re**) is a measure of a solid configuration
adjacent to fluid moving relative to it, that characterizes the
configuration's propensity to create turbulence in the fluid,
e.g., how much turbulence can be expected.
It is a dimensionless number defined as the ratio of the fluid's
**inertial forces** to **viscous forces**.
Inertial forces are the apparent (fictitious) forces
felt when momentum is changed. In the case of a fluid,
the momentum change in question is that produced by
a barrier guiding the fluid's motion into a new trajectory,
i.e., to some degree sideways from the way it approached.
The viscous forces are forces of friction of the fluid
on itself, i.e., a measure of the fluid's tendency to
drag along adjacent fluid as it is moving.
The higher the *Reynolds number*, the more of a tendency to
turbulence as opposed to **laminar flow** (all the
fluid moving in parallel, though perhaps at different
speeds).

Reynolds numbers are calculated to characterize the
behavior of pipes, of ships and things moving through
water, airplanes and things moving through the atmosphere.
The number potentially depends upon the velocity of
the flow and the characteristics of the fluid, e.g.,
for ships, its speed, salt water versus fresh,
the water temperature, etc.
Examples (given a typical speed and typical conditions):

*USS Iowa* battleship: about 4 billion.
- Boeing 747: about 2 billion.
*Great Republic* clipper ship: about 600 million.
- A seagull: about 60 thousand.
- A honeybee: about a thousand.

A **magnetic Reynolds number** (**Rm** or **R**_{m} or **MRe** or **Rem**)
is an analog of Reynolds number relating the same inertial forces
to **magnetic diffusivity**, and also is a measure of
a propensity to turbulence. It is inversely proportional to
**resistivity** of the material (plasma).
When both are under discussion, the "ordinary" *Reynolds number*
may be distinguished by the term **kinetic Reynolds number**.
Formation of an astrophysical dynamo typically requires
turbulence, requiring some level of magnetic Reynolds number,
but at a sufficiently high number, the magnetic field has more tendency
to dissipate.

(*fluid dynamics,measure,turbulence*)
**Further reading:**

https://en.wikipedia.org/wiki/Reynolds_number

https://en.wikipedia.org/wiki/Magnetic_Reynolds_number

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