### Reynolds number

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

A Reynolds number (Re) is a measure of a situation including a moving fluid that characterizes its propensity to create turbulence, e.g., how much turbulence can be expected. It is a dimensionless number defined as the ratio of 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 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 Rm 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)