Reynold’s Number is a descriptive property of a flow that can help determine how heat and mass is transported. It is the ratio of the inertial to viscous force in the fluid (i.e. how fast is the flow moving relative to how viscous it is). Specifically, it can predict if a flow is laminar (smooth with little to no intersection between flow lines) or turbulent (chaotic with a lot of mixing of flow lines). A flow will transition between laminar and turbulent when Reynold’s number approaches unity.

Reynold’s Number is defined as:

Re = \frac{uL}{\nu}

where u is the mean velocity of the flow, L is the characteristic length scale of the flow, and \nu is the kinematic viscosity of the fluid.

Low Reynold’s Number — Viscous forces dominate and the flow is laminar

High Reynold’s Number —  Inertial forces dominate and the flow is turbulent (i.e. chaotic)

This section of Saturn’s surface shows evidence for both laminar (red) and turbulent flow/vortices (blue) which means that the Reynold’s number greatly varies across Saturn’s atmosphere. Credit: NASA/JPL/Space Science Institute