# Mixing length

From AMS Glossary

## mixing length

- An average distance of air parcel turbulent movement toward a reference height, where the average is a root-mean-square distance.

It is also known as Prandtl's mixing length,*l*, after Ludwig Prandtl who devised it in 1925 to explain turbulent fluxes such as the Reynolds stress, τ. Prandtl started with Boussinesq's first- order turbulence closure hypothesis that , where ρ is density, is average horizontal velocity, and Κ is kinematic eddy viscosity. He further recognized that exchange coefficient Κ has units of length times velocity, and proposed that Κ =*l'***w****, where***w*is a representative average turbulent vertical velocity. Prandtl also suggested that turbulent vertical motions are caused by the collision of air parcels moving horizontally at different speeds. This results in turbulent vertical velocity being proportional to turbulent horizontal velocity. From this, it can be shown that eddy viscosity can be approximated by , which can be used in Boussinesq's first-order closure.

- A mean length of travel over which an air parcel maintains its identity before being mixed with the surrounding fluid; analogous to the mean free path of a molecule.

Stull, R. B. 1988. An Introduction to Boundary Layer Meteorology. 666 pp.