Mixing length theory

In fluid dynamics, the mixing length model is a method attempting to describe momentum transfer by turbulence Reynolds stresses within a newtonian fluid boundary layer by means of an eddy viscosity. The model was developed by Ludwig Prandtl in the early 20th century. Prandtl himself had reservations about the model, describing it as, "only a rough approximation," but it has been used in numerous fields ever since, including atmospheric science, oceanography and stellar structure.

The mixing length is conceptually analogous to the concept of mean free path in thermodynamics: a fluid parcel will conserve its properties for a characteristic length, ${\displaystyle \ \xi '}$, before mixing with the surrounding fluid. Prandtl described that the mixing length,

In the figure above, temperature, ${\displaystyle \ T}$, is conserved for a certain distance as a parcel moves across a temperature gradient. The fluctuation in temperature that the parcel experienced throughout the process is ${\displaystyle \ T'}$. So ${\displaystyle \ T'}$ can be seen as the temperature deviation from its surrounding environment after it has moved over this mixing length ${\displaystyle \ \xi '}$.

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