Mixing length model

The mixing length is a distance that a fluid parcel will keep its original characteristics before dispersing them into the surrounding fluid. Here, the bar on the left side of the figure is the mixing length.

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.[1] Prandtl himself had reservations about the model,[2] describing it as, "only a rough approximation,"[3] but it has been used in numerous fields ever since, including atmospheric science, oceanography and stellar structure.[4] Also, Ali and Dey[5] hypothesized an advanced concept of mixing instability.

  1. ^ Holton, James R. (2004). "Chapter 5 – The Planetary Boundary Layer". Dynamic Meteorology. International Geophysics Series. Vol. 88 (4th ed.). Burlington, MA: Elsevier Academic Press. pp. 124–127.
  2. ^ Prandtl, L. (1925). "7. Bericht über Untersuchungen zur ausgebildeten Turbulenz". Z. Angew. Math. Mech. 5 (1): 136–139. Bibcode:1925ZaMM....5..136P. doi:10.1002/zamm.19250050212.
  3. ^ Bradshaw, P. (1974). "Possible origin of Prandt's mixing-length theory". Nature. 249 (6): 135–136. Bibcode:1974Natur.249..135B. doi:10.1038/249135b0. S2CID 4218601.
  4. ^ Chan, Kwing; Sabatino Sofia (1987). "Validity Tests of the Mixing-Length Theory of Deep Convection". Science. 235 (4787): 465–467. Bibcode:1987Sci...235..465C. doi:10.1126/science.235.4787.465. PMID 17810341. S2CID 21960234.
  5. ^ Ali, S.Z.; Dey, S. (2020). "The law of the wall: A new perspective". Physics of Fluids. 36: 121401. doi:10.1063/5.0036387.