Physics & Chemistry

Batchelor scale

December 15, 2011, 8:20 pm

The Batchelor scale is a length scale at which the steepening of scalar concentration gradients by the rate–of–strain is balanced by diffusive smoothing. It is defined as:

caption Image:Img34.png

where υ is the kinematic viscosity of seawater, κ is the molecular diffusivity, and ε is the rate at which turbulent kinetic energy is lost, i.e.

caption Image:Img38.png


caption Image:Img39.png

is the rate of strain tensor (with units of meter squared/s−3 or W/kg).




This article is written at a definitional level only. Authors wishing to expand this entry are inivited to expand the present treatment, which additions will be peer reviewed prior to publication of any expansion.

Further Reading

  • Physical Oceanography Index
  • Trevor McDougall, Steve Thorpe, and Carl Gibson. Small–scale turbulence and mixing in the ocean: a glossary. In J. Nihoul and B. Jamart, editors, Small–Scale Turbulence and Mixing in the Ocean, pages 3–9. Elsevier, 1987.
  • G.K., Batchelor. (1959), Small-scale variation of convected quantities like temperature in turbulent fluid. Part 1. General discussion and the case of small conductivity, Journal of Fluid Mechanics 5: 113–133
  • Paul, Edward L.; Atiemo-Obeng, Victor A.; Kresta, Suzanne M. (2004), Handbook of industrial mixing: science and practice (1st ed.), Wiley-IEEE, pp. 49–52,  ISBN 0471269190




Baum, S. (2011). Batchelor scale. Retrieved from


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