Density ratio

The density ratio of a column of seawater is a measure of the relative contributions of temperature and salinity in determining the density gradient.[1] At a density ratio of 1, temperature and salinity are said to be compensated: their density signatures cancel, leaving a density gradient of zero. The formula for the density ratio, R, is:

R = αθz/βSz, where

  • θ is the potential temperature
  • S is the salinity
  • z is the vertical coordinate (with subscript denoting differentiation by z)
  • ρ is the density
  • α = −ρ−1∂ρ/∂θ is the thermal expansion coefficient
  • β = ρ−1∂ρ/∂S is the haline contraction coefficient

When a water column is "doubly stable"--both temperature and salinity contribute to the stable density gradient--the density ratio is negative (a doubly unstable water column would also have a negative density ratio, but does not commonly occur). A statically stable water column with a density ratio between 0 and 1 (cool fresh overlying warm salty) can support diffusive convection, and a statically stable water column with a density ratio larger than 1 can support salt fingering.

Density ratio may also be used to describe thermohaline variability over a non-vertical spatial interval, such as across a front in the mixed layer.[2]

If the signs of both the numerator and denominator are reversed, the density ratio remains unchanged. A related quantity which avoids this ambiguity as well as the infinite values possible when the denominator vanishes is the Turner angle, Tu.[3]

See also

References
  1. You, Yuzhu. "A global ocean climatological atlas of the Turner angle: implications for double-diffusion and water-mass structure." Deep Sea Research Part I: Oceanographic Research Papers 49.11 (2002): 2075-2093.
  2. Rudnick, Daniel L., and Raffaele Ferrari. "Compensation of horizontal temperature and salinity gradients in the ocean mixed layer." Science 283.5401 (1999): 526-529.
  3. American Meteorological Society Glossary


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