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 = αθ_z/βS_z, 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

• Spice (oceanography)

References