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. 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,, is:
where

θ is the potential temperature
S is the salinity
z is the vertical coordinate
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. When either the temperature- or salinity-induced stratification is statically unstable, while the overall density stratification is statically stable, double-diffusive instability exists in the water column. Double-diffusive instability can be separated into two different regimes of statically stable density stratification: a salt fingering regime when the density ratio is greater than 1, and a diffusive convection regime when the density ratio is between 0 and 1.
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.

Diffusive density ratio

In place of the density ratio, sometimes the diffusive density ratio is used, which is defined as

Turner Angle

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,, which was introduced by Barry Ruddick and named after Stewart Turner. It is defined by
The Turner angle is related to the density ratio by