Measure used in calculating seawater density gradient
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, formula_1, is:
formula_2
where
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). 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 (warm salty overlying cool fresh) when the density ratio is greater than 1, and a diffusive convection regime (cool fresh overlying warm salty) 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 formula_3 is used, which is defined as
formula_4
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, formula_5, which was introduced by Barry Ruddick and named after Stewart Turner. It is defined by
formula_6
The Turner angle is related to the density ratio by
formula_7
References.
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