Contents

Density ratio

${\displaystyle R_{\rho }={\frac {\alpha d\theta /dz}{\beta dS/dz}}}$

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). 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.^[2][3] 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,^[4] and a diffusive convection regime (cool fresh overlying warm salty) when the density ratio is between 0 and 1.^[5]

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.^[6]

Diffusive density ratio[edit]

In place of the density ratio, sometimes the diffusive density ratio ${\displaystyle R_{\rho }^{*}}$ is used, which is defined as^[7]

${\displaystyle R_{\rho }^{*}={\frac {1}{R_{\rho }}}={\frac {\alpha dS/dz}{\beta d\theta /dz}}}$

Turner Angle[edit]

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, ${\displaystyle Tu}$, which was introduced by Barry Ruddick and named after Stewart Turner.^[8][9] It is defined by

${\displaystyle Tu={\frac {3\pi }{4}}-\mathrm {arg} \left(\beta {\frac {dS}{dz}}+i\alpha {\frac {d\theta }{dz}}\right).}$

The Turner angle is related to the density ratio by

${\displaystyle R_{\rho }=-\tan \left(Tu+{\frac {\pi }{4}}\right).}$

See also[edit]

• Spice (oceanography)
• Double diffusive convection

References[edit]

This oceanography article is a stub. You can help Wikipedia by expanding it.