Earth: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). 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 between 0 and 1,[4] and a diffusive convection regime (cool fresh overlying warm salty) when the density ratio is greater than 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]
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.[7]
See also
References
- ↑ 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.
- ↑ van der Boog, Carine G.; Dijkstra, Henk A.; Pietrzak, Julie D.; Katsman, Caroline A. (2021-02-24). "Double-diffusive mixing makes a small contribution to the global ocean circulation" (in en). Communications Earth & Environment 2 (1): 1–9. doi:10.1038/s43247-021-00113-x. ISSN 2662-4435.
- ↑ Stern, Melvin E. (1960). "The "Salt-Fountain" and Thermohaline Convection" (in en). Tellus 12 (2): 172–175. doi:10.3402/tellusa.v12i2.9378. ISSN 0040-2826.
- ↑ Sirevaag, Anders; Fer, Ilker (2012). "Vertical heat transfer in the Arctic Ocean: The role of double-diffusive mixing" (in en). Journal of Geophysical Research: Oceans 117 (C7): 1–16. doi:10.1029/2012JC007910. http://doi.wiley.com/10.1029/2012JC007910.
- ↑ Kelley, D. E.; Fernando, H. J. S.; Gargett, A. E.; Tanny, J.; Özsoy, E. (2003-03-01). "The diffusive regime of double-diffusive convection" (in en). Progress in Oceanography. Double-Diffusion in Oceanography 56 (3): 461–481. doi:10.1016/S0079-6611(03)00026-0. ISSN 0079-6611. https://www.sciencedirect.com/science/article/pii/S0079661103000260.
- ↑ Rudnick, Daniel L., and Raffaele Ferrari. "Compensation of horizontal temperature and salinity gradients in the ocean mixed layer." Science 283.5401 (1999): 526-529.
- ↑ American Meteorological Society Glossary
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