# Potential density

The

**potential density**of a fluid parcel atpressure $P$ is thedensity that the parcel would acquire if adiabatically brought to a reference pressure $P\_\{0\}$, often 1 bar (100 kPa). Whereas density changes with changing pressure, potential density of a fluid parcel is conserved as the pressure experienced by the parcel changes (provided no mixing with other parcels or net heat flux occurs). The concept is used inoceanography [*http://oceanworld.tamu.edu/resources/ocng_textbook/contents.html*] and (to a lesser extent)atmospheric science .Potential density is a dynamically important property: for static stability potential density must decrease upward. If it doesn't, a fluid parcel displaced upward finds itself lighter than its neighbors, and continues to move upward; similarly, a fluid parcel displaced downward would be heavier than its neighbors. This is true even if the density of the fluid decreases upward. In stable conditions (potential density decreasing upward) motion along surfaces of constant potential density (

isopycnal s) is energetically favored over flow across these surfaces (diapycnal flow), so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.In oceanography, the symbol $ho\_\; heta$ is used to denote "potential density", with the reference pressure $P\_0$ taken to be the pressure at the ocean surface. The corresponding "potential density anomaly" is denoted by $sigma\_\; heta\; =\; ho\_\; heta\; -\; 1000$ kg/m$^3$. Because the

compressibility ofseawater varies withsalinity andtemperature , the reference pressure must chosen to be near the actual pressure to keep the definition of potential density dynamically meaningful. Reference pressures are often chosen as a whole multiple of 100 bar; for water near a pressure of 400 bar (40 MPa), say, the reference pressure 400 bar would be used, and the potential density anomaly symbol would be written $sigma\_4$.Potential density adjusts for the effect of

compression in two ways:

*The effect of a parcel's change in volume due to a change in pressure (as pressure increases, volume decreases).

*The effect of the parcels change in temperature due to adiabatic change in pressure (as pressure increases, temperature increases).A parcel's density may be calculated from an

equation of state ::$ho\; =\; ho(P,T,S\_1,S\_2,...)$where $T$ is temperature, $P$ is pressure and $S\_n$ are othertracer s that affect density (e.g.salinity ofseawater ). The potential density would then be calculated as::$ho\_\; heta\; =\; ho(P\_0,\; heta,S\_1,S\_2,...)$where $heta$ is thepotential temperature of the fluid parcel for the same reference pressure $P\_0$.**References***cite book | author=John M. Wallace and Peter V. Hobbs | title=Atmospheric Science, An Introductory Survey, Second Edition | publisher=Academic Press | year=2006 | id=ISBN 0-12-732950-1

*cite book | author=Robert H. Stewart | title=Introduction to Physical Oceanography | year=2002 | http://oceanworld.tamu.edu/resources/ocng_textbook/chapter06/chapter06_05.htm

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