Potential density


The potential density of a fluid parcel at pressure is the density that the parcel would acquire if adiabatically brought to a reference pressure, often 1 bar. Whereas density changes with changing pressure, potential density of a fluid parcel is conserved as the pressure experienced by the parcel changes. The concept is used in oceanography and 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 motion along surfaces of constant potential density is energetically favored over flow across these surfaces, so most of the motion within a 3-D geophysical fluid takes place along these 2-D surfaces.
In oceanography, the symbol is used to denote potential density, with the reference pressure taken to be the pressure at the ocean surface. The corresponding potential density anomaly is denoted by kg/m3. Because the compressibility of seawater varies with salinity and temperature, 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, say, the reference pressure 400 bar would be used, and the potential density anomaly symbol would be written.
Surfaces of constant potential density are used in the analyses of ocean data and to construct models of ocean currents. Neutral density surfaces, defined using another variable called neutral density, can be considered the continuous analog of these potential density surfaces.
Potential density adjusts for the effect of compression in two ways:
A parcel's density may be calculated from an equation of state:
where is temperature, is pressure, and are other tracers that affect density. The potential density would then be calculated as:
where is the potential temperature of the fluid parcel for the same reference pressure.