The potential density of a fluid parcel at pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

  is the density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 that the parcel would acquire if adiabatically

Adiabatic process

In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...

 brought to a reference pressure , often 1 bar

Bar (unit)

The bar is a unit of pressure equal to 100 kilopascals, and roughly equal to the atmospheric pressure on Earth at sea level. Other units derived from the bar are the megabar , kilobar , decibar , centibar , and millibar...

 (100 kPa). Whereas density changes with changing pressure, potential density of a fluid parcel is conserved

Conservation law

In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....

 as the pressure experienced by the parcel changes (provided no mixing with other parcels or net heat flux occurs). The concept is used in oceanography

Oceanography

Oceanography , also called oceanology or marine science, is the branch of Earth science that studies the ocean...

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

Isopycnal

An isopycnal is a surface of constant potential density of water. In the ocean, as the depth increases, so too does the density. Varying degrees of salinity and temperature act to modify the density of water, and the denser water always lies below the less dense water. Because of the action of...

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 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

Kilogram

The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

/m. Because the compressibility of seawater

Seawater

Seawater is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% . This means that every kilogram of seawater has approximately of dissolved salts . The average density of seawater at the ocean surface is 1.025 g/ml...

 varies with salinity

Salinity

Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...

 and temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, 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 .

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 parcel's 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

Equation of state

In physics and thermodynamics, an equation of state is a relation between state variables. More specifically, an equation of state is a thermodynamic equation describing the state of matter under a given set of physical conditions...

:
where is temperature, is pressure and are other tracer

Tracer

Tracer may refer to:* Histochemical tracer, a substance used for tracing purposes in histochemistry, the study of the composition of cells and tissues...

s that affect density (e.g. salinity

Salinity

Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...

 of seawater

Seawater

Seawater is water from a sea or ocean. On average, seawater in the world's oceans has a salinity of about 3.5% . This means that every kilogram of seawater has approximately of dissolved salts . The average density of seawater at the ocean surface is 1.025 g/ml...

). The potential density would then be calculated as:
where is the potential temperature of the fluid parcel for the same reference pressure .