Neutral density

The neutral density ( ) is used in oceanography to describe areas along which a water package moves in the deep ocean. The concept of neutral density was created in 1997 by David R. Jackett and Trevor McDougall. The neutral density has the unit of density and is dependent on salinity , temperature , pressure , location (the geographic coordinates ) and also the condition of the surrounding ocean. ${\ displaystyle \ gamma ^ {n}}$

Because water moves along surfaces of the same neutral density (“neutral density surfaces”), these surfaces are helpful in analyzing the spread of water masses and their lateral mixing. While small-scale processes near the surface, where potential density and neutral density differ only slightly, can usually be explained sufficiently well on the basis of the potential density, this is not the case for large-scale water movements in the depths: if one imagines, for example, the movement of a water package along a constant level If there is a neutral density in an ocean-wide circular flow , the water packet will not be exactly at the starting point after a single cycle, but about 10 m away from it. If, however, potential density is used to determine the path of the water package, the difference between the starting point and the end point after a single cycle can even be several 100 m - a much larger error.

Basis of calculation

A water package that moves along a neutral density surface does not experience any deflection by the buoyancy force . As shown by McDougall and Jacket, such movement is orthogonal to the direction of the gradient difference . Here S is the salinity and the specific coefficient of contraction with respect to the salinity, the potential temperature and the coefficient of thermal expansion . ${\ displaystyle \ beta \ nabla S- \ alpha \ nabla \ theta}$ ${\ displaystyle \ beta}$ ${\ displaystyle \ theta}$ ${\ displaystyle \ alpha}$

Neutral density areas are therefore defined as areas that are orthogonal to at each point . here is the in-situ density. ${\ displaystyle \ rho (\ beta \ nabla S- \ alpha \ nabla \ theta)}$ ${\ displaystyle \ rho}$

The calculation of neutral density areas requires the solution of a system of partial differential equations, which must be determined numerically. In the real ocean, however, the condition for a clear solution is often not met. The neutral density areas can therefore only be determined approximately, and there is always a weak flow of water through the calculated areas. This computational inaccuracy is smaller than current measurement inaccuracies.

To calculate the neutral density, knowledge of the salinity and potential temperature in the vicinity of the water package is required. McDougall and Jacket defined the neutral density using Levitus climatology, a global ocean dataset. Based on this, neutral density areas can be adapted to all other hydrological data.

Concept of density, potential density and neutral density

Problem of potential density: adiabatic curves of (sea) water with different temperature and salinity properties

Problem of potential density: Density of (sea) water as a function of potential temperature and salinity at different pressures

The idea that packets of water of the same density could freely exchange their position without the need for additional energy led to the historical idea that water in the ocean circulates along in-situ density surfaces. As early as the 1930s, G. Wust (1933) and RB Montgomery (1938) first established that this concept hardly corresponds to reality, even near the ocean surface, because the density of a water package is not maintained when it rises or sinks.

Analogous to the potential temperature , the potential density was introduced, defined as the density that a water packet would have if it were brought adiabatically to a normal pressure (reference value). In a stable stratified water column, water with a lower potential density is always above water with a higher potential density, since if both water packages were brought to the same pressure, according to Archimedes principle, the former would rise and the latter would sink.

According to the equation of state, the density of seawater is not only dependent on pressure, but also on temperature and salinity. This means that the densities of two water packages that differ in temperature and salinity would each behave differently if these water packages were brought to a normal pressure level. The more the selected normal pressure deviates from the in-situ pressure, the more significant the deviation. Only a normal pressure which is close to the in-situ pressure gives a meaningful dynamic meaning of the potential density. Since the 1970s, ocean currents have therefore mostly been analyzed with a series of potential densities, defined at different normal pressure levels adapted to the in-situ pressure.

A water packet moves locally along lines of constant potential density σ _r normalized to the local pressure r. A neutral density surface must therefore run tangential to the potential density surface, which is normalized to the local pressure , at every point . Neutral density areas can therefore be understood as the transition from a series of potential density areas to a continuous area.

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^ ^A ^b ^c ^d ^e David R. Jackett, Trevor J. McDougall: A Neutral Density Variable for the World's Oceans . In: American Meteorological Society (Ed.): Journal of Physical Oceanography . tape 27 , no. 2 , February 1997, p. 237-263 , doi : 10.1175 / 1520-0485 (1997) 027 <0237: ANDVFT> 2.0.CO; 2 (English).
^ ^A ^b ^c ^d Robert H. Stewart: Introduction to Physical Oceanography . Ed .: Texas A&M University. September 2008, 6.5 Density, Potential Temperature, and Neutral Density, p. 87 (English, tamu.edu [PDF]).
↑ Andreas Klocker, Trevor J. McDougall: Quantifying the Consequences of the Ill-Defined Nature of Neutral Surfaces . In: Journal of Physical Oceanography . tape 40 , no. 8 , August 2010, ISSN 0022-3670 , p. 1866–1880 , doi : 10.1175 / 2009jpo4212.1 ( ametsoc.org [accessed July 8, 2018]).
^ Joseph L Reid: On the total geostrophic circulation of the North Atlantic Ocean: Flow patterns, tracers, and transports . In: Progress in Oceanography . tape 33 , no. 1 , January 1994, ISSN 0079-6611 , pp. 1-92 , doi : 10.1016 / 0079-6611 (94) 90014-0 .
^ Carsten Eden, Jürgen Willebrand: Neutral density revisited . In: Deep Sea Research Part II: Topical Studies in Oceanography . tape 46 , no. 1-2 , January 1999, ISSN 0967-0645 , pp. 33-54 , doi : 10.1016 / s0967-0645 (98) 00113-1 .

[:0-1] A ^b ^c ^d ^e David R. Jackett, Trevor J. McDougall: A Neutral Density Variable for the World's Oceans . In: American Meteorological Society (Ed.): Journal of Physical Oceanography . tape 27 , no. 2 , February 1997, p. 237-263 , doi : 10.1175 / 1520-0485 (1997) 027 <0237: ANDVFT> 2.0.CO; 2 (English).

[:1-2] A ^b ^c ^d Robert H. Stewart: Introduction to Physical Oceanography . Ed .: Texas A&M University. September 2008, 6.5 Density, Potential Temperature, and Neutral Density, p. 87 (English, tamu.edu [PDF]).

[3] Andreas Klocker, Trevor J. McDougall: Quantifying the Consequences of the Ill-Defined Nature of Neutral Surfaces . In: Journal of Physical Oceanography . tape 40 , no. 8 , August 2010, ISSN 0022-3670 , p. 1866–1880 , doi : 10.1175 / 2009jpo4212.1 ( ametsoc.org [accessed July 8, 2018]).

[4] Joseph L Reid: On the total geostrophic circulation of the North Atlantic Ocean: Flow patterns, tracers, and transports . In: Progress in Oceanography . tape 33 , no. 1 , January 1994, ISSN 0079-6611 , pp. 1-92 , doi : 10.1016 / 0079-6611 (94) 90014-0 .

[5] Carsten Eden, Jürgen Willebrand: Neutral density revisited . In: Deep Sea Research Part II: Topical Studies in Oceanography . tape 46 , no. 1-2 , January 1999, ISSN 0967-0645 , pp. 33-54 , doi : 10.1016 / s0967-0645 (98) 00113-1 .