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Adiabatic Density Surface, Neutral Density Surface, Potential Density Surface, and Mixing Path*

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Adiabatic Density Surface, Neutral Density Surface, Potential Density Surface, and Mixing Path* 热带海洋学报 JOURNAL OF TROPICAL OCEANOGRAPHY 2014 年 第 33 卷 第 4 期: 1−19 海洋水文学 doi:10.3969/j.issn.1009-5470.2014.04.001 http://www.jto.ac.cn Adiabatic density surface, neutral density surface, potential * density surface, and mixing path HUANG Rui-xin Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA Abstract: In this paper, adiabatic density surface, neutral density surface and potential density surface are compared. The adiabatic density surface is defined as the surface on which a water parcel can move adiabatically, without changing its potential temperature and salinity. For a water parcel taken at a given station and pressure level, the corresponding adiabatic density surface can be determined through simple calculations. This family of surface is neutrally buoyant in the world ocean, and different from other surfaces that are not truly neutrally buoyant. In order to explore mixing path in the ocean, a mixing ratio m is introduced, which is defined as the portion of potential temperature and salinity of a water parcel that has exchanged with the environment during a segment of migration in the ocean. Two extreme situations of mixing path in the ocean are m=0 (no mixing), which is represented by the adiabatic density curve, and m=1, where the original information is completely lost through mixing. The latter is represented by the neutral density curve. The reality lies in between, namely, 0<m<1. In the turbulent ocean, there are potentially infinite mixing paths, some of which may be identified by using different tracers (or their combinations) and different mixing criteria. Searching for mixing paths in the real ocean presents a great challenge for further research. Key words: adiabatic density surface, neutral density surface, potential density surface, mixing path CLC number: P731 Document code: A Serial number: 1009-5470(2014)04-0001-19 Water mass analysis, including its spreading follows. and transformation, has been a classical topic in 1) Finding the trajectories/surfaces along physical oceanography. For example, the core layer which a water parcel can travel adiabatically and method was widely used in many classical papers, net-buoyancy-freely. such as Wust (1935); a more concise description can 2) Finding the surfaces on which two water be found in Stewart (2009). As an improvement, parcels can adiabatically exchange their horizontal different surfaces were introduced for analyzing the positions and without changing the shape of the lateral distribution of water properties. A landmark original surface. was the pioneering work of Montgomery (1938) on 3) Finding the mixing trajectories or mixing isentropic analysis. Since then many attempts have surfaces. been made to find suitable surfaces for isentropic The mixing path is the trajectory of a water (or adiabatic, i.e. without changing potential mass spreading/ transforming in the ocean. In the temperature and salinity) motions, such as the turbulent ocean, this is a loosely defined term. By potential temperature surface and the isopycnal definition, it is a Lagrangian trajectory along which surface (including the potential density surface and certain water properties are conserved. In addition, different types of approximately neutral density mixing takes place along the trajectory, leading to a surfaces). The essential criteria/goals in searching gradual modification of water properties. As a result, for suitable surfaces for water mass analysis are as the trajectory of a Lagrangian float may be different Received date: 2013-11-26; Revised date: 2013-11-26. Editor: LIN Qiang Biography: HUANG Rui-xin (1942~), male, scientist emeritus, theory and numerical modeling of large-scale oceanic circulation. E-mail: [email protected] *I have benefited through discussions with many of my colleagues. In particular, critical comments and constructive suggestions from Drs. Kenneth H. Brink and M. Susan Lozier helped me greatly in correcting some misconceptions and improving the presentation. 2 热带海洋学报 Vol. 33, No. 4 / Jul., 2014 from the trajectory of a water mass because the Due to the nonlinearity of equation of state, the former involves no mixing, but the latter involves helicity of seawater is non-zero. (Helicity for a mixing. vector A is defined as H =⋅∇×AA. For the A mixing surface is a generalization of mixing application to the NDS, A =∇−∇Θρ ()βαS (where path, and it is defined as the surface on which a β is the haline constraction coefficient, and α is the water parcel can move around, spreading and thermal expansion coefficient) is the neutral vector, mixing with the environment. Movement of a water see Jackett, et al, 1997). Thus, a NDS may depend parcel on the mixing surface is always involved on the paths chosen in defining it. As a result, an with a gradual modification of its properties. exact three-dimensional neutral surface does not The specific entropy of seawater is closely exist in the ocean (McDougall, 1987a). In addition linked to its potential temperature (Feistel, 2003, to the approximate NDS algorithm postulated by 2005). Water parcels continuously change their Jackett and McDougall (1997), there are other ways entropy due to lateral and vertical diffusion. Thus, to define an approximate NDS, such as the constant entropy surfaces diagnosed from the ocean minimization technique postulated by Eden, et al cannot be used as the surfaces for analyzing a water (1999), or the orthobaric density surface by de mass’s movement in the ocean. Szoeke, et al (2009). Montgomery’s (1938) analysis was based on However, on any 2-D (two-dimensional) the σt surface. By definition, σt=ρ(S, T, p=0) (where vertical plane the situation is different. On a 2-D ρ is density, S is salinity, T is temperature, and p is surface, the slope of the potential density surface pressure) is not a conserved quantity, so this does (using the local pressure as the reference) is a 2-D not lead to an isentropic surface. As a better vector field. If the stratification is stable, the local alternative, the potential density surface (PDS isopycnal slope cannot be vertical. Thus, from this hereafter) σp=ρ(Θ, S, pr)=const. (where Θ is 2-D vector field, a family of neutral curves can be potential temperature, pr is reference pressure) was constructed. For example, one can use the simple introduced and widely used in hydrographic data Euler method or any similar, more accurate, method. analysis. However, the PDS is not perfect either, This family of curve has the following properties. because at depths away from the reference pressure, First, everywhere the tangent of these neutral curves potential density cannot accurately represent the matches the tangent of the local potential density local stratification. In fact, stratification or static surface. Second, through any given point on this stability is defined using the local pressure as 2-D surface, there is only one neutral curve. reference. Due to the nonlinearity of the equation Although the neutral density and the NDS are of the state, using a non-local reference pressure to now often used in oceanographic data analysis, calculate the static stability can lead to a value some of their fundamental properties have not yet quite different from the truth. To overcome this been examined thoroughly. In particular, it is not problem, the patched potential density method was clear whether a water parcel moving on a NDS will introduced, e.g. Reid (1994) or de Szoeke, et al always have the same in-situ density as the local (2005). water parcel originally sitting on the surface. In fact, As an improvement, the neutral density surface whether the so-called NDS is really neutrally (NDS hereafter) was introduced. The basic concept buoyant has not been rigorously proven. of a NDS was to build up a surface whose tangent at There is another type of density surface, first each point matches the local potential density discussed by McDougall (1987b) in connection with surface tangent, as first postulated by Forster, et al the propagation of the Submesoscale Coherent (1976); their idea has been generalized into a theory Vorticies (SCV). In this study, we will call this of neutral density and NDS, e.g., McDougall surface the adiabatic density surface (ADS hereafter) (1987a), Jackett, et al (1997). and will show that a water parcel can adiabatically HUANG Rui-xin: Adiabatic density surface, neutral density surface, potential density surface, and mixing path 3 travel on its ADS and net-buoyancy-freely, i.e., that current stemming from a site of deep water it satisfies the first of the above criteria. formation. The other means is through turbulent Unfortunately, due to thermobaricity, there is diffusion, which is closely linked to mesoscale and no surface in the ocean along which two water submesoscale eddies. A good example is the parcels can exchange their horizontal positions spreading of the Mediterranean Overflow Water through adiabatic motions without changing the (MOF) in the North Atlantic. The tongue-like shape of the corresponding surface. This can be feature of MOF has been known for a long time, but shown as follows. there is no permanent current associated with it. In Assume that on a thermodynamic surface (a fact, the spreading of MOF is primarily due to the PDS, a quasi-NDS or any other similar surface) westward propagating mesoscale eddies, called there are two water parcels A and B with unit mass, Meddies, e.g., Armi, et al (1989). sitting on pressure levels ρA and ρB, Δρ=ρA–ρB >0. Another example is AABW (Antarctic Bottom If we adiabatically move parcel A to the position of Water), which influences properties as far as into B, its in-situ density change is the Northern Hemisphere. Wijffels, et al (1996) analyzed water masses and circulation at 10°N in Δ=ρρAB→ A()BA − ρ A( )() ρκ 0 Δp η A, the Pacific, and they were able to identify a where ρA(A) and ρA(B) depict water parcel A’s substantial contribution of bottom water having density at location A and B, ρ is the reference 0 Antarctic origin.
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