Abstract
In this paper, a theory for constructing quasi-neutral density variables γ directly in thermodynamic space is formulated, which is based on minimising the absolute value of a purely thermodynamic quantity J n . Physically, J n has a dual dynamic/thermodynamic interpretation as the quantity controlling the energy cost of adiabatic and isohaline parcel exchanges on material surfaces, as well as the dependence of in-situ density on spiciness, in a description of water masses based on γ, spiciness and pressure. Mathematically, minimising | J n | in thermodynamic space is showed to be equivalent to maximising neutrality in physical space. The physics of epineutral dispersion is also reviewed and discussed. It is argued, in particular, that epineutral dispersion is best understood as the aggregate effect of many individual non-neutral stirring events (being understood here as adiabatic and isohaline events with non-zero buoyancy), so that it is only the net displacement aggregated over many events that is approximately neutral. This new view resolves an apparent paradox between the focus in neutral density theory on zero-buoyancy motions and the overwhelming evidence that lateral dispersion in the ocean is primarily caused by non-zero buoyancy processes such as tides, residual currents and sheared internal waves. The efficiency by which a physical process contributes to lateral dispersion can be characterised by its energy signature, with those processes releasing available potential energy (negative energy cost) being more efficient than purely neutral processes with zero energy cost. The latter mechanism occurs in the wedge of instability, and its source of energy is the coupling between baroclinicity, thermobaricity, and density compensated temperature/salinity anomalies. Such a mechanism, which can only exist in a salty ocean, is speculated to be important for dissipating spiciness anomalies and neutral helicity. The paper also discusses potential conceptual difficulties with the use of neutral rotated diffusion tensors in numerical ocean models, as well as with the construction of neutral density variables in physical space. It also emphasises the irreducible character of thermobaric forces in the ocean. These are argued to be the cause for adiabatic thermobaric dianeutral dispersion, and to forbid the existence of density surfaces along which fluid parcels can be exchanged without experiencing buoyancy forces, in contrast to what is assumed in the theory of neutral surfaces.
Highlights
The concepts of neutral surface and neutral density popularised by [1,2]—following earlier attempts by [3,4]—have been influential in shaping up thinking about the preferred directions for mixing and stirring in the ocean, extending Montgomery’s [5] ideas for tracking ocean water masses
Equation (1) is most commonly interpreted as a statement that fluid parcels conserve their locally referenced potential density (LRPD), where LRPD is envisioned as a density variable whose value is everywhere equal to that of in-situ density, but which for all practical purposes related to the study of stirring and mixing can be regarded locally as behaving quasi-materially
The definition of the buoyancy force acting on a single fluid parcel entering the dynamical interpretation of the neutral tangent plane Equation (1), the assumption that it is physically meaningful to parameterise isopycnal and diapycnal dispersion in terms of second-rank diffusion tensor as proposed by [29], the observation that lateral dispersion is about 7 orders of magnitude larger than quasi-vertical dispersion, the observed smallness of viscous dissipation in the ocean, the assumption that it is legitimate to regard the displacement δx entering the neutral tangent plane Equation (1) as an actual fluid parcel displacement
Summary
The concepts of neutral surface and neutral density popularised by [1,2]—following earlier attempts by [3,4]—have been influential in shaping up thinking about the preferred directions for mixing and stirring in the ocean, extending Montgomery’s [5] ideas for tracking ocean water masses. Equation (1) is most commonly interpreted as a statement that fluid parcels conserve their locally referenced potential density (LRPD), where LRPD is envisioned as a density variable whose value is everywhere equal to that of in-situ density (which is non-material and strongly pressure dependent), but which for all practical purposes related to the study of stirring and mixing can be regarded locally as behaving quasi-materially Regardless of how it is justified, the construction of d and of the neutral tangent plane Equation (1) entail a number of unclear approximations and justifications. Appendix B provides an alternative treatment of the energetics of adiabatic and isohaline exchanges in physical space, which in textbooks (see pages 280–282 of [25], pages 262–263 of [26], or [27]) is usually discussed in the context of baroclinic instability theory
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