Neutral-surface potential vorticity

Abstract

The use of potential density in ocean models does not overcome all the annoying problems caused by the compressible nature of seawater. For example, the reduced gravity for layered ocean models is not proportional to the difference of potential density across an interface. The appropriate reduced gravity is derived and it is shown to be relatively easy to incorporate in future layered models. Potential-density surfaces are commonly inclined with respect to neutral surfaces and so lateral motion along neutral surfaces gives rise to unwanted diapycnal velocities that are unrelated to vertical mixing processes. This unphysical part of the diapycnal motion is quantified, emphasizing the need for performing ocean-circulation studies in the neutral-surface framework. If there were no variations of θ and S along neutral surfaces in the ocean, then lateral mixing would occur along potential-density surfaces. A perfectly respectable potential vorticity variable would then be isopycnal potential vorticity, IPV, defined by -gf[∂ρ θ/∂z]/ρ θ. However, there is mixing in the ocean, and neutral surfaces do not coincide with potential density surfaces. Since the efficient lateral mixing processes occur along neutral trajectories, and vertical velocities through neutral surfaces occur only in response to mixing processes of a vertical nature (including the two dianeutral advection processes, thermobaricity and cabbeling), it is logical to seek a potential vorticity variable that is proportional to f/h, where h is the vertical distance between adjacent neutral surfaces. This form of potential vorticity is here referred to as “neutral-surface potential vorticity”, NSPV. Its epineutral variations can be significantly different to those of the two other commonly used potential vorticity variables, IPV, and fN 2. The difference between NSPV and fN 2 is shown to result from the path-dependence inherent in integrating N 2 in the vertical plane between two neutral trajectories. The β-spiral equations are derived for a fully non-linear equation of state, and neutral surfaces emerge as the dynamically relevant surfaces for these studies. It is also shown that IPV is not conserved on potential-density surfaces because of the non-linear nature of the equation of state; this problem does not arise in the neutral tangent plane. Mixing processes cause scalar properties to change at different rates on a potential-density surface than in a neutral tangent plane. In particular, potential density itself is mixed and advected by epineutral processes, thereby complicating the interpretation of inversemodels that use potential density surfaces. The dynamical equations governing the ocean circulation take simple and exact forms with respect to the neutral tangent plane at eaach point, but when an interface or surface must be formed over an extended geographical region, the ambiguity associated with defining a neutral surface raises its ugly head. Here it is shown that the approximately neutral surfaces of McDougall and Jackett (1988) are the most appropriate surfaces for this purpose.