A new paradigm for lateral stirring and lateral stirring surfaces in the oceans

By analogy with the case of a simple fluid, lateral stirring in the oceans has been traditionally envisioned as the notional form of stirring that minimally perturb the ocean stratification and its potential energy, as originally proposed over 80 years ago. If considered from the viewpoint of adiabatic and isohaline permutations of two fluid parcels, such a view leads to the idea that lateral stirring preferentially takes place on the ‘locally-referenced potential density surfaces’. To remedy the mathematically and physically ambiguous character of the latter, oceanographers then developed the concepts of potential density surfaces, patched potential density surfaces, and approximately neutral surfaces, which have been the cornerstone of isopycnal analysis for many decades. It has also provided the justification for constructing rotated diffusion tensors in terms of the directions parallel and perpendicular to the neutral directions. Nevertheless, while the concepts of neutral directions and neutral surfaces have been around for decades, their validity has never been really challenged nor confirmed experimentally. Worse, there has been little clue so far about how one might go about testing or refuting these concepts.

Part of the problem is that the current theory of quasi-neutral density variables is not currently formulated as a classical falsifiable (in Popper’s sense) physical theory capable of making testable predictions but more as unfalsifiable dogma. To improve on this situation, this work shows how to embed the theory of lateral stirring and lateral stirring surfaces into the APE-based study of the compressible Navier-Stokes equations for realistic seawater (APE standing as Available Potential Energy, as per Lorenz concept). Doing so succeeds in identifying the kind of models that can be studied to shed light on the issue while also making new predictions about lateral stirring that significantly depart from the prevailing view. A key new result is that isoneutral stirring must involve compensating work between buoyancy and thermobaric forces, which cast doubt on its physical realisability. Another key result is that the ‘true’ neutral directions are not those associated with the standard neutral vector, but rather with an APE-based form of the P vector previously identified by Nycander. Although the P-neutrality thus defined appears to coincide with the standard N-neutrality in most of the oceans, the two are found to significantly differ in the polar region and Gulf Stream area, where neutral rotated diffusion tensors are likely to be potentially a significant source of spurious diapycnal mixing. Evidence that this is the case and how to go about remedying the problem will be discussed.