Neutral surfaces, along which most of the mixing in the ocean occurs, are notoriously difficult objects: they do not exist as well-defined surfaces, and as such can only be approximated. In a hypothetical ocean where neutral surfaces are well-defined, the in-situ density on the surface is a multivalued function of the pressure on the surface, p . The surface is decomposed into geographic regions where there is one connected pressure contour per pressure value, making this function single-valued in each region. The regions are represented by arcs of the Reeb graph of p . The regions meet at saddles of p which are represented by internal nodes of the Reeb graph. Leaf nodes represent extrema of p . Cycles in the Reeb graph are created by islands and other holes in the neutral surface. This topological theory of neutral surfaces is used to create a new class of approximately neutral surfaces in the real ocean, called topobaric surfaces, which are very close to neutral and fast to compute. Topobaric surfaces are the topologically correct extension of orthobaric density surfaces to be geographically dependent, which is fundamental to neutral surfaces. Also considered is the possibility that helical neutral trajectories might have a larger pitch around islands than in the open ocean.

It has been estimated that much of the wind energy input to the ocean general circulation is removed by mesoscale eddies via baroclinic instability. While the fate of this energy remains a subject of research, arguments have been presented suggesting that a fraction of it may get transferred to lee waves that, upon breaking, result in bottom-enhanced diapycnal mixing. Here the authors propose several parameterizations of this process and explore their impact in a low-resolution ocean-climate model, focusing on their impact on the abyssal meridional overturning circulation (MOC) of Antarctic Bottom Water. This study shows that, when the eddy energy is allowed to maintain diapycnal mixing, the abyssal MOC generally intensifies with increasing wind energy input to the ocean. In such a case, the whole system is driven by the wind: wind steepens isopycnals and generates eddies, and the (parameterized) eddies generate small-scale mixing, driving the MOC. It is also demonstrated that if the model diapycnal diffusivity, eddy transfer coefficient, and surface climate are decoupled from the winds, then stronger wind stress in the Southern Ocean may lead to a weaker MOC in the abyss-in line with previous results. A simple scaling theory, describing the response of the abyssal MOC strength to wind energy input, is developed, providing a better insight on the numerical results.

SignificanceProcellariiform seabirds homing from distant foraging locations present a natural situation in which the homing route can become obstructed by islands or peninsulas because birds will not travel long distances over land. By measuring initial orientation from Global Positioning System (GPS) tracks during homing, we found that the Manx shearwater fails to encode such obstacles while homing, implying a navigation system that encodes the direction of home rather than a learned route. Nonetheless, shearwaters timed their journeys home, implying that their navigational system provides them with information about both direction and distance home, providing evidence that for routine, yet long-distance navigation, seabirds probably ascertain homeward direction by comparing their current position and the location of home with 2 or more intersecting field gradients.

In this paper we discuss some published versions of a "spice" variable which physical oceanographers have used to measure the contrasts between water masses. Veronis (1972) pursued an oceanographic variable whose contours are orthogonal to isolines of potential density on the salinity-temperature diagram. Veronis (1972) aimed to produce a variable that was (1) dynamically passive and (2) the best available measure of isopycnal mixing, and he suggested these aims might be achieved by constructing a variable whose isolines are orthogonal to potential density contours on the salinity-temperature diagram. Jackett and McDougall (1985) (hereinafter JMcD85) pointed out that adopting the property of being orthogonal to potential density contours on the salinity-temperature diagram leads to a variable that achieves neither of these two properties. First, they showed that passivity is a feature of the isopycnal variations of any variable; for example, the isopycnal variations of salinity are passive, whereas salinity itself contributes to density and so is not passive. Second, JMcD85 showed that enforcing the orthogonal property caused the isopycnal variations of the resulting variable to not be proportional to physically based measures of water-mass variations. JMcD85 derived a different version of "spice," one which did not depend on an arbitrary scaling factor, and they called their variable "spiciness." JMcD85 built their spiciness variable using EOS-80. Subsequently, spiciness was updated to be consistent with TEOS-10 by McDougall and Krzysik (2015) (hereinafter McDK15).

McDougall (1989) proved that neutral surfaces possess an exact geostrophic streamfunction, but its form has remained unknown. The exact geostrophic streamfunction for neutral surfaces is derived here. It involves a path integral of the specific volume along a neutral trajectory. On a neutral surface, the specific volume is a multivalued function of the pressure on the surface, p . By decomposing the neutral surface into regions where the specific volume is a single-valued function of p , the path integral is simply a sum of integrals of these single-valued functions. The regions are determined by the Reeb graph of p , and the neutral trajectory is encoded by a walk on this graph. Islands, and other holes in the neutral surface, can create cycles in the Reeb graph, causing the exact geostrophic streamfunction on a neutral surface to be multivalued. Moreover, neutral surfaces are ill-defined in the real ocean. Hence, the topobaric geostrophic streamfunction is presented: a single-valued approximation of the exact geostrophic streamfunction for neutral surfaces, for use on any well-defined, approximately neutral surface. Numerical tests on several approximately neutral surfaces reveal that the topobaric geostrophic streamfunction estimates the geostrophic velocity with an error that is about an order of magnitude smaller than that for any previously known geostrophic streamfunction. Also, the Montgomery potential is generalized, leading to an alternate form of the exact geostrophic streamfunction for neutral surfaces. This form is used to construct the orthobaric Montgomery potential, an easily computable geostrophic streamfunction that estimates the geostrophic velocity more accurately than any previously known geostrophic streamfunction, but less so than the topobaric geostrophic streamfunction.