Canonical connection on a class of Riemannian almost product manifolds

The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an example by a Lie group.Comment: 19 pages, some corrections in the example; J. Geom. (2012

Observation of a large lee wave in the Drake Passage

Lee waves are thought to play a prominent role in Southern Ocean dynamics, facilitating a transfer of energy from the jets of the Antarctic Circumpolar Current to microscale, turbulent motions important in water mass transformations. Two EM-APEX profiling floats deployed in the Drake Passage during the Diapycnal and Isopycnal Mixing Experiment (DIMES) independently measured a 120 ± 20-m vertical amplitude lee wave over the Shackleton Fracture Zone. A model for steady EM-APEX motion is developed to calculate absolute vertical water velocity, augmenting the horizontal velocity measurements made by the floats. The wave exhibits fluctuations in all three velocity components of over 15 cm s−1 and an intrinsic frequency close to the local buoyancy frequency. The wave is observed to transport energy and horizontal momentum vertically at respective peak rates of 1.3 ± 0.2 W m−2 and 8 ± 1 N m−2. The rate of turbulent kinetic energy dissipation is estimated using both Thorpe scales and a method that isolates high-frequency vertical kinetic energy and is found to be enhanced within the wave to values of order 10−7 W kg−1. The observed vertical flux of energy is significantly larger than expected from idealized numerical simulations and also larger than observed depth-integrated dissipation rates. These results provide the first unambiguous observation of a lee wave in the Southern Ocean with simultaneous measurements of its energetics and dynamics

On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and non-vacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of spacetimes with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the non-existence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein-Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to detect them. In particular a characterization of the Reissner-Nordstr\"{o}m metric is accomplished.Comment: 29 pages, 0 figure

Spatiotemporal Characteristics of the Near-Surface Turbulent Cascade at the Submesoscale in the Drake Passage.

Submesoscale currents and internal gravity waves achieve an intense turbulent cascade near the ocean surface [depth of 0–O(100) m], which is thought to give rise to significant energy sources and sinks for mesoscale eddies. Here, we characterize the contributions of nonwave currents (NWCs; including eddies and fronts) and internal gravity waves (IGWs; including near-inertial motions, lee waves, and the internal wave continuum) to near-surface submesoscale turbulence in the Drake Passage. Using a numerical simulation, we combine Lagrangian filtering and a Helmholtz decomposition to identify NWCs and IGWs and to characterize their dynamics (rotational versus divergent). We show that NWCs and IGWs contribute in different proportions to the inverse and forward turbulent kinetic energy cascades, based on their dynamics and spatiotemporal scales. Purely rotational NWCs cause most of the inverse cascade, while coupled rotational–divergent components of NWCs and coupled NWC–IGWs cause the forward cascade. The cascade changes direction at a spatial scale at which motions become increasingly divergent. However, the forward cascade is ultimately limited by the motions’ spatiotemporal scales. The bulk of the forward cascade (80%–95%) is caused by NWCs and IGWs of small spatiotemporal scales (L < 10 km; T < 6 h), which are primarily rotational: submesoscale eddies, fronts, and the internal wave continuum. These motions also cause a significant part of the inverse cascade (30%). Our results highlight the requirement for high spatiotemporal resolutions to diagnose the properties and large-scale impacts of near-surface submesoscale turbulence accurately, with significant implications for ocean energy cycle study strategies

Differences between 1999 and 2010 across the Falkland Plateau: fronts and water masses

Decadal differences in the Falkland Plateau are studied from the two full-depth hydrographic data collected during the ALBATROSS (April 1999) and MOC-Austral (February 2010) cruises. Differences in the upper 100 dbar are due to changes in the seasonal thermocline, as the ALBATROSS cruise took place in the austral fall and the MOCAustral cruise in summer. The intermediate water masses seem to be very sensitive to the wind conditions existing in their formation area, showing cooling and freshening for the decade as a consequence of a higher Antarctic Intermediate Water (AAIW) contribution and of a decrease in the Subantarctic Mode Water (SAMW) stratum. The deeper layers do not exhibit any significant change in the water mass properties. The Subantarctic Front (SAF) in 1999 is observed at 52.2–54.8 W with a relative mass transport of 32.6 Sv. In contrast, the SAF gets wider in 2010, stretching from 51.1 to 57.2 W (the Falkland Islands), and weakening to 17.9 Sv. Changes in the SAF can be linked with the westerly winds and mainly affect the northward flow of Subantarctic Surface Water (SASW), SAMW and AAIW/Antarctic Surface Water (AASW). The Polar Front (PF) carries 24.9 Sv in 1999 (49.8–44.4 W), while in 2010 (49.9–49.2 W) it narrows and strengthens to 37.3 Sv.En prens

Recent wind-driven variability in Atlantic water mass distribution and meridional overturning circulation

Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 47 (2017): 633-647, doi:10.1175/JPO-D-16-0089.1.Interannual variability in the volumetric water mass distribution within the North Atlantic Subtropical Gyre is described in relation to variability in the Atlantic meridional overturning circulation. The relative roles of diabatic and adiabatic processes in the volume and heat budgets of the subtropical gyre are investigated by projecting data into temperature coordinates as volumes of water using an Argo-based climatology and an ocean state estimate (ECCO version 4). This highlights that variations in the subtropical gyre volume budget are predominantly set by transport divergence in the gyre. A strong correlation between the volume anomaly due to transport divergence and the variability of both thermocline depth and Ekman pumping over the gyre suggests that wind-driven heave drives transport anomalies at the gyre boundaries. This wind-driven heaving contributes significantly to variations in the heat content of the gyre, as do anomalies in the air–sea fluxes. The analysis presented suggests that wind forcing plays an important role in driving interannual variability in the Atlantic meridional overturning circulation and that this variability can be unraveled from spatially distributed hydrographic observations using the framework presented here.DGE was supported by a Natural Environment Research Council studentship award at the University of Southampton. JMT’s contribution was supported by the U.S. National Science Foundation (Grant OCE-1332667). GF’s contribution was supported by the U.S. National Science Foundation through Grant OCE-0961713 and by the U.S. National Oceanic and Atmospheric Administration through Grant NA10OAR4310135. The contributions of JDZ and AJGN were supported by the NERC Grant ‘‘Climate scale analysis of air and water masses’’ (NE/ K012932/1). ACNG gratefully acknowledges support from the Leverhulme Trust, the Royal Society, and the Wolfson Foundation. LY was supported by NASA Ocean Vector Wind Science Team (OVWST) activities under Grant NNA10AO86G

Observed eddy-internal wave interactions in the Southern Ocean

The physical mechanisms that remove energy from the Southern Ocean’s vigorous mesoscale eddy field are not well understood. One proposed mechanism is direct energy transfer to the internal wave field in the ocean interior, via eddy-induced straining and shearing of preexisting internal waves. The magnitude, vertical structure, and temporal variability of the rate of energy transfer between eddies and internal waves is quantified from a 14-month deployment of a mooring cluster in the Scotia Sea. Velocity and buoyancy observations are decomposed into wave and eddy components, and the energy transfer is estimated using the Reynolds-averaged energy equation. We find that eddies gain energy from the internal wave field at a rate of −2.2 ± 0.6 mW m−2, integrated from the bottom to 566 m below the surface. This result can be decomposed into a positive (eddy to wave) component, equal to 0.2 ± 0.1 mW m−2, driven by horizontal straining of internal waves, and a negative (wave to eddy) component, equal to −2.5 ± 0.6 mW m−2, driven by vertical shearing of the wave spectrum. Temporal variability of the transfer rate is much greater than the mean value. Close to topography, large energy transfers are associated with low-frequency buoyancy fluxes, the underpinning physics of which do not conform to linear wave dynamics and are thereby in need of further research. Our work suggests that eddy–internal wave interactions may play a significant role in the energy balance of the Southern Ocean mesoscale eddy and internal wave fields