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Mesoscale features present at the Denmark Strait sill regularly enhance the volume transport of the Denmark Strait overflow (DSO). They are important for the Atlantic Meridional Overturning Circulation and ultimately, for the global climate system. Using a realistic numerical model, we find new evidence of the causal relationship between overflow surges (i.e., mesoscale features associated with high‐transport events) and DSO cyclones observed downstream. Most of the cyclones form at the Denmark Strait sill during overflow surges and, because of potential vorticity conservation and stretching of the water column, grow as they move equatorward. A fraction of the cyclones form downstream of the sill, when anticyclonic vortices formed during high‐transport events start collapsing. Regardless of their formation mechanism, DSO cyclones weaken starting roughly 150 km downstream of the sill, and potential vorticity is only materially conserved during the growth phase.

 

Prior mathematical work of Constantin & Iyer ( Commun. Pure Appl. Maths , vol. 61, 2008, pp. 330–345; Ann. Appl. Probab. , vol. 21, 2011, pp. 1466–1492) has shown that incompressible Navier–Stokes solutions possess infinitely many stochastic Lagrangian conservation laws for vorticity, backward in time, which generalize the invariants of Cauchy ( Sciences mathématiques et physique , vol. I, 1815, pp. 33–73) for smooth Euler solutions. We reformulate this theory for the case of wall-bounded flows by appealing to the Kuz'min ( Phys. Lett. A , vol. 96, 1983, pp. 88–90)–Oseledets ( Russ. Math. Surv. , vol. 44, 1989, p. 210) representation of Navier–Stokes dynamics, in terms of the vortex-momentum density associated to a continuous distribution of infinitesimal vortex rings. The Constantin–Iyer theory provides an exact representation for vorticity at any interior point as an average over stochastic vorticity contributions transported from the wall. We point out relations of this Lagrangian formulation with the Eulerian theory of Lighthill (Boundary layer theory. In Laminar Boundary Layers (ed. L. Rosenhead), 1963, pp. 46–113)–Morton ( Geophys. Astrophys. Fluid Dyn. , vol. 28, 1984, pp. 277–308) for vorticity generation at solid walls, and also with a statistical result of Taylor ( Proc. R. Soc. Lond. A , vol. 135, 1932, pp. 685–702)–Huggins ( J. Low Temp. Phys. , vol. 96, 1994, pp. 317–346), which connects dissipative drag with organized cross-stream motion of vorticity and which is closely analogous to the ‘Josephson–Anderson relation’ for quantum superfluids. We elaborate a Monte Carlo numerical Lagrangian scheme to calculate the stochastic Cauchy invariants and their statistics, given the Eulerian space–time velocity field. The method is validated using an online database of a turbulent channel-flow simulation (Graham et al. , J. Turbul. , vol. 17, 2016, pp. 181–215), where conservation of the mean Cauchy invariant is verified for two selected buffer-layer events corresponding to an ‘ejection’ and a ‘sweep’. The variances of the stochastic Cauchy invariants grow exponentially backward in time, however, revealing Lagrangian chaos of the stochastic trajectories undergoing both fluid advection and viscous diffusion. 

We use an online database of a turbulent channel-flow simulation at $Re_\tau =1000$ (Graham et al. J. Turbul. , vol. 17, issue 2, 2016, pp. 181–215) to determine the origin of vorticity in the near-wall buffer layer. Following an experimental study of Sheng et al. ( J. Fluid Mech. , vol. 633, 2009, pp.17–60), we identify typical ‘ejection’ and ‘sweep’ events in the buffer layer by local minima/maxima of the wall stress. In contrast to their conjecture, however, we find that vortex lifting from the wall is not a discrete event requiring $\sim$ 1 viscous time and $\sim$ 10 wall units, but is instead a distributed process over a space–time region at least $1\sim 2$ orders of magnitude larger in extent. To reach this conclusion, we exploit a rigorous mathematical theory of vorticity dynamics for Navier–Stokes solutions, in terms of stochastic Lagrangian flows and stochastic Cauchy invariants, conserved on average backward in time. This theory yields exact expressions for vorticity inside the flow domain in terms of vorticity at the wall, as transported by viscous diffusion and by nonlinear advection, stretching and rotation. We show that Lagrangian chaos observed in the buffer layer can be reconciled with saturated vorticity magnitude by ‘virtual reconnection’: although the Eulerian vorticity field in the viscous sublayer has a single sign of spanwise component, opposite signs of Lagrangian vorticity evolve by rotation and cancel by viscous destruction. Our analysis reveals many unifying features of classical fluids and quantum superfluids. We argue that ‘bundles’ of quantized vortices in superfluid turbulence will also exhibit stochastic Lagrangian dynamics and satisfy stochastic conservation laws resulting from particle relabelling symmetry. 

Abstract The Denmark Strait Overflow (DSO) is an important contributor to the lower limb of the Atlantic meridional overturning circulation (AMOC). Determining DSO formation and its pathways is not only important for local oceanography but also critical to estimating the state and variability of the AMOC. Despite prior attempts to understand the DSO sources, its upstream pathways and circulation remain uncertain due to short-term (3–5 days) variability. This makes it challenging to study the DSO from observations. Given this complexity, this study maps the upstream pathways and along-pathway changes in its water properties, using Lagrangian backtracking of the DSO sources in a realistic numerical ocean simulation. The Lagrangian pathways confirm that several branches contribute to the DSO from the north such as the East Greenland Current (EGC), the separated EGC (sEGC), and the North Icelandic Jet (NIJ). Moreover, the model results reveal additional pathways from south of Iceland, which supplied over 16% of the DSO annually and over 25% of the DSO during winter of 2008, when the NAO index was positive. The southern contribution is about 34% by the end of March. The southern pathways mark a more direct route from the near-surface subpolar North Atlantic to the North Atlantic Deep Water (NADW), and needs to be explored further, with in situ observations. 

Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension$D\approx 7/3$, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of$D=2.36\pm 0.03$over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertaining to the dependence on height above the surface are also presented. Results provide evidence that turbulent spots exhibit high-Reynolds-number fractal-scaling properties already during early transitional and nonisotropic stages of the flow evolution.

 

A high-resolution numerical model, together with in situ and satellite observations, is used to explore the nature and dynamics of the dominant high-frequency (from one day to one week) variability in Denmark Strait. Mooring measurements in the center of the strait reveal that warm water “flooding events” occur, whereby the North Icelandic Irminger Current (NIIC) propagates offshore and advects subtropical-origin water northward through the deepest part of the sill. Two other types of mesoscale processes in Denmark Strait have been described previously in the literature, known as “boluses” and “pulses,” associated with a raising and lowering of the overflow water interface. Our measurements reveal that flooding events occur in conjunction with especially pronounced pulses. The model indicates that the NIIC hydrographic front is maintained by a balance between frontogenesis by the large-scale flow and frontolysis by baroclinic instability. Specifically, the temperature and salinity tendency equations demonstrate that the eddies act to relax the front, while the mean flow acts to sharpen it. Furthermore, the model reveals that the two dense water processes—boluses and pulses (and hence flooding events)—are dynamically related to each other and tied to the meandering of the hydrographic front in the strait. Our study thus provides a general framework for interpreting the short-time-scale variability of Denmark Strait Overflow Water entering the Irminger Sea.

 

OceanSpy is an open-source and user-friendly Python package that enables scientists and interested amateurs to analyze and visualize oceanographic data sets. OceanSpy builds on software packages developed by the Pangeo community, in particular Xarray (Hoyer & Hamman, 2017), Dask (Dask Development Team, 2016), and Xgcm (“Xgcm,” n.d.). The integration of Dask facilitates scalability, which is important for the petabyte-scale simulations that are becoming available. OceanSpy can be used as a standalone package for analysis of local circulation model output, or it can be run on a remote data-analysis cluster, such as the Johns Hopkins University SciServer system (Medvedev, Lemson, & Rippin, 2016), which hosts several simulations and is publicly available. OceanSpy enables extraction, processing, and visualization of model data to (i) compare with oceanographic observations, and (ii) portray the kinematic and dynamic space-time properties of the circulation.