Potential vorticity fronts and the late-time evolution of large-scale quasi-geostrophic flows

Funding: BHB acknowledges support for this research from a Leverhulme Trust Early Career Fellowship.The late-time behaviour of freely evolving quasi-geostrophic flows with initial characteristic length scale L0 larger than or equal to the deformation radius LD, L0/LD≥1 , is studied. At late time the flows are dominated by large multi-level vortices consisting of ascending terraces of well-mixed potential vorticity (PV), i.e. PV staircases. We examine how the number of mixed PV levels depends on the initial conditions, in particular L0/LD . For sufficiently large values of L0/LD≈5 , a complete staircase with regular steps forms, but as L0/LD decreases, the staircase becomes more irregular, with fewer mixed levels and the appearance of a large step centred on zero PV, corresponding to large regions of near-zero PV separating the multi-level vortices. This occurs because weak PV features in the initial field with scales smaller than LD undergo filamentation and are coarse-grained away or homogenised. For all values of L0/LD considered, inverse cascades of potential energy commence at sufficiently late times. The onset of these cascades, even when the flow is initialised well within the ‘asymptotic model’ (AM) regime, suggests that the AM regime is not self-consistent: when potential vorticity fronts are well-resolved, frontal dynamics eventually drive ongoing flow evolution.Publisher PDFPeer reviewe

On the spacing of meandering jets in the strong-stair limit

Based on an assumption of strongly inhomogeneous potential vorticity mixing in quasi-geostrophic -plane turbulence, a relation is obtained between the mean spacing of latitudinally meandering zonal jets and the total kinetic energy of the flow. The relation applies to cases where the Rossby deformation length is much smaller than the Rhines scale, in which kinetic energy is concentrated within the jet cores. The relation can be theoretically achieved in the case of perfect mixing between regularly spaced jets with simple meanders, and of negligible kinetic energy in flow structures other than in jets. Incomplete mixing or unevenly spaced jets will result in jets being more widely separated than the estimate, while significant kinetic energy outside the jets will result in jets closer than the estimate. An additional relation, valid under the same assumptions, is obtained between the total kinetic and potential energies. In flows with large-scale dissipation, the two relations provide a means to predict the jet spacing based only on knowledge of the energy input rate of the forcing and dissipation rate, regardless of whether the latter takes the form of frictional or thermal damping. Comparison with direct numerical integrations of the forced system shows broad support for the relations, but differences between the actual and predicted jet spacings arise both from the complex structure of jet meanders and the non-negligible kinetic energy contained in the turbulent background and in coherent vortices lying between the jets.PostprintPeer reviewe

Vortex scaling ranges in two-dimensional turbulence

We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.PostprintPeer reviewe

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.Comment: 33 pages, 17 figure

Motion of Three Vortices near Collapse

A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, vortex triangle remains similar to the original one, while its area decreases (grows) at a constant rate. A contracting configuration brings three vortices to a single point in a finite time; this phenomenon known as vortex collapse is of principal importance for many-vortex systems. Dynamics of close-to-collapse vortex configurations depends on the way the collapse conditions are violated. Using an effective potential representation, a detailed quantitative analysis of all the different types of near-collapse dynamics is performed when two of the vortices are identical. We discuss time and length scales, emerging in the problem, and their behavior as the initial vortex triangle is approaching to an exact collapse configuration. Different types of critical behaviors, such as logarithmic or power-law divergences are exhibited, which emphasizes the importance of the way the collapse is approached. Period asymptotics for all singular cases are presented as functions of the initial vortices configurations. Special features of passive particle mixing by a near-collapse flows are illustrated numerically.Comment: 45 pages, 22 figures Last version of the paper with all update

On the Formation of Collective Memories: The Role of a Dominant Narrator.

To test our hypothesis that conversations can contribute to the formation of collective memory, we asked participants to study stories and to recall them individually (pregroup recollection), then as a group (group recounting), and then once again individually (postgroup recollection). One way that postgroup collective memories can be formed under these circumstances is if unshared pregroup recollections in the group recounting influences others\u27 postgroup recollections. In the present research, we explored (using tests of recall and recognition) whether the presence of a dominant narrator can facilitate the emergence of unshared pregroup recollections in a group recounting and whether this emergence is associated with changes in postgroup recollections. We argue that the formation of a collective memory through conversation is not inevitable but is limited by cognitive factors, such as conditions for social contagion, and by situational factors, such as the presence of a narrator

Self-sharpening induces jet-like structure in seafloor gravity currents

Gravity currents are the primary means by which sediments, solutes and heat are transported across the ocean-floor. Existing theory of gravity current flow employs a statistically-stable model of turbulent diffusion that has been extant since the 1960s. Here we present the first set of detailed spatial data from a gravity current over a rough seafloor that demonstrate that this existing paradigm is not universal. Specifically, in contrast to predictions from turbulent diffusion theory, self-sharpened velocity and concentration profiles and a stable barrier to mixing are observed. Our new observations are explained by statistically-unstable mixing and self-sharpening, by boundary-induced internal gravity waves; as predicted by recent advances in fluid dynamics. Self-sharpening helps explain phenomena such as ultra-long runout of gravity currents and restricted growth of bedforms, and highlights increased geohazard risk to marine infrastructure. These processes likely have broader application, for example to wave-turbulence interaction, and mixing processes in environmental flows