Self-organized criticality of turbulence in strongly stratified mixing layers

Motivated by the importance of stratified shear flows in geophysical and environmental circumstances, we characterize their energetics, mixing and spectral behaviour through a series of direct numerical simulations of turbulence generated by Holmboe wave instability (HWI) under various initial conditions. We focus on circumstances where the stratification is sufficiently ‘strong’ so that HWI is the dominant primary instability of the flow. Our numerical findings demonstrate the emergence of self-organized criticality (SOC) that is manifest as an adjustment of an appropriately defined gradient Richardson number, $Ri_{g}$, associated with the horizontally averaged mean flow, in such a way that it is continuously attracted towards a critical value of $Ri_{g}\sim 1/4$. This self-organization occurs through a continuously reinforced localization of the ‘scouring’ motions (i.e. ‘avalanches’) that are characteristic of the turbulence induced by the breakdown of Holmboe wave instabilities and are developed on the upper and lower flanks of the sharply localized density interface, embedded within a much more diffuse shear layer. These localized ‘avalanches’ are also found to exhibit the expected scale-invariant characteristics. From an energetics perspective, the emergence of SOC is expressed in the form of a long-lived turbulent flow that remains in a ‘quasi-equilibrium’ state for an extended period of time. Most importantly, the irreversible mixing that results from such self-organized behaviour appears to be characterized generically by a universal cumulative turbulent flux coefficient of \unicode[STIX]{x1D6E4}_{c}\sim 0.2 only for turbulent flows engendered by Holmboe wave instability. The existence of this self-organized critical state corroborates the original physical arguments associated with self-regulation of stratified turbulent flows as involving a ‘kind of equilibrium’ as described by Turner (1973, Buoyancy Effects in Fluids, Cambridge University Press).H.S. acknowledges the SOSCIP TalentEdge post doctoral fellowship and is grateful to the David Crighton Fellowship from D.A.M.T.P., University of Cambridge. All the computations were performed on the BG/Q supercomputer at the University of Toronto which is operated by SciNet for the Southern Ontario Smart Computing Innovation Platform. SciNet is funded by: the Canada Foundation for Innovation under the auspices of Compute Canada; the Government of Ontario; Ontario Research Fund - Research Excellence; and the University of Toronto. The research of W.R.P. at the University of Toronto is sponsored by NSERC Discovery Grant A9627. The research activity of C.P.C. is supported by EPSRC Programme Grant EP/K034529/1 entitled `Mathematical Underpinning of Stratified Turbulence'

Turbulent mixing due to the Holmboe wave instability at high Reynolds number

We consider numerically the transition to turbulence and associated mixing in stratified shear flows with initial velocity distribution $\overline{U}(z,0)\,\boldsymbol{e}_{x}=U_{0}\,\boldsymbol{e}_{x}\tanh (z/d)$ and initial density distribution \overline{\unicode[STIX]{x1D70C}}(z,0)=\unicode[STIX]{x1D70C}_{0}[1-\tanh (z/\unicode[STIX]{x1D6FF})] away from a hydrostatic reference state \unicode[STIX]{x1D70C}_{r}\gg \unicode[STIX]{x1D70C}_{0}. When the ratio R=d/\unicode[STIX]{x1D6FF} of the characteristic length scales over which the velocity and density vary is equal to one, this flow is primarily susceptible to the classic well-known Kelvin–Helmholtz instability (KHI). This instability, which typically manifests at finite amplitude as an array of elliptical vortices, strongly ‘overturns’ the density interface of strong initial gradient, which nevertheless is the location of minimum initial gradient Richardson number Ri_{g}(0)=Ri_{b}=g\unicode[STIX]{x1D70C}_{0}d/\unicode[STIX]{x1D70C}_{r}U_{0}^{2}, where Ri_{g}(z)=-([g/\unicode[STIX]{x1D70C}_{r}]\,\text{d}\overline{\unicode[STIX]{x1D70C}}/\text{d}z)/(\text{d}\overline{U}/\text{d}z)^{2} and $Ri_{b}$ is a bulk Richardson number. As is well known, at sufficiently high Reynolds numbers ($Re$), the primary KHI induces a vigorous but inherently transient burst of turbulence and associated irreversible mixing localised in the vicinity of the density interface, leading to a relatively well-mixed region bounded by stronger density gradients above and below. We explore the qualitatively different behaviour that arises when $R\gg 1$, and so the density interface is sharp, with $Ri_{g}(z)$ now being maximum at the density interface $Ri_{g}(0)=RRi_{b}$. This flow is primarily susceptible to Holmboe wave instability (HWI) (Holmboe, Geophys. Publ., vol. 24, 1962, pp. 67–113), which manifests at finite amplitude in this symmetric flow as counter-propagating trains of elliptical vortices above and below the density interface, thus perturbing the interface so as to exhibit characteristically cusped interfacial waves which thereby ‘scour’ the density interface. Unlike previous lower-$Re$ experimental and numerical studies, when $Re$ is sufficiently high the primary HWI becomes increasingly more three-dimensional due to the emergence of shear-aligned secondary convective instabilities. As $Re$ increases, (i) the growth rate of secondary instabilities appears to saturate and (ii) the perturbation kinetic energy exhibits a $k^{-5/3}$ spectrum for sufficiently large length scales that are influenced by anisotropic buoyancy effects. Therefore, at sufficiently high $Re$, vigorous turbulence is triggered that also significantly ‘scours’ the primary density interface, leading to substantial irreversible mixing and vertical transport of mass above and below the (robust) primary density interface. Furthermore, HWI produces a markedly more long-lived turbulence event compared to KHI at a similarly high $Re$. Despite their vastly different mechanics (i.e. ‘overturning’ versus ‘scouring’) and localisation, the mixing induced by KHI and HWI is comparable in both absolute terms and relative efficiency. Our results establish that, provided the flow Reynolds number is sufficiently high, shear layers with sharp density interfaces and associated locally high values of the gradient Richardson number may still be sites of substantial and efficient irreversible mixing.This research has been conducted in part while H.S. visited DAMTP, University of Cambridge. H.S. is grateful to the David Crighton Fellowship from DAMTP. All the computations were performed on the BG/Q supercomputer of SOSCIP (the Southern Ontario Smart Computing Innovation Platform) which is hosted by the University of Toronto. The research activity of C.P.C. is supported by EPSRC Programme Grant EP/K034529/1 entitled `Mathematical Underpinning of Strati ed Turbulence'. The research of W.R.P. at the University of Toronto is supported by NSERC Discovery Grant A9627.This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Cambridge University Press

Databases for Managing Genetic Resources Collections and Mapping Populations of Forage and Related Species

Effective management of plant material used in crop improvement and underpinning research is greatly facilitated by a properly designed data structure accessible by all those working with the material. At IGER we have developed the Aberystwyth Genetic Resources Information System, AGRIS, for managing genetic resources acquired through collecting trips, seed exchange, breeding and transgenic programmes. Recently this has been complemented by MaPIS, a Mapping Populations Information System, which links with AGRIS and allows for storage and documentation of information about plant mapping populations, including pedigrees, status and physical locations of accessions and individual genotypes. IGER also maintains the European Central Crop Databases for Lolium species and Trifolium repens, and the UK National Inventory of all plant genetic resources conserved ex situ in the UK; by November 2004, the UKNI had contributed over 220000 accessions to the 900000 in the Europe-wide database EURISCO

Deceleration of probe beam by stage bias potential improves resolution of serial block-face scanning electron microscopic images.

Serial block-face scanning electron microscopy (SBEM) is quickly becoming an important imaging tool to explore three-dimensional biological structure across spatial scales. At probe-beam-electron energies of 2.0 keV or lower, the axial resolution should improve, because there is less primary electron penetration into the block face. More specifically, at these lower energies, the interaction volume is much smaller, and therefore, surface detail is more highly resolved. However, the backscattered electron yield for metal contrast agents and the backscattered electron detector sensitivity are both sub-optimal at these lower energies, thus negating the gain in axial resolution. We found that the application of a negative voltage (reversal potential) applied to a modified SBEM stage creates a tunable electric field at the sample. This field can be used to decrease the probe-beam-landing energy and, at the same time, alter the trajectory of the signal to increase the signal collected by the detector. With decelerated low landing-energy electrons, we observed that the probe-beam-electron-penetration depth was reduced to less than 30 nm in epoxy-embedded biological specimens. Concurrently, a large increase in recorded signal occurred due to the re-acceleration of BSEs in the bias field towards the objective pole piece where the detector is located. By tuning the bias field, we were able to manipulate the trajectories of the  primary and secondary electrons, enabling the spatial discrimination of these signals using an advanced ring-type BSE detector configuration or a standard monolithic BSE detector coupled with a blocking aperture

Computing and reducing slope complexes

In this paper we provide a new characterization of cell de- composition (called slope complex) of a given 2-dimensional continuous surface. Each patch (cell) in the decomposition must satisfy that there exists a monotonic path for any two points in the cell. We prove that any triangulation of such surface is a slope complex and explain how to obtain new slope complexes with a smaller number of slope regions decomposing the surface. We give the minimal number of slope regions by counting certain bounding edges of a triangulation of the surface obtained from its critical points.Ministerio de Economía y Competitividad MTM2015-67072-

Sulfonated copolymers as heparin-mimicking stabilizer of fibroblast growth factor : size, architecture, and monomer distribution effects

Fibroblast growth factors (FGF) are involved in a wide range of biological processes such as cell proliferation and differentiation. In living organisms, the binding of FGF to its receptors are mediated through electrostatic interactions between FGF and naturally occurring heparin. Despite its prevalent use in medicine, heparin carries notable limitations, namely; its extraction from natural sources (expensive, low yield and extensive purification), viral contamination, and batch-to-batch heterogeneity. In this work a range of synthetic homopolymers and copolymers of sodium 2-acrylamido-2-methylpropane sulfonate (AMPS®) were evaluated as potential FGF stabilisers. This was studied by measuring the proliferation of BaF3-FR1c cells, as a model assay, and the results will be compared with the natural stabilisation and activation of FGF by heparin. This study explores the structure-activity relationship of these polysulfonated polymers with a focus on the effect of molecular weight, co-monomer type, charge dispersion and polymer architecture on protein stabilisation

Influence of block versus random monomer distribution on the cellular uptake of hydrophilic copolymers

The use of polymers has revolutionized the field of drug delivery in the past two decades. Properties such as polymer size, charge, hydrophilicity, or branching have all been shown to play an important role in the cellular internalization of polymeric systems. In contrast, the fundamental impact of monomer distribution on the resulting biological properties of copolymers remains poorly studied and is always only investigated for biologically active self-assembling polymeric systems. Here, we explore the fundamental influence of monomer distribution on the cellular uptake of nonaggregating and biologically passive copolymers. Reversible addition–fragmentation chain-transfer (RAFT) polymerization was used to prepare precisely defined copolymers of three hydrophilic acrylamide monomers. The cellular internalization of block copolymers was compared with the uptake of a random copolymer where monomers are statistically distributed along the chain. The results demonstrate that monomer distribution in itself has a negligible impact on copolymer uptake

Dispelling the myths of online education: learning via the information superhighway

There continues to be a perception that online education is inferior to traditional education. In the U.S. online learning is more developed than in the U.K. This paper provides insights into a U.S. provision and takes a close look at what are perceived as weaknesses of on line learning and argues that these are not necessarily inherent weaknesses of this form of educational delivery. Then, results of two major studies, undertaken in the U.S. are provided comparing the effectiveness of online education to traditional education as perceived by current MBA students and past graduates. Results of these studies suggest that students of MBA modules and MBA graduates perceive the quality and effectiveness of online education to be similar to, if not higher than, the quality and effectiveness of traditional modules and programmes

Internal convection in thermoelectric generator models

Coupling between heat and electrical currents is at the heart of thermoelectric processes. From a thermal viewpoint this may be seen as an additional thermal flux linked to the appearance of electrical current in a given thermoelectric system. Since this additional flux is associated to the global displacement of charge carriers in the system, it can be qualified as convective in opposition to the conductive part associated with both phonons transport and heat transport by electrons under open circuit condition, as, e.g., in the Wiedemann-Franz relation. In this article we demonstrate that considering the convective part of the thermal flux allows both new insight into the thermoelectric energy conversion and the derivation of the maximum power condition for generators with realistic thermal coupling.Comment: 8 pages, 3 figure

Connectivity forests for homological analysis of digital volumes

In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of “tunnels” and “holes”, classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs