Steady Rayleigh–Bénard convection between no-slip boundaries

The central open question about Rayleigh–Bénard convection – buoyancy-driven flow in a fluid layer heated from below and cooled from above – is how vertical heat flux depends on the imposed temperature gradient in the strongly nonlinear regime where the flows are typically turbulent. The quantitative challenge is to determine how the Nusselt number $Nu$ depends on the Rayleigh number $Ra$ in the $Ra\to \infty$ limit for fluids of fixed finite Prandtl number $Pr$ in fixed spatial domains. Laboratory experiments, numerical simulations and analysis of Rayleigh's mathematical model have yet to rule out either of the proposed ‘classical’ $Nu \sim Ra^{1/3}$ or ‘ultimate’ $Nu \sim Ra^{1/2}$ asymptotic scaling theories. Among the many solutions of the equations of motion at high $Ra$ are steady convection rolls that are dynamically unstable but share features of the turbulent attractor. We have computed these steady solutions for $Ra$ up to $10^{14}$ with $Pr=1$ and various horizontal periods. By choosing the horizontal period of these rolls at each $Ra$ to maximize $Nu$ , we find that steady convection rolls achieve classical asymptotic scaling. Moreover, they transport more heat than turbulent convection in experiments or simulations at comparable parameters. If heat transport in turbulent convection continues to be dominated by heat transport in steady rolls as $Ra\to \infty$ , it cannot achieve the ultimate scaling.

Anisotropic Diffusion in Driven Convection Arrays

We numerically investigate the transport of a Brownian colloidal particle in a square array of planar counter-rotating convection rolls at high Péclet numbers. We show that an external force produces huge excess peaks of the particle’s diffusion constant with a height that depends on the force orientation and intensity. In sharp contrast, the particle’s mobility is isotropic and force independent. We relate such a nonlinear response of the system to the advection properties of the laminar flow in the suspension fluid.

New forms of structure in ecosystems revealed with the Kuramoto model

Ecological systems, as is often noted, are complex. Equally notable is the generalization that complex systems tend to be oscillatory, whether Huygens' simple patterns of pendulum entrainment or the twisted chaotic orbits of Lorenz’ convection rolls. The analytics of oscillators may thus provide insight into the structure of ecological systems. One of the most popular analytical tools for such study is the Kuramoto model of coupled oscillators. We apply this model as a stylized vision of the dynamics of a well-studied system of pests and their enemies, to ask whether its actual natural history is reflected in the dynamics of the qualitatively instantiated Kuramoto model. Emerging from the model is a series of synchrony groups generally corresponding to subnetworks of the natural system, with an overlying chimeric structure, depending on the strength of the inter-oscillator coupling. We conclude that the Kuramoto model presents a novel window through which interesting questions about the structure of ecological systems may emerge.

Persistent westward drift of the geomagnetic field at the core–mantle boundary linked to recurrent high-latitude weak/reverse flux patches

SUMMARY Observations of changes in the geomagnetic field provide unique information about processes in the outer core where the field is generated. Recent geomagnetic field reconstructions based on palaeomagnetic data show persistent westward drift at high northern latitudes at the core–mantle boundary (CMB) over the past 4000 yr, as well as intermittent occurrence of high-latitude weak or reverse flux patches. To further investigate these features, we analysed time-longitude plots of a processed version of the geomagnetic field model pfm9k.1a, filtered to remove quasi-stationary features of the field. Our results suggest that westward drift at both high northern and southern latitudes of the CMB have been a persistent feature of the field over the past 9000 yr. In the Northern Hemisphere we detect two distinct signals with drift rates of 0.09° and 0.25° yr−1 and dominant zonal wavenumbers of m = 2 and 1, respectively. Comparisons with other geomagnetic field models support these observations but also highlight the importance of sedimentary data that provide crucial information on high-latitude geomagnetic field variations. The two distinct drift signals detected in the Northern Hemisphere can largely be decomposed into two westward propagating waveforms. We show that constructive interference between these two waveforms accurately predicts both the location and timing of previously observed high-latitude weak/reverse flux patches over the past 3–4 millennia. In addition, we also show that the 1125-yr periodicity signal inferred from the waveform interference correlates positively with variations in the dipole tilt over the same time period. The two identified drift signals may partially be explained by the westward motion of high-latitude convection rolls. However, the dispersion relation might also imply that part of the drift signal could be caused by magnetic Rossby waves riding on the mean background flow.

Unexpected segregation patterns in high speed granular flows

<p align="JUSTIFY">Classically, for free surface flows of binary granular mixture, large particles migrate at the top of the flow while small ones percolate to the bottom. The key mechanisms at the origin of this segregation behavior have been identified as a combination of squeeze expulsion and kinetic sieving (Savage & Lun J. Fluid Mech. 1988). In this case, the segregation process is governed by the gravity. We <span>discovered</span> here by means of numerical simulations a new segregation pattern in high speed granular flows where size segregation is driven mostly by granular temperature gradients rather than gravity, which highlight the complexity of providing a complete description of segregation processes.</p><p align="JUSTIFY">High speed granular flows are obtained by means of discrete numerical simulations (DEM) in a confined geometry with lateral frictional side-walls. Recently, Brodu et al. (Phys. Rev. E 2013, J. Fluid Mech. 2015) highlighted that this confined geometry allows to produce steady and fully-developed flows at relatively high angles of inclination, including a rich and broad variety of new regimes. In particular, they showed the existence of supported regimes, characterized by a dense and cold (in terms of granular temperature) core floating over a dilute and highly agitated layer of grains, accompanied with longitudinal convection rolls.</p><p align="JUSTIFY">We performed extensive numerical simulations within this geometry with binary mixture of spheres with a given size ratio of 2. We analyzed segregation patterns of steady and fully-developed flows for inclination angles ranging from 18° to 50° and various mixture proportions of large particles ranging from 0 to 100%. We evidenced a new segregation pattern that emerge in the supported flow regimes: large particles no longer accumulate in the upper layers of the flow but are trapped in the dense core and localized at the center of the convection rolls. The strong temperature gradients that develop between the dense core and the surrounding dilute layer seem to govern the segregation mechanism. The accumulation of large particles in the dense core, which is the fastest region of the flow, also tends to enhance the total mass flux in comparison with similar mono-disperse flows.</p>