Resolving the fine-scale structure in turbulent Rayleigh-Benard convection

We present high-resolution direct numerical simulation studies of turbulent Rayleigh-Benard convection in a closed cylindrical cell with an aspect ratio of one. The focus of our analysis is on the finest scales of convective turbulence, in particular the statistics of the kinetic energy and thermal dissipation rates in the bulk and the whole cell. The fluctuations of the energy dissipation field can directly be translated into a fluctuating local dissipation scale which is found to develop ever finer fluctuations with increasing Rayleigh number. The range of these scales as well as the probability of high-amplitude dissipation events decreases with increasing Prandtl number. In addition, we examine the joint statistics of the two dissipation fields and the consequences of high-amplitude events. We also have investigated the convergence properties of our spectral element method and have found that both dissipation fields are very sensitive to insufficient resolution. We demonstrate that global transport properties, such as the Nusselt number, and the energy balances are partly insensitive to insufficient resolution and yield correct results even when the dissipation fields are under-resolved. Our present numerical framework is also compared with high-resolution simulations which use a finite difference method. For most of the compared quantities the agreement is found to be satisfactory.Comment: 33 pages, 24 figure

Turbulent superstructures in Rayleigh-B\'enard convection

Turbulent Rayleigh-B\'enard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. They are analyzed by numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to $10^7$. For each case, we identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also found to be correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.Comment: 16 pages (incl. Supplementary Material), 12 figures (all with downsized figure size

Rotating Rayleigh-Bénard Convection

Rotating Rayleigh-Benard convection (rRBC) is studied as a paradigmatic example of pattern formation and spatiotemporal chaos. For large enough rotation rates, this system undergoes a supercritical bifurcation from the uniform state to a state known as domain chaos. In domain chaos, domains of straight parallel rolls change their orientation and size discretely. This roll switching causes an overall counterclockwise precession of the pattern. An additional mechanism of precession, glide-induced precession, is introduced here, by deriving the rRBC amplitude equation to higher order. New terms due to the rotation cause rolls to precess whenever there is an amplitude gradient in the direction parallel to the rolls. Hence, dislocations which are stationary in a nonrotating system will glide in a rotating frame, causing the overall precession. Theory that includes the Coriolis force but ignores the centrifugal force predicted scaling laws near the transition to domain chaos. However, experimenters found different scaling laws. The scaling laws are studied here by direct numerical simulations (DNS) for the exact parameters as experiments. When only the Coriolis force is included, the DNS scaling laws agree with theory. When the centrifugal force is also included, the DNS scaling laws agree better with experiment; hence the centrifugal force cannot be neglected from theory. The coefficients of the amplitude equation for the Complex Ginzburg-Landau equation (CGLE) are found for DNS of traveling waves. They agree well with experimental results. The CGLE is chaotic for certain values of the coefficients. However, for the parameters in the DNS, those chaotic regimes were not realized. Leading order Lyapunov exponents (LLE) and eigenvectors are computed for both rotating and nonrotating convection. For certain parameters, these systems are found to have positive LLEs; hence they are truly chaotic. For time-dependent systems, the leading eigenvector is characterized by localized bursts of activity which are associated with dynamical events. The short-time dynamics of the LLE is correlated with these dynamical events. However, contributions to the LLE are due to non-periodic events only. Lagrangian particle tracking methods are employed for rRBC. These systems exhibit chaotic advection in that initially localized particle trajectories explore the available phase space.</p

Supergranule aggregation for constant heat flux-driven turbulent convection

Turbulent convection processes in nature are often found to be organized in a hierarchy of plume structures and flow patterns. The gradual aggregation of convection cells or granules to a supergranule which eventually fills the whole horizontal layer is reported and analysed in spectral element direct numerical simulations of three-dimensional turbulent Rayleigh-B\'{e}nard convection at an aspect ratio of $60$. The formation proceeds over a time span of more than $10^4$ convective time units for the largest accessible Rayleigh number and occurs only when the turbulence is driven by a constant heat flux which is imposed at the bottom and top planes enclosing the convection layer. The resulting gradual inverse cascade process is observed for both temperature variance and turbulent kinetic energy. An additional analysis of the leading Lyapunov vector field for the full turbulent flow trajectory in its high-dimensional phase space demonstrates that turbulent flow modes at a certain scale continue to give rise locally to modes with longer wavelength in the turbulent case. As a consequence successively larger convection patterns grow until the horizontal extension of the layer is reached. This instability mechanism, which is known to exist near the onset of constant heat flux-driven convection, is shown here to persist into the fully developed turbulent flow regime thus connecting weakly nonlinear pattern formation with the one in fully developed turbulence. We discuss possible implications of our study for observed, but not yet consistently numerically reproducible, solar supergranulation which could lead to improved simulation models of surface convection in the Sun.Comment: 15 pages, 11 figure

Association of low center performance evaluations and pediatric heart transplant center behavior in the United States

BACKGROUND: To date, no study has evaluated the effects of low center performance evaluations (CPE) on pediatric heart transplant center behavior. We sought to assess the impact of low CPE flags on pediatric heart transplant center listing and transplant volumes and center recipient and donor characteristics. METHODS: We included centers performing at least 10 pediatric (age \u3c18 years) transplants during the Scientific Registry of Transplant Recipients reporting period January 2009-June 2011 and evaluated consecutive biannual program specific reports until the last reporting period January 2016-June 2018. We evaluated changes in center behavior at following time points: a year before flagging, a year and two years after the flag; and at last reporting period. RESULTS: During our study period, 24 pediatric centers were non-flagged and 6 were flagged. Compared to non-flagged centers, there was a decline in candidate listings in flagged centers at the last reporting period (mean increase of 5.5 ± 12.4 listings vs ?\u3e mean decrease of 14.0 ± 14.9 listings; p = .003). Similarly, the number of transplants declined in flagged centers (mean increase of 2.6 ± 9.6 transplants vs ?\u3e mean decrease of 10.0 ± 12.8 transplants; p = .012). Flagged centers had declines in listings for patients with restrictive cardiomyopathy, re-transplant, renal dysfunction, those on mechanical ventilation and extracorporeal membrane oxygenation. There was no significant change in donor characteristics between flagged and non-flagged centers. CONCLUSIONS: Low CPE may have unintended negative consequences on center behavior leading to declines in listing and transplant volumes and potentially leading to decreased listing for higher risk recipients

Quantitative cardiac magnetic resonance T2 imaging offers ability to non-invasively predict acute allograft rejection in children

BACKGROUND: Monitoring for acute allograft rejection improves outcomes after cardiac transplantation. Endomyocardial biopsy is the gold standard test defining rejection, but carries risk and has limitations. Cardiac magnetic resonance T2 mapping may be able to predict rejection in adults, but has not been studied in children. Our aim was to evaluate T2 mapping in identifying paediatric cardiac transplant patients with acute rejection. METHODS: Eleven paediatric transplant patients presenting 18 times were prospectively enrolled for non-contrast cardiac magnetic resonance at 1.5 T followed by endomyocardial biopsy. Imaging included volumetry, flow, and T2 mapping. Regions of interest were manually selected on the T2 maps using the middle-third technique in the left ventricular septal and lateral wall in a short-axis and four-chamber slice. Mean and maximum T2 values were compared with Student\u27s t-tests analysis. RESULTS: Five cases of acute rejection were identified in three patients, including two cases of grade 2R on biopsy and three cases of negative biopsy treated for clinical symptoms attributed to rejection (new arrhythmia, decreased exercise capacity). A monotonic trend between increasing T2 values and higher biopsy grades was observed: grade 0R T2 53.4 ± 3 ms, grade 1R T2 54.5 ms ± 3 ms, grade 2R T2 61.3 ± 1 ms. The five rejection cases had significantly higher mean T2 values compared to cases without rejection (58.3 ± 4 ms versus 53 ± 2 ms, p = 0.001). CONCLUSIONS: Cardiac magnetic resonance with quantitative T2 mapping may offer a non-invasive method for screening paediatric cardiac transplant patients for acute allograft rejection. More data are needed to understand the relationship between T2 and rejection in children