Probing turbulent superstructures in Rayleigh-B\'{e}nard convection by Lagrangian trajectory clusters

We analyze large-scale patterns in three-dimensional turbulent convection in a horizontally extended square convection cell by Lagrangian particle trajectories calculated in direct numerical simulations. A simulation run at a Prandtl number Pr $=0.7$, a Rayleigh number Ra $=10^5$, and an aspect ratio $\Gamma=16$ is therefore considered. These large-scale structures, which are denoted as turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. Our investigation, which follows Hadjighasem {\it et al.}, Phys. Rev. E {\bf 93}, 063107 (2016), builds a weighted and undirected graph from the trajectory points of Lagrangian particles. Weights at the edges of the graph are determined by a mean dynamical distance between different particle trajectories. It is demonstrated that the resulting trajectory clusters, which are obtained by a subsequent $k$-means clustering, coincide with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times $\tau^L$ and lengths $\lambda_U^L$ of the superstructures in the Lagrangian frame of reference agree very well with their Eulerian counterparts, $\tau$ and $\lambda_U$, respectively. This trajectory-based clustering is found to work for times $t\lesssim \tau\approx\tau^L$. Longer time periods $t\gtrsim \tau^L$ require a change of the analysis method to a density-based trajectory clustering by means of time-averaged Lagrangian pseudo-trajectories, which is applied in this context for the first time. A small coherent subset of the pseudo-trajectories is obtained in this way consisting of those Lagrangian particles that are trapped for long times in the core of the superstructure circulation rolls and are thus not subject to ongoing turbulent dispersion.Comment: 12 pages, 7 downsized figures, to appear in Phys. Rev. Fluid

Role of critical points of the skin friction field in formation of plumes in thermal convection

The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-B\'{e}nard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-B\'{e}nard convection in a closed cylindrical cell of aspect ratio $\Gamma=1$ and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of line-like thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian Coherent Structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincar\'{e}-Hopf index theorem for two-dimensional vector fields

Lagrangian analysis of long-term dynamics of turbulent superstructures

In Rayleigh-Bénard convection, turbulent superstructures are large-scale patterns of circulation rolls created by hot ascending and cold descending thermal plumes. The evolution of these large-scale patterns happens on very large time scales τ [1]. Spectral clustering applied to Lagrangian particle trajectories on time intervals smaller than τ can be used to create clusters displaying a structure similar to the patterns detected in the Eulerian frame of reference [2]. However, this technique is unfeasible for the analysis of the evolution of turbulent superstructures due to turbulent dispersion. Therefore, we test the application of concepts of evolutionary spectral clustering [3] on Lagrangian particle trajectories to analyze the long-term dynamics of turbulent superstructures in the Lagrangian frame of reference

Penalty contracts: is it all about paying the cash upfront?

We experimentally investigate the relevance of a cash upfront payment for the effort-enhancing effect of penalty contracts. We find that penalty contracts where participants receive the upfront payment physically before working on a real effort task induce more effort than penalty contracts where participants are only informed about the upfront payment. When comparing penalty contracts with economically-equivalent bonus contracts, we find that penalty contracts lead to higher effort provision than bonus contracts, but only if participants physically receive the upfront cash payment in advance. We suggest that the higher salience of the cash upfront payment might be a core driver of the detected framing effect. Our findings emphasize the importance of experimental design choices when studying framed incentive contracts

Lagrangian heat transport in turbulent three-dimensional convection

Spatial regions that do not mix effectively with their surroundings and thus contribute less to the heat transport in fully turbulent three-dimensional Rayleigh-B\'{e}nard flows are identified by Lagrangian trajectories that stay together for a longer time. These trajectories probe Lagrangian coherent sets (CS) which we investigate here in direct numerical simulations in convection cells with square cross section of aspect ratio $\Gamma = 16$, Rayleigh number $Ra = 10^{5}$, and Prandtl numbers $Pr = 0.1, 0.7$ and $7$. The analysis is based on $N=524,288$ Lagrangian tracer particles which are advected in the time-dependent flow. Clusters of trajectories are identified by a graph Laplacian with a diffusion kernel, which quantifies the connectivity of trajectory segments, and a subsequent sparse eigenbasis approximation (SEBA) for cluster detection. The combination of graph Laplacian and SEBA leads to a significantly improved cluster identification that is compared with the large-scale patterns in the Eulerian frame of reference. We show that the detected CS contribute by a third less to the global turbulent heat transport for all investigated $Pr$ compared to the trajectories in the spatial complement. This is realized by monitoring Nusselt numbers along the tracer trajectory ensembles, a dimensionless local measure of heat transfer.Comment: 8 pages, 5 figure

Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-B\'enard convection

We explore the mechanisms of heat transfer in a turbulent constant heat flux-driven Rayleigh-B\'enard convection flow, which exhibits a hierarchy of flow structures from granules to supergranules. Our computational framework makes use of time-dependent flow networks. These are based on trajectories of Lagrangian tracer particles that are advected in the flow. We identify coherent sets in the Lagrangian frame of reference as those sets of trajectories that stay closely together for an extended time span under the action of the turbulent flow. Depending on the choice of the measure of coherence, sets with different characteristics are detected. First, the application of a recently proposed evolutionary spectral clustering scheme allows us to extract granular coherent features that are shown to contribute significantly less to the global heat transfer than their spatial complements. Moreover, splits and mergers of these (leaking) coherent sets leave spectral footprints. Secondly, trajectories which exhibit a small node degree in the corresponding network represent objectively highly coherent flow structures and can be related to supergranules as the other stage of the present flow hierarchy. We demonstrate that the supergranular flow structures play a key role in the vertical heat transport and that they exhibit a greater spatial extension than the granular structures obtained from spectral clustering.Comment: 21 pages, 15 figure

Lagrangian perspectives on turbulent superstructures in Rayleigh-Bénard convection

We analyze large‐scale patterns in three‐dimensional turbulent convection in a horizontally extended square convection cell by means of Lagrangian particle trajectories calculated in direct numerical simulations. Different Lagrangian computational methods, i.e. finite‐time Lyapunov exponents, spectral and density‐based clustering and transfer operator approaches, are used to detect these large‐scale structures, which are denoted as turbulent superstructures of convection

The influence of farming on weed flora in the Gäu region of Southwestern Germany with an emphasis on rare arable weed species

Highly developed weed control strategies manage to suppress weeds and therefore contribute to a shift in weed community composition as well as a decline in rare weed occurrence. To counteract this decline fields containing rare weed species are taken under contract for preservation purposes, however only time limited. We mapped the weed flora in cereals of conventional (K) and organic (O) fields as well as current (V) and former (E) rare species conservation fields in the Gäu region of Southwestern Germany in 2016. We found similar weed species numbers in O (24 – 38 species) and V (36 – 43 species) and in C (7 – 17 species) and E (13 – 15 species). Weed community composition varied considerably between fields. By performing a CCA (Canonical Correspondence Analysis) we were able to explain 23% of the weed community composition by the parameters seeding rate and nitrogen fertilization. Nevertheless species such as Alopecurus myosuroides, Geranium dissectum, Papaver rhoeas, Poa trivialis and Veronica persica showed a high consistency in all observations. Rare and endangered weed species like Papaver argemone, Consolida regalis, Ranunculus arvensis and Galium tricornutum were only present in V and occasionally E and O. This indicates a rapid decline of weed species diversity after contracts expire, which slowly leads to a similar floral composition as in conventional fields. Therefore new concepts for constant protection of rare weed species should be put into action to ensure conservation success

Does cardiac surgery in newborn infants compromise blood cell reactivity to endotoxin?

INTRODUCTION: Neonatal cardiac surgery is associated with a systemic inflammatory reaction that might compromise the reactivity of blood cells against an inflammatory stimulus. Our prospective study was aimed at testing this hypothesis. METHODS: We investigated 17 newborn infants with transposition of the great arteries undergoing arterial switch operation. Ex vivo production of the pro-inflammatory cytokine tumor necrosis factor-α (TNF-α), of the regulator of the acute-phase response IL-6, and of the natural anti-inflammatory cytokine IL-10 were measured by enzyme-linked immunosorbent assay in the cell culture supernatant after whole blood stimulation by the endotoxin lipopolysaccharide before, 5 and 10 days after the operation. Results were analyzed with respect to postoperative morbidity. RESULTS: The ex vivo production of TNF-α and IL-6 was significantly decreased (P < 0.001 and P < 0.002, respectively), whereas ex vivo production of IL-10 tended to be lower 5 days after the operation in comparison with preoperative values (P < 0.1). Ex vivo production of all cytokines reached preoperative values 10 days after cardiac surgery. Preoperative ex vivo production of IL-6 was inversely correlated with the postoperative oxygenation index 4 hours and 24 hours after the operation (P < 0.02). In contrast, postoperative ex vivo production of cytokines did not correlate with postoperative morbidity. CONCLUSION: Our results show that cardiac surgery in newborn infants is associated with a transient but significant decrease in the ex vivo production of the pro-inflammatory cytokines TNF-α and IL-6 together with a less pronounced decrease in IL-10 production. This might indicate a transient postoperative anti-inflammatory shift of the cytokine balance in this age group. Our results suggest that higher preoperative ex vivo production of IL-6 is associated with a higher risk for postoperative pulmonary dysfunction