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In this paper we propose a method to reconstruct the flow at a given time over a region of space using partial instantaneous measurements and full-space proper orthogonal decomposition (POD) statistical information. The procedure is tested for the flow past an open cavity. 3D and 2D POD analysis are used to characterize the physics of the flow. We show that the full 3D flow can be estimated from a 2D section at an instant in time provided that some 3D statistical information--i.e., the largest POD modes of the flow--is made available. [DOI: 10.1115/1.2175159]

Introduction: The first-step in diagnosis of myelodysplastic neoplasms (MDS) is essentially based on bone marrow cytomorphology. However, cytomorphology of MDS is often a difficult exercise, subject to inter-operator variability. Our study aims to evaluate whether the combination of two dysplasia scores, the extended Ogata score and the MDS-CBC score, could improve the screening of MDS patients among patients with chronic cytopenia., Methods: Extended Ogata score and MDS-CBC score have been measured on a retrospective cohort of 63 patients with a clinical suspicion of MDS based on the presence of cytopenia. Among these patients, 33 patients were diagnosed as MDS (MDS group) and 30 patients were diagnosed with another cause of cytopenia (non-MDS cytopenic control group)., Results: Our results show excellent performance of the combined scores in predicting MDS when the two scores are concordant: positive predictive value (PPV) = 96% and negative predictive value (NPV) = 92%. In comparison, in the same cohort, extended Ogata score alone showed a PPV = 90% and NPV = 79%, MDS-CBC score alone showed a PPV = 85% and NPV = 86%., Conclusion: For the first time, our results show that the combination of these two dysplasia scores constitutes a useful and rapid tool for the assessment of dysplasia associated with MDS. In the MDS diagnostic process, the use of combined scores could constitute a valuable tool to enable early strong prediction of MDS in cytopenic patients and to target patients who initially require additional genetic assays., (© 2024 The Author(s). International Journal of Laboratory Hematology published by John Wiley & Sons Ltd.)

Turbulent Rayleigh-Bénard convection in a 2D square cell is characterized by the existence of a large-scale circulation which varies intermittently. We focus on a range of Rayleigh numbers where the large-scale circulation experiences rapid non-trivial reversals from one quasi-steady (or meta-stable) state to another. In previous work [B. Podvin and A. Sergent, J. Fluid Mech. 766, 172201 (2015); B. Podvin and A. Sergent, Phys. Rev. E 95, 013112 (2017)], we applied proper orthogonal decomposition (POD) to the joint temperature and velocity fields at a given Rayleigh number, and the dynamics of the flow were characterized in a multi-dimensional POD space. Here, we show that several of those findings, which required extensive data processing over a wide range of both spatial and temporal scales, can be reproduced, and possibly extended, by application of the embedding theory to a single time series of the global angular momentum, which is equivalent here to the most energetic POD mode. Specifically, the embedding theory confirms that the switches among meta-stable states are uncorrelated. It also shows that, despite the large number of degrees of freedom of the turbulent Rayleigh Bénard flow, a low dimensional description of its physics can be derived with low computational efforts, providing that a single global observable reflecting the symmetry of the system is identified. A strong connection between the local stability properties of the reconstructed attractor and the characteristics of the reversals can also be established.

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Ra_{c}, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra=1.05Ra_{c}, but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

We investigate large-scale circulation reversals in a two-dimensional Rayleigh-Bénard cell using a proper orthogonal decomposition (POD)-based, five-mode model. The Rayleigh number considered is Ra=5×10^{7} and the Prandtl number is Pr=4.3. A precursor event, corresponding to the action of a mode L_{*} which disconnects the core region from the boundary layers before the onset of the reversal, is identified in the simulation. The five-mode model predicts correctly the behavior of the POD modes observed in the simulation, and in particular that of mode L_{*}. The presence of mode L_{*}, which was not included in an earlier, lower-dimensional version of the model [Podvin and Sergent, J. Fluid Mech. 766, 172 (2015)JFLSA70022-112010.1017/jfm.2015.15], is found to be instrumental for the reversal dynamics of the model, which suggests that it may also be important for those of the simulation. Reversals can therefore be characterized by three time scales: the transition duration, the interreversal time, and the precursor duration, which separates the precursor event from the onset of the reversal. The distribution of the time scales is found to agree well with the simulation when small-scale intermittency is taken into account through the introduction of noise in the model coefficients.

Direct numerical simulation is used to study the air flow between two vertical plates maintained at different temperatures. The periodic dimensions of the plates are small so as to accommodate only one flow structure, which consists of a convection roll with oblique vorticity braids. At lower Rayleigh numbers, the roll and the braids grow and shrink alternatively following a cyclical process. As the Rayleigh number is increased, the flow becomes temporally chaotic through a period-doubling cascade. Windows corresponding to multiperiodic regimes and interior crises are observed. As the Rayleigh number is further increased, the structure intermittently switches between two vertical positions, which is seen to correspond to an "attractor-merging" crisis. The chaotic flow dynamics are characterized and the corresponding physical mechanisms are identified. We show that some of the flow key features, such as the chaotic oscillation and intermittency, can be captured by a low-order model.

Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D) for Rayleigh numbers Ra up to 3 times the critical value Ra(c)=5708. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS). In two dimensions, DNS shows that the rolls become unstable via a Hopf bifurcation. As Ra is further increased, the flow becomes quasiperiodic, and then temporally chaotic for a limited range of Rayleigh numbers, beyond which the flow returns to a steady state through a spatial modulation instability. In three dimensions, the rolls instead undergo another pitchfork bifurcation to 3D structures, which consist of transverse rolls connected by counter-rotating vorticity braids. The flow then becomes time dependent through a Hopf bifurcation, as exchanges of energy occur between the rolls and the braids. Chaotic behavior subsequently occurs through two competing mechanisms: a sequence of period-doubling bifurcations leading to intermittency or a spatial pattern modulation reminiscent of the Eckhaus instability.