Nonlinear dynamics and pattern formation in turbulent wake transition

Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for fixed Reynolds number and increasing spanwise dimension show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simulations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000

Details of the drag curve near the onset of vortex shedding

A closer look at the drag curve for a circular cylinder near the onset of vortex shedding reveals that there is a sharp transition in the forces acting on a body moving through a fluid when it produces an unsteady wake. In this Letter results from high‐resolution computer simulations are presented to quantify the change in viscous drag, pressure drag, and base pressure coefficients

Secondary instability in the wake of a circular cylinder

Secondary instability of flow past a circular cylinder is examined using highly accurate numerical methods. The critical Reynolds number for this instability is found to be Re_c=188.5. The secondary instability leads to three‐dimensionality with a spanwise wavelength at onset of 4 cylinder diameters. Three‐dimensional simulations show that this bifurcation is weakly subcritical

Speaking of trade: Key issues for agriculture

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Histone modification signature at myeloperoxidase and proteinase 3 in patients with anti-neutrophil cytoplasmic autoantibody-associated vasculitis

Abstract Background Anti-neutrophil cytoplasmic autoantibody (ANCA)-associated vasculitis (AAV) is a systemic autoimmune disease characterized by destructive vascular inflammation. Two prominent ANCA autoantigens are myeloperoxidase (MPO) and proteinase 3 (PR3), and transcription of MPO and PRTN3, the genes encoding the autoantigens, is associated with disease activity. We investigated whether patients with AAV have alterations in histone modifications, particularly those associated with transcriptional activation, at MPO and PRTN3. Results We identified a network of genes regulating histone modifications that were differentially expressed in AAV patients compared to healthy controls. We focused on four genes (EHMT1 and EHMT2, ING4, and MSL1) and found their expression correlated with expression of MPO and PRTN3. Methylation of histone H3K9, catalyzed by EHMT1 and EHMT2 and associated with gene silencing, was most depleted at MPO and PRTN3 in patients with active disease and the highest MPO and PRTN3 expression. Acetylation of histone H4K16, modified by complexes containing ING4 and MSL1 and associated with gene activation, was most enriched at MPO and PRTN3 in patients with active disease and the highest MPO and PRTN3 expression. Methylation at H3K4, a mark of transcriptional activation, was enriched at MPO and PRTN3 in patients and healthy controls. Conclusions MPO and PRTN3 in neutrophils of AAV patients with active disease have a distinct pattern of histone modifications, which implicates epigenetic mechanisms in regulating expression of autoantigen genes and suggests that the epigenome may be involved in AAV pathogenesis