Coherent pressure structures in turbulent channel flow

Most of the studies on pressure fluctuations in wall-bounded turbulent flows aim at obtaining statistics as power spectra and scaling laws, especially at the walls. In the present study we study energetic coherent pressure structures of turbulent channel flows, aiming at a characterization of dominant coherent structures throughout the channel. Coherent structures are detected using spectral proper orthogonal decomposition (SPOD) and modeled using resolvent analysis, similar to related works dealing with velocity fluctuations, but using pressure fluctuations as the output of interest. The resolvent operator was considered with and without the Cess eddy viscosity model. Direct numerical simulations (DNSs) of incompressible turbulent channel flows at friction Reynolds numbers of approximately 180 and 550 were employed as databases. Three representative dominant structures emerged from a preliminary spectral analysis: near-wall, large-scale and spanwise-coherent structures. For frequency-wavenumber combinations corresponding to these three representative structures, SPOD results show a strong dominance of the leading mode, highlighting low-rank behavior of pressure fluctuations. The leading resolvent mode closely agrees with the first SPOD mode, providing support to studies that showed better performance of resolvent-based estimators when predicting pressure fluctuations compared to velocity fluctuations. The dominant mechanisms of the analyzed modes are seen to be the generation of quasi-streamwise vortices with pressure fluctuations appearing close to vortex centers. A study on the individual contributions of the nonlinear terms (treated as forcing in resolvent analysis) to the pressure output reveals that each forcing component plays a constructive role to the input-output formulation, which also helps understanding the weaker role of forcing color in driving pressure fluctuations.Comment: 24 pages, 23 figure

Reduced-order Galerkin models of plane Couette flow

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without sign of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.Comment: 10 pages, 4 figure

On the Low-Frequency Dynamics of Turbulent Separation Bubbles

The low-frequency modal and non-modal stability characteristics of an incompressible, pressure-gradient-induced turbulent separation bubble (TSB) are investigated with the objective of studying the mechanism responsible for the low-frequency contraction and expansion (breathing) commonly observed in experimental studies. The configuration of interest is a TSB generated on a flat test surface by a succession of adverse and favourable pressure gradients. The base flow selected for the analysis is the average TSB from the direct numerical simulation of Coleman et al. (J. Fluid Mech., vol. 847, 2018). Global linear stability analysis reveals that the flow is globally stable for wavenumbers. The mode closest to the stability threshold appears to occur at zero frequency and low, non-zero spanwise wavenumber. Resolvent analysis is then employed to examine the forced dynamics of the flow. At low frequency, a region of low, non-zero spanwise wavenumber is also discernible, where the receptivity appears to be driven by the identified weakly damped global mode. The results from resolvent analysis are compared to the unsteady experimental database of Le Floc'h et al. (J. Fluid Mech., vol. 902, 2020) in a similar TSB flow. The alignment between the optimal response and the first spectral proper orthogonal decomposition mode computed from the experiments is shown to exceed 95 %, while the spanwise wavenumber of the optimal response is consistent with that of the low-frequency breathing motion captured experimentally. This indicates that the fluctuations observed experimentally at low frequency closely match the response computed from resolvent analysis. Based on these results, we propose that the forced dynamics of the flow, driven by the weakly damped global mode, serve as a plausible mechanism for the origin of the low-frequency breathing motion commonly observed in experimental studies of TSBs

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core

Transition to chaos in a reduced-order model of a shear layer

The present work studies the non-linear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira \& Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of methods of dynamical systems theory. A basis of eight modes is used in the Galerkin projection, representing the mean flow, Kelvin-Helmholtz vortices, rolls, streaks and oblique waves, structures observed in the cited work, and also present in shear layers and jets. A dynamical system is obtained, and its transition to chaos is studied. Increasing Reynolds number $Re$ leads to pitchfork and Hopf bifurcations, and the latter leads to a limit cycle with amplitude modulation of vortices, as in the DNS by Nogueira \& Cavalieri. Further increase of $Re$ leads to the appearance of a chaotic saddle, followed by the emergence of quasi-periodic and chaotic attractors. The chaotic attractors suffer a merging crisis for higher $Re$, leading to chaotic dynamics with amplitude modulation and phase jumps of vortices. This is reminiscent of observations of coherent structures in turbulent jets, suggesting that the model represents dynamics consistent with features of shear layers and jets.Comment: 28 pages, 18 figure

Evaluation of PSE as a Model for Supersonic Jet Using Transfer Functions

Parabolized Stability Equations (PSE) have been shown to model wavepackets and, consequently, the near field of turbulent jets with reasonable accuracy. Because of these capabilities, PSE is a promising reduced-order model to derive control laws that could be employed to reduce the sound generation of a jet. The purpose of this work is to apply PSE to obtain time-domain transfer functions that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet. The results of this model were compared to results obtained from a database of a well-validated large-eddy simulation of a supersonic jet. Based on the unsteady pressure data at a input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and an empirical method based on the LES data. The prediction scheme employed is a single-input-single-output (SISO), linear model. The unsteady pressure predicted by PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer. For this region, the prediction capabilities of PSE are comparable to those of empirical transfer functions. The agreement is good even for output points taken in the acoustic field, showing that it is possible to estimate the time-domain behaviour of Mach-wave radiation using transfer functions. This indicates that PSE could not only be used to predict the sound generation, but also to open up new potentialities to attenuate noise by means of closed-loop control of the flow. The exploration of the regions where the method displayed good agreement, presented in this work, can guide the positioning of sensors and actuators for experimental implementation of closed-loop control in a jet

An update on the human and animal enteric pathogen Clostridium perfringens

Clostridium perfringens, a rapid-growing pathogen known to secrete an arsenal of >20 virulent toxins, has been associated with intestinal diseases in both animals and humans throughout the past century. Recent advances in genomic analysis and experimental systems make it timely to re-visit this clinically and veterinary important pathogen. This Review will summarise our understanding of the genomics and virulence-linked factors, including antimicrobial potentials and secreted toxins of this gut pathogen, and then its up-to-date clinical epidemiology and biological role in the pathogenesis of several important human and animal-associated intestinal diseases, including pre-term necrotising enterocolitis. Finally, we highlight some of the important unresolved questions in relation to C. perfringens-mediated infections, and implications for future research directions

Dessins, their delta-matroids and partial duals

Given a map $\mathcal M$ on a connected and closed orientable surface, the delta-matroid of $\mathcal M$ is a combinatorial object associated to $\mathcal M$ which captures some topological information of the embedding. We explore how delta-matroids associated to dessins d'enfants behave under the action of the absolute Galois group. Twists of delta-matroids are considered as well; they correspond to the recently introduced operation of partial duality of maps. Furthermore, we prove that every map has a partial dual defined over its field of moduli. A relationship between dessins, partial duals and tropical curves arising from the cartography groups of dessins is observed as well.Comment: 34 pages, 20 figures. Accepted for publication in the SIGMAP14 Conference Proceeding