Sinuous Mode Research Articles

The efficiency of detecting seabird behaviour from movement patterns: the effect of sampling frequency on inferring movement metrics in Procellariiformes

BackgroundRecent technological advances have resulted in low-cost GPS loggers that are small enough to be used on a range of seabirds, producing accurate location estimates (± 5 m) at sampling intervals as low as 1 s. However, tradeoffs between battery life and sampling frequency result in studies using GPS loggers on flying seabirds yielding locational data at a wide range of sampling intervals. Metrics derived from these data are known to be scale-sensitive, but quantification of these errors is rarely available. Very frequent sampling, coupled with limited movement, can result in measurement error, overestimating movement, but a much more pervasive problem results from sampling at long intervals, which grossly underestimates path lengths.MethodsWe use fine-scale (1 Hz) GPS data from a range of albatrosses and petrels to study the effect of sampling interval on metrics derived from the data. The GPS paths were sub-sampled at increasing intervals to show the effect on path length (i.e. ground speed), turning angles, total distance travelled, as well as inferred behavioural states.ResultsWe show that distances (and per implication ground speeds) are overestimated (4% on average, but up to 20%) at the shortest sampling intervals (1–5 s) and underestimated at longer intervals. The latter bias is greater for more sinuous flights (underestimated by on average 40% when sampling > 1-min intervals) as opposed to straight flight (11%). Although sample sizes were modest, the effect of the bias seemingly varied with species, where species with more sinuous flight modes had larger bias. Sampling intervals also played a large role when inferring behavioural states from path length and turning angles.ConclusionsLocation estimates from low-cost GPS loggers are appropriate to study the large-scale movements of seabirds when using coarse sampling intervals, but actual flight distances are underestimated. When inferring behavioural states from path lengths and turning angles, moderate sampling intervals (10–30 min) may provide more stable models, but the accuracy of the inferred behavioural states will depend on the time period associated with specific behaviours. Sampling rates have to be considered when comparing behaviours derived using varying sampling intervals and the use of bias-informed analyses are encouraged.

Mechanism of sinuous and varicose modes in electrokinetic instability.

The flow of miscible electrolyte streams with mismatched electrical conductivities in the presence of a parallel applied electric field is known to exhibit electrokinetic instability (EKI). This paper deals with EKI in a configuration where the base state is established by electro-osmotic flow (EOF) of three coflowing streams, with the center stream having different conductivity than the sheath streams. All reported experiments of this EKI have shown that the instability exhibits either sinuous or varicose modes depending upon whether the center stream has higher or lower conductivity than the sheath streams, respectively. In this paper we elucidate the physical mechanism underlying the selection of these unstable modes in EKI using linear stability analysis. The stability analysis shows that the EOF simply convects the unstable modes besides establishing the base state. The instability occurs due to stationary convection cells, in the reference frame moving with the EOF, resulting from the coupling of the applied electric field with free charge in the regions with conductivity gradients. Importantly, we show that the unstable and stable disturbances for the configuration with a higher conductivity center stream have opposite stability characteristics when the center stream has lower conductivity than the sheath streams. Our analysis correctly explains the numerous experimental observations showing the consistent appearance of sinuous modes for higher conductivity and varicose modes for lower conductivity center streams.

Boundary layer transition due to distributed roughness: effect of roughness spacing

The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared with isolated roughness elements at the same Reynolds number $Re_h=U_eh/\nu$ ( $U_e$ is the boundary layer edge velocity, h is roughness height and $\nu$ is the kinetic viscosity of the fluid). Small spanwise spacing ( $\lambda _z=2.5h$ ) inhibits the formation of counter-rotating vortex pairs (CVP) and, as a result, hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda _z=5h$ , the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. The temporal periodicity of the primary hairpin vortices appears to be independent of the streamwise spacing. Distributed roughness leads to a lower critical roughness Reynolds number for instability to occur and a more significant breakdown of the boundary layer compared with isolated roughness. When the streamwise spacing is $\lambda _x=5h$ , the high-momentum fluid barely moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ( $\lambda _x=10h$ ), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interact with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs into the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.

Breakup of planar liquid sheets injected at high speed in a quiescent gas environment

Using a combination of mean flow spatial linear stability and two-dimensional volume-of-fluid (VoF) simulations, the physics governing the instability of high-speed liquid sheets being injected into a quiescent gas environment is studied. It is found that the gas shear layer thickness $\delta _G$ plays an influential role, where for values $\delta _G/H\lesssim 1/8$ , the growth of sinuous and varicose modes is nearly indistinguishable. Here, $H$ is the liquid sheet thickness. With larger values of $\delta _G/H$ , a second peak develops in the lower wavenumber region of the dispersion relation, and becomes increasingly dominant. This second peak corresponds to a large-scale sinuous mode, and its critical wavelength $\lambda _{crit,sinuous}$ is found to scale as $\lambda _{crit,sinuous}/H = 14.26 (\delta _G/H)^{0.766}$ . This scaling behaviour collapses onto a single curve for various combinations of the liquid-based Reynolds ( $Re_L$ ) and Weber ( $We_L$ ) numbers, provided that $\delta _G/H > O({10^{-1}})$ . For the varicose modes, the shape of the dispersion relation does not change with variations in $\delta _G/H$ , and the liquid shear layer thickness has an almost negligible influence on the growth of instabilities. Two-dimensional VoF simulations are employed to examine the validity of the linear stability assumptions. These simulations also show that the dominant sinuous mode remains active as the process transitions into the nonlinear regime, and that this mode is ultimately responsible for fragmenting the sheet. Based on an energy budget analysis, the most influential contributors to the growth of the sinuous mode are the gas Reynolds shear stress and the lateral working of pressure on the gas side.

Three-dimensional global instability analysis for high-speed boundary layer flow

Herein, a numerical approach for the three-dimensional global instability analysis of high-speed boundary layer is developed. The approach is based on the Krylov–Schur method for large-scale eigenproblems. A shift-and-invert spectral transformation is employed to accelerate the convergence for eigenvalues of interest. Iterative linear solver is adopted in the transformation to reduce memory usage by avoiding the fill-in problem of direct solver and the explicit construction of matrices. A Robin condition based on BiGlobal instability analysis is imposed at the inflow boundary, and a non-reflecting condition derived from inviscid flow is used for the far-field boundary. The approach is validated in a Blasius boundary layer. According to a comparison between the performances of several algorithms in this case, the conjugate gradient squared method with no preconditioning is chosen as the linear solver. The results provided by three-dimensional global instability analysis consist with those from linear stability theory and BiGlobal instability analysis. A further demonstration of our approach is provided for a three-dimensional roughness-disturbed boundary layer. The fluctuations extracted from direct numerical simulation results illustrate that the symmetric component is the dominant unstable mode in roughness wake, as it grows twice as fast as the antisymmetric component. Two eigenvalues are obtained from the three-dimensional global instability analysis, and these represent the symmetric and antisymmetric unstable modes. The wavelengths and growth rates of both modes delivered by instability analysis agree well with the direct numerical simulation results, and the profiles of disturbance amplitude match the features of the varicose and sinuous modes.

Impact of Transverse Acoustic Excitation and Air Swirl on a Confined Hollow Cone Sheet

Abstract This study investigates the effect of imposing symmetric transverse acoustic excitation and counter-rotating air swirl flow on a confined hollow cone spray sheet. We study the impact of these forcing conditions on two unstable modes—sheet flapping and sinuous wave growth modes—and their phasic relationship. We used the shadowgraphy technique, and only the sheet edges were analyzed using the method of snapshot proper orthogonal decomposition (POD). In this study, we used postprocessing techniques to estimate the nondimensional breakup length, phase averaged cone angle, and continuous wavelet transform (CWT) frequency. Results show that imposing acoustic excitation alone causes the sheet edges to flap, axisymmetrically, at the pressure antinode, while at the pressure node and base flow condition, the asymmetric sinuous wave mode is dominant. At the pressure intermediary, we find the possible dominance of both modes. While the dominant effect of air swirl alone was difficult to ascertain, results from CWT analysis show that POD mode 1 and mode 3 have very similar spectral content, with mode 3 showing a flapping mode. Finally, air swirl flow has a more dominant effect than acoustics in causing sheet breakup.

Response to comment on “Stability of a moving radial liquid sheet: Time-dependent equations” [Phys. Fluids 35, 099101 (2023)

In a recent comment, Mehring and Gyurkovich show that in our derivation of the time-dependent equations, we have neglected the perturbed term in the interface location while applying the kinematic boundary condition. When the neglected term is incorporated in the analysis, the time-dependent equation for the sinuous mode is different from our original expression. They conclude that the instability predicted by the original model does not exist for their new model. We show that, on the contrary, the new model predicts spatial growth of sinuous disturbance that depends on forcing frequency and the slope of the forcing disturbance.

Stability of a particle-laden planar jet in the dilute suspension limit

Particle laden flows are commonly seen in many industrial applications, such as fluidized beds in process industry, air laden with abrasive particles in abrasive machining, and particle laden plumes in chemical industries. In the present work, we perform local analysis of a particle laden planar jet in the dilute suspension regime. Unladen parallel planar jets have been extensively studied using normal modes and are shown to have two unstable modes, namely, sinuous and varicose modes. Sinuous modes are found to be more unstable compared to the varicose modes. In the present study, we investigate the effect of particles on the stability of planar jets. Addition of particles at low Stokes numbers (St) (fine particles) results in higher growth rates than that of the unladen jet. In the intermediate Stokes number regime, addition of particles has a stabilizing effect on both the sinuous and the varicose modes. Interestingly, for St∼10, the unstable varicose mode is completely damped. Increasing the Stokes number by increasing the particle size, both sinuous and varicose modes, shows increasing growth rates, while increasing the density ratio has a stabilizing effect on the flow. For non-uniform particle loading, additional modes apart from the sinuous and varicose modes are observed. These modes suggest the occurrence of compositional instability with an increased particle accumulation in the shear layer that is an order of magnitude higher compared to that of the sinuous and varicose modes.

Prediction of Self-Sustained Oscillations of an Isothermal Impinging Slot Jet

The present results are focused on the self-sustained oscillations of a confined impinging slot jet and their role in the flow structure and modeling requirements. Unsteady laminar, large-eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS) predictions of an isothermal confined impinging jet were validated for several nozzle-to-plate ratios (H/B=4–15) and for laminar (Re=340 and 480) and turbulent (Re=104–2.7×104) conditions. The impinging flow structure was found to be highly influenced by the H/B ratio. For high ratios (H/B>5), the studied steady RANS turbulence models could not satisfactorily predict the high diffusion reported experimentally in the jet-impinging influence zone. The failure of these models has been attributed to the modeling issues of turbulence closures. However, for H/B=8, unsteady laminar 3D and LES calculations were verified, and a sinuous oscillation mode was developed, revealing self-sustained oscillations and the display of periodic flapping of the impinging jet in good agreement with the experiments. The predicted flapping oscillation is one of the reasons for the higher diffusion near the impingement wall, which was verified in several time-averaged experimental studies. The presence of jet flapping matters for clarifying the already long discussion on the RANS model’s validation in predicting impinging jets with high H/B ratios, adding justification to the failure of these turbulence models. This unsteady behavior is correctly computed through LES.

Dynamics of a liquid sheet with a broken time reversal

With the presence of the odd viscosity, the linear instability of a planar jet (sheet) surrounded by an inviscid gas medium is explored for varicose and sinuous modes. The previous studies on sheet mechanics did not consider the role of the odd viscosity when measuring the maximum growth rate, dominant wave number, instability limit, and breakup length. Semi-dominant characteristic of the odd viscosity is that it is a stabilizing factor for the state of a liquid sheet. It is an unstable factor in a few cases as dictated by the model parameters, such as the odd viscosity number, aerodynamic force, Reynolds number, ambient gas density, and Weber number. In the production of metal alloys, metal powders, and the cooling and descaling stages of downstream metal manufacturing processes, particularly in the steel industry, sprays may be employed in a variety of ways.

Instability of Viscoelastic Liquid Sheets in a Transverse Electric Field

The temporal linear instability of a viscoelastic liquid sheet moving around an inviscid gas in a transverse electrical field is analyzed. The fluid is described by the leaky dielectric model, which is more complex than existing models and enables a characterization of the liquid electrical properties. In addition, the liquid is assumed to be viscoelastic, and the dimensionless dispersion relation of the sinuous and varicose modes between the wavenumber and the temporal growth rate can be derived as a 3 × 3 matrix. According to this relationship, the effects of the liquid properties on the sheet instability are determined. The results suggest that, as the electrical Euler number and the elasticity number increase and the time constant ratio decreases, the sheet becomes more unstable. Finally, an energy budget approach is adopted to investigate the instability mechanism for the sinuous mode.

Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element

Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$ ) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{*}$ ) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{*}$ , sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$ ), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$ , the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$ , the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the ‘wiggling’ of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$ . An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$ .

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

The computation of invariant solutions and the visualisation of the associated state space have played a key role in the understanding of transition and the self-sustaining process in wall-bounded shear flows. In this study, an extension of this approach is sought for a turbulent flow which explicitly exhibits multi-scale behaviour. The minimal unit of multi-scale near-wall turbulence, which resolves two adjacent spanwise integral length scales of motion, is considered using a shear stress-driven flow model (Doohan, Willis & Hwang J. Fluid Mech., vol. 913, 2021, A8). The edge state, 26 travelling waves and two periodic orbits are computed, which represent either the large- or small-scale self-sustaining processes. Given that the spanwise length scales are not widely separated here, it could be envisaged that turbulent trajectories visit these solutions in the state space. Considering the intra- and inter-scale dynamics of the flow, numerous phase portraits are examined, but the turbulent state is not found to approach any of these solutions. A detailed analysis reveals that this is due to the lack of scale interaction processes captured by the invariant solutions, including the mean–fluctuation interaction, the energy cascade in the streamwise wavenumber space and the cascade-driven energy production discovered recently. There is a single solution that resembles turbulence much more than the others, which captures two-scale energetics and a scale interaction process involving energy feeding from small to large spanwise scales through the subharmonic sinuous streak instability mode. Based on these observations, it is conjectured that the state space view of turbulent trajectories wandering between solutions would need suitable refinement to model multi-scale turbulence, when each solution does not represent multi-scale processes of turbulence. In particular, invariant solutions that are inherently multi-scale would be required.

Dual-scale folding in cutting of commercially pure aluminum alloys

We examine a, hitherto, little-studied and curious machining chip morphology, with tell-tale signs of folding at two different length scales, that is common in cutting of certain ductile and highly strain-hardening metals like soft aluminum alloys, tantalum and niobium. This chip morphology does not appear in the usual catalogues of common chip types. The mechanics of formation of the “dual-scale folded chip” is studied in model material systems of commercially pure aluminum alloys (AA 1100 and AA 8040), that prominently exhibit this chip morphology. The flow, folding and associated plastic instabilities are investigated using micro/macro structure observations of the chip in a plane-strain cutting framework, with high-speed in situ imaging and image analysis of material flow; and force measurements. The smaller-scale folding is shown to develop in the primary deformation zone while the larger-scale folding occurs as the chip traverses the rake face of the tool. The resulting chip is composed of irregularly-spaced large folds, superimposed onto which are the quasi-periodic small folds. The representative wavelengths of the two folds differ on average by an order of magnitude, 0.1 mm vs. 2 mm. The observations reveal a direct coupling between the material flow and chip morphology, and how specific attributes of the dual-scale folded chip arise from the flow mechanism. Plastic buckling is found to play a key role in the folding at both length scales. The small-scale folds are characteristic of a sinuous plastic flow mode, while the large-scale folding is characterized by buckling and stick-slip along the tool rake face, triggered by adhesive pinning of the chip to the tool. Important consequences of the dual-scale folding are very large cutting forces, and force oscillations of large amplitude, despite the alloys being very soft, only ∼25 HV. The dual-scale folding is why many of these alloys are classified as “gummy” to machine. Since the dual-scale folded chip is associated with large cutting forces and poor surface quality, there is much to be gained by disrupting this flow type in practical machining applications. Methods for controlling the folding to improve machining performance with the gummy alloys are briefly discussed.

Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer

The essence of sub-critical transition of oscillatory boundary-layer flows is the non-modal growth of finite-amplitude disturbances. The current understanding of the mechanisms of the orderly and bypass transitions of oscillatory boundary-layer flows is limited. The present study adopts optimisation approaches to predict the maximum energy amplification of two- and three-dimensional perturbations in response to the optimal initial disturbance with or without external forcing. A series of direct numerical simulations are also performed to compare with the results obtained from the stability analyses. In particular, the optimal initial perturbation similar to a Tollmien–Schlichting (T–S) wave yields the largest transient growth under the combined effects of the Orr mechanism and inflectional point instability. With a considerable level of two-dimensional disturbance, the vortex tube nonlinearly develops from the T–S-like wave, and then either deforms into a $\varLambda$ -vortex in the near-wall region or rolls up to the free shear region. The further burst of turbulence can follow the first pathway as K-type transition or the second one as vortex tube breakdown due to the elliptical instability. Additionally, non-modal growth can initiate the inception of streaky structures by favourable three-dimensional initial perturbations and/or forcing. The secondary instabilities responsible for the streak breakdown are classified as the varicose (symmetric) and sinuous (anti-symmetric) modes. Under a sufficiently high level of three-dimensional disturbance, the bypass transition is predominantly characterised by the formation of the sinuous mode and turbulent spots, which leads to the suppression of inflection point instability.

Precursors of backflow events and their relationship with the near-wall self-sustaining process

This study examines the precursors and consequences of rare backflow events at the wall using direct numerical simulation of turbulent pipe flow with a high spatiotemporal resolution. The results obtained from conditionally averaged fields reveal that the precursor of a backflow event is the asymmetric collision between a high- and a low-speed streak (LSS) associated with the sinuous mode of the streaks. As the collision occurs, a lifted shear layer with high local azimuthal enstrophy is formed at the trailing end of the LSS. Subsequently, a spanwise or an oblique vortex spontaneously arises. The dominant nonlinear mechanism by which this vortex is engendered is enstrophy intensification due to direct stretching of the lifted vorticity lines in the azimuthal direction. As time progresses, this vortex tilts and orientates towards the streamwise direction and, as its enstrophy increases, it induces the breakdown of the LSS located below it. Subsequently, this vortical structure advects as a quasi-streamwise vortex, as it tilts and stretches with time. As a result, it is shown that reverse flow events at the wall are the signature of the nonlinear mechanism of the self-sustaining process occurring at the near-wall region. Additionally, each backflow event has been tracked in space and time, showing that approximately 50 % of these events are followed by at least one additional vortex generation that gives rise to new backflow events. It is also found that up to a maximum of seven regenerations occur after a backflow event has appeared for the first time.

Instability of a viscous liquid sheet under the influence of a tangential electric field

The linear stability analysis has been analyzed for an electrified liquid sheet confined between two symmetric dielectric movable ambient gas. The present study aims to estimate the planer jet systems response when applying a tangential electric field. The dispersion relations for varicose and sinuous modes have been formulated. The electrical Euler number and some flow parameters have been tested for their influence on the electrified liquid sheet instability. In other words, the effects of electric field on the dominant wave number, and instability range (cutoff wave number) are discussed. The results clarify that the tangential electric field has a stabilizing effect for sinuous mode over the whole range of gas velocity ratio. On the other hand, for varicose mode, the electric field slightly improves the system stability to a certain limit, but it has a great role in stability for higher values of gas velocity ratio.

Secondary instability of the spike-bubble structures induced by nonlinear Rayleigh-Taylor instability with a diffuse interface.

Laminar-turbulent transition in Rayleigh-Taylor (RT) flows usually starts with infinitesimal perturbations, which evolve into the spike-bubble structures in the nonlinear saturation phase. It is well accepted that the emergence and rapid amplification of the small-scale perturbations are attributed to the Kelvin-Helmholtz-type secondary instability due to the high velocity shears induced by the stretch of the spike-bubble structures, however, there has been no quantitative description on such a secondary instability in literature. Moreover, the instability mechanism may not be that simple, because the acceleration or the "rising bubble" effect could also play a role. Therefore, based on the two-dimensional diffuse-interface RT nonlinear flows, the present paper employs the Arnoldi iteration and generalized Rayleigh quotient iteration methods to provide a quantitative study on the secondary instability. Both sinuous and varicose instability modes with high growth rates are observed, all of which are confirmed to be attributed to both the Rayleigh-Taylor and Kelvin-Helmholtz regimes. The former regime dominates the early-time instability due to the "rising bubble" effect, whereas the latter regime becomes more significant as time advances. Being similar to the primary RT instability [Yu et al., Phys. Rev. E 97, 013102 (2018)2470-004510.1103/PhysRevE.97.013102, Dong et al., Phys. Rev. E 99, 013109 (2019)2470-004510.1103/PhysRevE.99.013109, Fan and Dong, Phys. Rev. E 101, 063103 (2020)2470-004510.1103/PhysRevE.101.063103], the diffuse interface also leads to a multiplicity of the secondary instability modes and higher-order modes are found to exhibit more local extremes than the lower-order ones. Direct numerical simulations are carried out, which confirm the linear growth of the secondary instability modes with infinitesimal amplitudes and show their evolution to the turbulent-mixing state.

Modal decomposition analysis of unsteady viscous liquid sheet flows

The unsteady dynamics of a gravitational liquid sheet, driven by a continuous harmonic perturbation in the lateral velocity component applied at the inlet section, is analyzed. The topology and the dynamics of the relevant flow structures are characterized by applying POD (Proper Orthogonal Decomposition) and spectral POD (SPOD) modal decompositions on two-dimensional two-phase numerical simulation data obtained with the volume-of-fluid approach. The investigation is carried out by varying the Weber number, the forcing frequency (Strouhal number), and the Reynolds number. The supercritical regime (We > 1) features a traveling perturbation, exhibiting a spatial structure with leading sinuous modes. SPOD spectra confirm the occurrence of a discontinuity in frequency response between the supercritical and subcritical regimes. In the subcritical regime (We < 1), the investigation highlights the excitation of a combined sinuous–varicose motion when the system is driven at resonance frequency for a relatively high Reynolds number (approaching the inviscid limit). The emergence of varicose modes is favored by low Weber numbers. The excitation of these modes occurs when the Weber number is decreased from We = 0.90 down to 0.75, with a progressive shift of the varicose mode from higher harmonics toward the main frequency; it can be considered as a possible mechanism of breakup observed in experiments when the inlet flow rate is progressively reduced. The flow reconstruction based on both POD and SPOD confirms the good capability of SPOD modes to capture dynamically relevant features of the fluid motion in subcritical conditions.

Global hydrodynamic instability and blowoff dynamics of a bluff-body stabilized lean-premixed flame

We experimentally study the hydrodynamic instability of a lean-premixed flame stabilized behind a circular cylinder. On reducing the equivalence ratio (ϕ) at a fixed Reynolds number (ReD), we find that the flame transitions from a steady mode to a varicose mode and then to a sinuous mode. By examining time-resolved CH* chemiluminescence images and analyzing how the Strouhal number scales with ReD, we determine that the varicose mode is convectively unstable, maintained by the amplification of disturbances in the turbulent base flow, whereas the sinuous mode is globally unstable as a result of the constructive interaction between the two diametrically opposite shear layers (Bénard–von Kármán instability). We attribute the emergence of the sinuous global mode to the flame moving sufficiently far downstream with decreasing ϕ that it is out of the wavemaker region. Finally, we investigate the lean blowoff dynamics and find that local flame pinch-off, which occurs at the end of the recirculation zone, is a reliable precursor of global flame blowoff.