Turbulent Shear Layer Research Articles

A simple hot wire temperature drift correction based on temperature sensitivity applied to a turbulent shear layer

A procedure is proposed to correct temperature drift for hot wire anemometry measurements in turbulent fields where the facility is not equipped with temperature control. The procedure consists of evaluating the wire sensitivity to the temperature by building a voltage-temperature curve. The voltages of both the calibration points and the measurement points are corrected, shifting the voltage values to an arbitrary reference temperature. The correction can be applied to the instantaneous voltages by performing synced temperature measurements with constant current anemometry or constant voltage anemometry cold wire. The efficacy of the method is tested on a turbulent shear layer that develops on the side of an open jet wind tunnel not equipped with temperature control. The velocity statistics show a good match with respect to reference particle image velocimetry measurements, evidencing the self-similarity of the shear layer in contrast with the non-corrected data and the data corrected using the semi-empirical and analytical relation based on King's law modification. A correction based only on the temperature statistics shows indistinguishable results with respect to the instantaneous correction.

A study of arc plasma energy deposition flow control on blunt-headed protuberance induced STBLI

This paper presents experimental results of flow control method using plasma energy deposition on shock wave interactions induced by blunt-headed protuberance on a flat plate at Mach 2.0. Upstream of the leading edge of the protuberance, plasma energy deposition was generated by high-frequency pulsed discharge at three streamwise locations on the flat plate. High-speed Schlieren technique was utilized to investigate the unsteadiness characteristics of shock wave/turbulent boundary layer interaction (STBLI). The visualization results reveal that thermal bubble structures formed by the pulsed discharge could attenuate the separation shock continuously, resulting in a 12.8% decrease in the maximum pressure in the interaction wall. Experimental findings disclosed the dependency of this mitigation efficacy on the average discharge power. The pulsation of the separation shock was also affected by average discharge power, while the pulsation of boundary layer and shear layer was linked to both the discharge power and frequency. The numerical results predicted flow topology under control well with experiment results, low-density plasma layer was formed by high-frequency discharge, which weakening the separation shock substantially, the “λ” shock intensity was also decreased. The flow field of numerical simulation and experiments are in good agreement. Additionally, the control of the thermal bubble structures on STBLI was very effective in terms of reducing the motion and weakening the intensity of the low-frequency separation shock, and augmenting the high frequency component in the turbulent boundary layer and shear layer.

Two-dimensional direct numerical simulation study of multicomponent mixing with phase transition in a transcritical shear layer

In this paper, we investigate two-dimensional direct numerical simulations of a transcritical shear layer. Three configurations are chosen, which are distinguished by the level of presence of two-phase phenomena. The thermodynamic model is based on a cubic equation of state. It was extended for multicomponent mixtures, and it is able to account for vapor–liquid equilibrium. The thermodynamic modeling with phase-transition is validated using experimental data from the literature. Special focus is put on the effect of the density gradient and the density changes caused by phase-transition on the development of the turbulent shear layer and the associated mixing. In addition to this, the vorticity distribution and the components of its transport equation are analyzed and compared for the different configurations.

Langmuir turbulence in suspended kelp farms

This study investigates the influence of suspended kelp farms on ocean mixed layer hydrodynamics in the presence of currents and waves. We use the large eddy simulation method, where the wave effect is incorporated by solving the wave-averaged equations. Distinct Langmuir circulation patterns are generated within various suspended farm configurations, including horizontally uniform kelp blocks and spaced kelp rows. Intensified turbulence arises from the farm-generated Langmuir circulation, as opposed to the standard Langmuir turbulence observed without a farm. The creation of Langmuir circulation within the farm is attributed to two primary factors depending on farm configuration: (i) enhanced vertical shear due to kelp frond area density variability, and (ii) enhanced lateral shear due to canopy discontinuity at lateral edges of spaced rows. Both enhanced vertical and lateral shear of streamwise velocity, representing the lateral and vertical vorticity components, respectively, can be tilted into downstream vorticity to create Langmuir circulation. This vorticity tilting is driven by the Craik–Leibovich vortex force associated with the Stokes drift of surface gravity waves. In addition to the farm-generated Langmuir turbulence, canopy shear layer turbulence is created at the farm bottom edge due to drag discontinuity. The intensity of different types of turbulence depends on both kelp frond area density and the geometric configuration of the farm. The farm-generated turbulence has substantial consequences for nutrient supply and kelp growth. These findings also underscore the significance of the presence of obstacle structures in modifying ocean mixed layer characteristics.

Flow–acoustic resonance mechanism in tandem deep cavities coupled with acoustic eigenmodes in turbulent shear layers

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$ , where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

Laser-induced indirect ignition of non-premixed turbulent shear layers

This study uses direct numerical simulations to investigate the forced ignition of temporally-evolving turbulent subsonic shear layers separating a gaseous stream of methane (CH4) and a stagnant gas environment of molecular oxygen (O2). Ignition is forced by a thermal-energy source that heats up a small volume of gas during periods of time much shorter than the characteristic acoustic time scale. The kernel, including its initial rounded conical shape, resembles experimental observations after optical breakdown is achieved in a gas irradiated by a focused laser. Particular emphasis is placed on ignition phenomena observed when the laser is focused on the O2 environment outside the turbulent shear layer, where the local composition is far beyond the lean flammability limit. This represents an indirect mode of non-premixed ignition that develops after a relatively long period of time has passed since laser-energy deposition, when the eddies near the oxidizer edge of the turbulent shear layer are intercepted by a baroclinically-generated subsonic vortex of hot dissociated O2 ejected from the laser-energy deposition zone. The success of indirect ignition depends on the orientation of the laser beam, the thickness of the shear layer, and the kernel standoff distance from the oxidizer edge of the shear layer. An ignition Damköhler number is defined that accounts for these averaged effects in six different simulation cases. For near-unity ignition Damköhler numbers, the solution is also sensitive to the local instantaneous flow field prevailing near the oxidizer edge of the shear layer, in that a modification of the instantaneous pre-deposition flow field, while preserving its turbulence statistics, can produce different ignition outcomes.Novelty and significance statement This work investigates forced ignition in a canonical flow configuration – a non-premixed turbulent CH4/O2 shear layer – and analyzes mechanisms by which ignition can be unexpectedly achieved in adverse conditions. In particular, an ensuing laser-generated advection of hot dissociated gas is observed to ignite the shear layer even when the mixture at the laser focal point is not flammable, an observation first made in early experiments. This flow phenomenon, whose consequences on ignition of non-premixed turbulent flows have not previously been analyzed by direct numerical simulation, can significantly separate the laser-energy deposition zone from the ignition location and is linked to baroclinically generated vorticity due to the rounded conical shape of the energy kernel. The phenomenology analyzed here may impact the design of laser-based ignition systems for chemical propulsion.

Unsteady Multiphase Simulation of Oleo-Pneumatic Shock Absorber Flow

The internal flow in oleo-pneumatic shock absorbers is a complex multiphysics problem combining the interaction between highly unsteady turbulent flow and multiphase mixing, among other effects. The aim is to present a validated simulation methodology that facilitates shock absorber performance prediction by capturing the dominant internal flow physics. This is achieved by simulating a drop test of approximately 1 tonne with an initial contact vertical speed of 2.7 m/s, corresponding to a light jet. The flow field solver is ANSYS Fluent, using an unsteady two-dimensional axisymmetric multiphase setup with a time-varying inlet velocity boundary condition corresponding to the stroke rate of the shock absorber piston. The stroke rate is calculated using a two-equation dynamic system model of the shock absorber under the applied loading. The simulation is validated against experimental measurements of the total force on the shock absorber during the stroke, in addition to standard physical checks. The flow field analysis focuses on multiphase mixing and its influence on the turbulent free shear layer and recirculating flow. A mixing index approach is suggested to facilitate systematically quantifying the mixing process and identifying the distinct stages of the interaction. It is found that gas–oil interaction has a significant impact on the flow development in the shock absorber’s upper chamber, where strong mixing leads to a periodic stream of small gas bubbles being fed into the jet’s shear layer from larger bubbles in recirculation zones, most notably in the corner between the orifice plate and outer shock absorber wall.

Flume Experiments for Flow around Debris Accumulation at a Bridge

We conducted flume experiments to study the flow behavior around a debris accumulation at a two-pier bridge. An Acoustic Doppler Velocimetry was utilized to measure velocity in cases with and without debris. We examined the impact of this accumulation on the velocity field and bed shear stress to better understand the flow and sediment transport mechanisms near the debris buildup at the bridge. Debris clusters were found to cause strong downward flows behind the bridge piers and to create turbulent shear layers emanating from the debris base. These flow patterns caused an increase in bed shear stress behind the piers by up to 40%. Downstream of the bridge, the debris-induced bed shear stress increase persisted for a distance equivalent to four times the spacing between the piers.

Non-periodic shear layer instabilities driving local extinction in premixed ramjet cavity flames

The local extinction characteristics of turbulent premixed ethylene-air flames are experimentally investigated in a high-speed cavity combustor to provide a full characterization of the temporally evolving non-periodic hydrodynamic instabilities that result in local extinction. The local flame extinction phenomenon is captured temporally using high-speed particle image velocimetry (PIV) and broadband chemiluminescence. The evolution of the flame topology, turbulent structures, and flame strain rate are analyzed through the extinction process to distinguish the turbulent shear layer mechanisms contributing to flame instabilities and extinction. A frequency analysis of the extinction event was performed and found the flame extinction to occur at non-periodic temporal intervals. A further wavelet decomposition revealed the presence of a non-periodic hydrodynamic instability in the shear layer causing extinction. The instability mechanism is related to the stability of vortex pairing in the shear layer, which were found to correspond to large-amplitude wave generation on the flame surface. In instances of flame extinction, the vortex pairs exhibit a core deformation from an elliptic instability mechanism, leading eventually to the shredding of the vortical cores, which is the primary mechanism for excessive turbulent flame strain and resulting extinction. Although the local flame extinction mechanism is driven from flame and shear layer interactions, the condition for local flame extinction to occur requires the flame to interact with an elliptical instability in the shear layer. The results can guide strategies to enhance combustion stability, performance, and efficiency.

Analysis of the effect of turbulent inflow on the flow-field and noise of supersonic jet flow using large eddy simulation

The impact of inflow flow state on the flow-field and far-field noise of supersonic jet flow has been studied. A new turbulent inflow boundary condition based on the synthetic eddy method is implemented in an in-house LES code. The implementation was validated using a turbulent channel flow. Simulation results of an under-expanded supersonic jet with a converging nozzle have shown that turbulent inflow leads to thicker and turbulent initial shear layer with rich vortical structures. The thick initial shear layer hinders the growth of flow instability and break the acoustic feedback loop, which is vital to the generation of screech tone. The alternation of the flow-field by the turbulent inflow also leads to changes in the far-field noise radiation. The screech tone is eliminated, the noise in the downstream direction is considerably suppressed, and the noise radiates in the upstream direction is slightly amplified.

Wall pressure fluctuations in wall heated and cooled shock wave and turbulent boundary layer interactions

Wall pressure fluctuations in shock wave and turbulent boundary layer interactions on heated and cooled walls are investigated by performing direct numerical simulations. The objectives of this study are to identify flow dynamics causing low- and high-frequency wall pressure fluctuations and evaluate wall heating and cooling effects on the wall pressure fluctuations. The wall pressure spectra highlight two characteristic low-frequency spectral peaks at the separation point and below the expansion waves. Conditional analysis reveals that the two spectral peaks originate from the oscillations of the reflected shock and expansion waves, coupled with the expansion and contraction motions of the separated turbulent shear layer. Regarding wall temperature effects, wall cooling enhances the magnitude of the wall pressure fluctuations regardless of the low- and high-frequency components. Furthermore, influences of the expansion waves are also enhanced by wall cooling, which increases the wall pressure fluctuations locally after the separation.

A numerical study on Langmuir circulations and coherent vortical structures beneath surface waves

Langmuir circulations (LCs) arise through the interaction between the Lagrangian drift of the surface waves and the wind-driven shear layer. Quasi-streamwise vortices (QSVs) also form in the turbulent shear layer next to a flat surface. Both vortical structures manifest themselves by inducing wind-aligned streaks on the surface. In this study, numerical simulations of a stress-driven turbulent shear layer bounded by monochromatic surface waves are conducted to reveal the vortical structures of LCs and QSVs, and their interactions. The LC structure is educed from conditional averaging guided by the signatures of predominant streaks obtained from empirical mode decomposition; the width of the averaged LC pair is found to be comparable to the most unstable wavelength of the Craik–Leibovich equation. Coherent vortical structures (CVSs) are identified using a detection criterion based on local analysis of the velocity-gradient tensor and their topological geometry; QSVs accumulated beneath the windward surface are found to dominate the distribution. Employing the variable-interval spatial average to the identified QSVs further reveals that QSVs tend to form in the edge vicinity of the surface streaks induced by the LCs. The transport budgets of streamwise enstrophy are examined to reveal the interaction. It is found that QSVs perturb the streaks resulting in a localized streamwise gradient of the spanwise velocity, that is, vertical vorticity. The vertical shear tilts the vertical vorticity, therefore enhancing streamwise enstrophy production and the formation of QSVs. The results highlight the differences in the CVSs between the Langmuir turbulence and the wall turbulence.

Wind Dependencies of Deep Cycle Turbulence in the Equatorial Cold Tongues

Abstract Several years of moored turbulence measurements from χpods at three sites in the equatorial cold tongues of Atlantic and Pacific Oceans yield new insights into proxy estimates of turbulence that specifically target the cold tongues. They also reveal previously unknown wind dependencies of diurnally varying turbulence in the near-critical stratified shear layers beneath the mixed layer and above the core of the Equatorial Undercurrent that we have come to understand as deep cycle (DC) turbulence. Isolated by the mixed layer above, the DC layer is only indirectly linked to surface forcing. Yet, it varies diurnally in concert with daily changes in heating/cooling. Diurnal composites computed from 10-min averaged data at fixed χpod depths show that transitions from daytime to nighttime mixing regimes are increasingly delayed with weakening wind stress τ. These transitions are also delayed with respect to depth such that they follow a descent rate of roughly 6 m h−1, independent of τ. We hypothesize that this wind-dependent delay is a direct result of wind-dependent diurnal warm layer deepening, which acts as the trigger to DC layer instability by bringing shear from the surface downward but at rates much slower than 6 m h−1. This delay in initiation of DC layer instability contributes to a reduction in daily averaged values of turbulence dissipation. Both the absence of descending turbulence in the sheared DC layer prior to arrival of the diurnal warm layer shear and the magnitude of the subsequent descent rate after arrival are roughly predicted by laboratory experiments on entrainment in stratified shear flows. Significance Statement Only recently have long time series measurements of ocean turbulence been available anywhere. Important sites for these measurements are the equatorial cold tongues where the nature of upper-ocean turbulence differs from that in most of the world’s oceans and where heat uptake from the atmosphere is concentrated. Critical to heat transported downward from the mixed layer is the diurnally varying deep cycle of turbulence below the mixed layer and above the core of the Equatorial Undercurrent. Even though this layer does not directly contact the surface, here we show the influence of the surface winds on both the magnitude of the deep cycle turbulence and the timing of its descent into the depths below.

On the pressure field, nuclei dynamics and their relation to cavitation inception in a turbulent shear layer

Cavitation inception in the turbulent shear layer developing behind a backward-facing step occurs at multiple points along quasi-streamwise vortices (QSVs), at a rate that increases with the Reynolds number (Re). This study investigates the evolution of the unsteady pressure field and the distribution of nuclei within and around the QSVs. The time-resolved volumetric velocity in the non-cavitating flow is measured using tomographic particle tracking, and the pressure is determined by spatial integration of the material acceleration. Analysis in Eulerian and Lagrangian reference frames reveals that the pressure is lower, and its minima last longer within the QSVs compared with the surrounding flow. The intermittent low pressure regions, whose sizes and shapes are consistent with those of the cavities, are likely to be preceded by axial vortex stretching and followed by contraction. Such phenomena have been observed before in simulations of stretched vortex elements. For the same axial straining, the pressure minima last longer with increasing Re, a trend elucidated in terms of viscous diffusion of the stretched vortex core. The impact of nuclei availability is studied under ‘natural’ and controlled seeding. Owing to differences in the saturation level of non-condensable gas, the microbubble concentration in the shear layer decreases with increasing Re, in contrast to the rate of cavitation events. Minor differences in entrainment rate into the shear layer also do not explain the substantial Re effects on cavitation inception. Hence, the Re scaling of inception appears to be dominated by trends of the pressure field.

Growth-Rate Prediction for Low-Speed Variable-Density Spatially Developing Turbulent Planar Shear Layers: Status and Prospects

Abstract Progress in analysis of the growth rate of low-speed variable-density spatially developing turbulent planar shear layers is examined from the viewpoint of global trends across the relevant parameter space. Several approaches have been shown to agree with available measurements. Here, it is noted that comparable agreement is also obtained using a simple extension of the canonical Kelvin–Helmholtz linear stability theory. Beyond the range of the experimentally explored parameter space, available predictions disagree qualitatively as well as quantitatively. To a degree that is not generally recognized, this indicates that the governing parameter dependences and associated phenomenology are open questions. Further investigation needed to address these questions is discussed.

Experimental study of two side-by-side decaying grid turbulent fields at different mean velocities

A Hot-wire anemometry experiment is conducted to investigate how two turbulent fields decaying with different mean velocities interact at their interface. A grid with different mesh sizes and solidities on either side of the grid centerline is used to generate two turbulent fields. It is found that the resulting turbulent shear layer created at the interface of the two fields evolves in a self-preserving manner. Further, the Taylor microscale Reynolds number, increases linearly while and become constants as the distance x downstream of the grids increases. Off the centerline one observes the classical decay of turbulence, e.g. varies like (n is negative) and decreases. It is observed that the transport equation for is dominated by the production and pressure-velocity correlation in the central region of the turbulent shear layer while production, dissipation, and turbulent diffusion of the transport equation for dominate in the central part of the shear layer. The pressure-velocity correlation term for is negligible on the centreline of the shear layer and important on the edges. The measurements of the scale-by-scale (SBS) energy terms on the shear layer centerline reveal that the energy transfer from large to small scales occurs in a non-trivial manner.

Dust Settling From Turbulent Layers in the Free Troposphere: Implications for the Saharan Air Layer

AbstractDesert dust accounts for a substantial fraction of the total atmospheric aerosol loading. It produces important impacts on the Earth system due to its nutrient content and interactions with radiation and clouds. However, current climate models greatly underestimate its airborne lifetime and transport. For instance, super coarse Saharan dust particles (with diameters greater than 10 µm) have repeatedly been detected in the Americas, but models fail to reproduce their transatlantic transport. In this study, we investigated the extent to which vertical turbulent mixing in the Saharan Air Layer (SAL) is capable of delaying particle deposition. We developed a theory based on the solution to a one‐dimensional dust mass balance and validated our results using large‐eddy simulation (LES) of a turbulent shear layer. We found that eddy motion can increase the lifetime of suspended particles by up to a factor of 2 when compared with laminar flows. Moreover, we found that the increase in a lifetime can be reliably estimated solely as a function of the particle Peclet number (the ratio of the mixing timescale to the settling timescale). By considering both the effects of turbulent mixing and dust asphericity, we explained to a large extent the presence of super coarse Saharan dust in the Caribbean observed during the Saharan Aerosol Long‐Range Transport and Aerosol‐Cloud‐Interaction Experiment (SALTRACE) field campaign. The theory for the lifetime of coarse particles in turbulent flows developed in this study is also expected to be applicable in other similar geophysical problems, such as phytoplankton sinking in the ocean mixed layer.

Vortex flow of downwind sails

This paper sets out to investigate the vortex flow of spinnaker yacht sails, which are low-aspect-ratio highly cambered wings used to sail downwind. We tested three model-scale sails with the same sections but different twists over a range of angles of attack in a water tunnel at a Reynolds number of 21 000. We measured the forces with a balance and the velocity field with particle image velocimetry. The sails experience massively separated three-dimensional flow and leading-edge vortices convect at half of the free-stream velocity in a turbulent shear layer. Despite the massive flow separation, the twist of the sail does not change the lift curve slope, in agreement with strip theory. As the angle of attack and the twist vary, flow reattachment might occur in the time-average sense, but this does not necessarily result in a higher lift to drag ratio as the vorticity field is marginally affected. Finally, we investigated the effect of secondary vorticity, vortex stretching and diffusion on the vorticity fluxes. Overall, these results provide new insights into the vortex flow and associated force generation mechanism of wings with massively separated flow.

Secondary flow and streamwise vortices in three-dimensional staggered wavy-wall turbulence

The present paper simplifies the naturally formed dunes (riverbeds) as large-scale three-dimensional staggered wavy walls to investigate the features of the accompanying secondary flows and streamwise vortices via large-eddy simulation. A comparison between the swirling strength and the mean velocities suggests where a secondary flow induces upwash or downwash motions. Moreover, we propose a pseudo-convex wall mechanism to interpret the directionality of the secondary flow. The centrifugal instability criterion is then used to reveal the generation of the streamwise vortices. Based on these analytical results, we found that the streamwise vortices are generated in the separation and reattachment points on both characteristic longitudinal–vertical and horizontal cross-sections, which is related to the curvature effect of the turbulent shear layer. Furthermore, the maximum Görtler number characterized by the ratio of centrifugal to viscous effects suggests that, for fixed ratio of spanwise- to streamwise-wavelength cases, the strongest centrifugal instability occurring on the longitudinal–vertical cross-section gradually dominates with the increases in amplitude. A similar trend for the cases with varied spanwise wavelength can also be found. It is also found that the streamwise vortices are generated more readily via transverse flow around the crest near the separation and reattachment points when the ratio of spanwise- to streamwise-wavelength equals 1.

Unsteadiness in hypersonic leading-edge separation

Hypersonic leading-edge separation is studied toward understanding the varying shock-related unsteadiness with freestream Reynolds number (\(1.66 \times 10^5 \le \text{Re}_D \le 5.85 \times 10^5\)) in the newly constructed hypersonic Ludwieg tunnel (HLT) at a freestream design Mach number of \(M_\infty =6.0\). An axisymmetric flat-face cylinder of base body diameter \(D=35\) mm is fitted with axial protrusions of different fineness (\(d/D=0.1,0.2,0.26,0.34\) at \(L/D=1.4\)) and slenderness (\(L/D=0.7,1,1.4,1.9\) at \(d/D=0.2\)) ratio to induce a wide range of leading-edge separation intensities. Qualitative and quantitative assessments are made using schlieren imaging, planar laser Rayleigh scattering, and unsteady pressure measurements. A well-known to-and-fro shock motion called pulsation and a flapping shock-shear layer oscillation is observed as \(\text{Re}_D\) changes. A shorter protrusion length (\(L/D=0.7\)), associated with pulsation, produces a pressure loading four orders higher than the cases with longer protrusion lengths associated with flapping. There exists a critical separation length (\(L/D \ge 1.4\)) beyond which the separated shear layer trips to turbulence and introduces fluctuations in the recirculation region as \(\text{Re}_D\) increases. The intensity of the separated turbulent shear layer is dampened by an order of magnitude, provided the reattachment angle is shallow by increasing the fineness ratio to \(d/D \ge 0.34\). There also exists a set of critical geometrical parameters (\(L/D=1, d/D=0.2\)) for which the unsteady modes (pulsation and flapping) switch between themselves during successive runs, probably due to upstream fluctuations. From the modal analysis of the Rayleigh scattering images, the first four dominant modes that drive flapping are identified as translatory flapping, sinuous flapping, and large and small-scale shedding.