Asymmetric Wake Research Articles

Mechanisms of wake asymmetry and secondary structures behind low aspect-ratio wall-mounted prisms

The wake of a wall-mounted finite prism is numerically studied and characterized with an aspect ratio (height-to-width) of$1$and varying depth ratios (length to width) of between$0.016$and$4$at Reynolds numbers of 50–500. The prism is immersed in a laminar boundary layer. The minimum depth ratio considered here accounts for the special case of a wall-mounted very thin prism (similar to a flat plate), which is used to establish the mechanism and evolution of the wake associated with free-end effects and the shear-layer dynamics in small aspect-ratio prisms. The onset of an unsteady wake behind a very thin prism at a Reynolds number of$200$is characterized by symmetric shedding of hairpin-like vortices. A unique asymmetric wake pattern appears at lower depth ratios starting at a Reynolds number of 250, which transitions to an symmetric wake with increasing depth ratio. The threshold depth ratio for this symmetric transition increases with Reynolds number. The asymmetric wake results from alternate shear-layer peel-off from either side of the prism, which itself is attributed to the out-of-phase shedding of tip vortices at a lower Strouhal number ($St_{sh}/2$) that interact with the detaching side shear layers. Alternate shedding of tip vortices form secondary vortex structures that are fed by the excess vorticity resulting from shear-layer detachment from either side of the prism. Increasing the depth ratio leads to simultaneous shedding of the tip vortices, which restores the commonly observed wake symmetric patterns. Thus, we identify and characterize the formation and interaction mechanisms of symmetric and asymmetric wakes during the transition process with increasing Reynolds number for different depth-ratio prisms.

An investigation on the switching of asymmetric wake flow and the bi-stable flow states of a simplified heavy vehicle

This study investigates the effect of aspect ratios (Ra*) on the wake bi-stability behind the GTS model using improved delayed-detached eddy simulation (IDDES) at a Reynolds number of 2.7×104. Eight cases with Ra* in the range of Ra*∈[0.5, 2.0] have been considered to investigate the asymmetric wake flow and the corresponding aerodynamic response. The primary objective of this study is to reveal the mechanism of the Ra* effects on the GTS’s flow topology, asymmetric wake flow and the bi-stable flow switching process. The accuracy of the numerical method has been validated by comparing the recirculation bubble, vortex core and aerodynamic drag with those obtained from the previous large-eddy simulation study and the water channel experiment. The results show that three typical flow topologies (FT-I, FT-II and FT-III) are classified according to the drag coefficient and the length relation between the vertical and horizontal recirculation region. The vertical and horizontal asymmetric characteristics can be transformed between two adjacent flow topologies. Moreover, a switching process of the bi-stable wake flow is also observed as Ra* is equal to 0.71. Additionally, the ground motion can reverse the dominated flow state and inhibiting the corresponding switching process.

Direct numerical simulation of transitional flow past an airfoil with partially covered wavy roughness elements

We perform direct numerical simulation of flow past the NACA (National Advisory Committee for Aeronautics) 0012 airfoil with partially covered wavy roughness elements near the leading edge. The Reynolds number Rec based on the freestream velocity (U0) and airfoil chord length (C), and the angle of attack (AoA) is fixed, i.e., Rec=5×104, AoA=10°. The leading edge roughness elements are characterized by streamwise sinusoidal-wave geometry that is uniform in the spanwise direction with fixed height, whereas varying wave numbers (k) from 0 to 12. Based on the validation of the smooth baseline case (k = 0), the roughness effects on the aerodynamic performance are evaluated in terms of the lift and drag coefficients. The drag coefficient decreases monotonically with k, while the variation of the lift coefficient with k is similar to the “drag crisis” phenomenon observed in cylinder flows. The sharp variations of lift and drag coefficients from k = 6 to 8 indicate that k = 8 is a critical case, beyond which massive separation occurs and almost covers the airfoil's suction side and dominates the airfoil aerodynamic performance. To further reveal the underlying mechanism, the flow structures, pressure, skin friction coefficients, shear layer transition onset, and boundary layer separation are quantified to investigate the roughness effects. The roughness elements strongly modify the separation behavior, whereas they have little effect on the transition onset. The unsteady interactions and convections of separation bubbles downward the trailing edge also change the wake evolution. Based on the scaling of the asymmetric wake profiles, we find that the wake defect is gently decreasing with k, but the increase in the wake width is much stronger. This scaling analysis gains a better insight into the roughness effects on the momentum deficit flow rate, which confirms the drag mechanism with different roughness wave numbers.

로터-기체 상호작용 소음에 관한 수치 예측 연구

Strong-intensity tip vortex generated from the tip of the rotor blade causes strong aerodynamic interactions with the fuselage and structures. This interaction phenomenon directly affects the aerodynamic performance and noise characteristics of the rotor blades. In this study, the computational analysis of rotor-airframe configuration is performed to investigate the effects of rotor-airframe interaction on thrust, wake structure, flow field, and noise levels using the Lattice-Boltzmann Method (LBM). The isolated rotor operating in hovering conditions is used for the validation model. The thrust force and tonal noise associated with the 1st and 2nd Blade Passage Frequency (BPF) of the isolated rotor are compared against the measurements. The validation results showed good agreement with the experimental data. When a conical airframe is placed under the rotor blade, the thrust force tends to oscillate periodically. In addition, rotor wake development along the downstream direction is obstructed, and asymmetric wake structure can be observed, thus leading to a faster tip vortex breakdown and an increase in turbulence intensity. Finally, the overall sound pressure level (OASPL) of the rotor-airframe is higher than that of the isolated rotor at all microphone positions due to thrust fluctuation and a highly unsteady flow field caused by the strong interaction.

On the wake response of a square cylinder subjected to an inline nonharmonic forcing

In this work, we study the effect of two spectrally simple nonharmonic inline forcing waveforms on the wake response of a square cylinder. The characteristics of wake response under nonharmonic forcing were studied and compared to wake response under harmonic forcing for a constant Reynolds number 100. By varying the relative strength of the spectral components and the secondary frequency of the nonharmonic forcing of the inflow, an asymmetric modulated wake and an asymmetric 2P + 2S wake were observed for a two-tone nonharmonic forcing. These modes combine the features of the wake response of individual spectral components. In some regions of the parameter space, the wake response did not correlate well with the spectral components of harmonic forcing. An amplitude-modulated forcing was also studied. For amplitude-modulated forcing, the additional frequency component did not affect the wake structure. This observation indicates that the wake may act as a low pass filter for inline flow frequency components above the natural vortex shedding frequency.

The impact of the atmospheric boundary layer on the asymmetric wake profile: A bivariate analysis

The complexities of wind turbine wake evolution necessitate the estimation of turbulence and horizontal and vertical wake expansion. The standard approach for developing a Gaussian wake model based on Gaussian similarity assumes that the turbine wake profile is symmetric around the hub height and approximates a normal distribution. The impacts of Atmospheric Boundary Layer (ABL) and ground surface roughness cause the wake to deviate from radial symmetry, resulting in a nonsymmetric wake around hub height. We develop the Bivariate Gaussian (B-Gaussian) Model to estimate the nonsymmetrical wind turbine wake expansion due to ABL effects. The B-Gaussian model factors the correlation coefficient (Ω) to compare the horizontal and vertical expansions. The radial profiles result for the B-Gaussian shows a faster wake decay for the unstable ABL because of faster mixing at higher-turbulence intensities, and slower wake decay is due to slower mixing at lower-turbulence intensities for the stable ABL. The radial wake profiles for the unstable ABL transition from vertical elliptical-shaped in the near wake region to double circular-shaped profiles in the far-wake region as Ω decreases. Finally, compared to preceding Gaussian models, the B-Gaussian outperforms previous Gaussian wake models and has the least overall and downstream entrainment errors.

An IDDES study of the near-wake flow topology of a simplified heavy vehicle

Abstract The complex wake flow of a GTS (ground transportation system) model contributes to large percentage of the aerodynamic drag force. Therefore, predicting accurate wake flow will help carry out the drag reduction strategies. In this paper, the near-wake flow topology of the GTS was studied at Re = 2.7×104 to assess the capability of a hybrid RANS/LES (Reynolds-averaged Navier–Stokes/large eddy simulation) approach, known as IDDES (improved delayed detached eddy simulation). The current study also aims to understand the effects of different computational parameters, e.g. the spatial resolution, time step, residual level, discretization scheme and turbulence model, on this asymmetrical wake flow configuration. A comparison of IDDES with previous water channel tests, well-resolved LES, partially averaged Navier–Stokes and URANS (unsteady RANS) was included to better understand the benefits of this hybrid RANS/LES approach. The results show that on the medium and fine grids, the IDDES produces an asymmetrical flow topology (known as flow state I) in the near-wake of the vertical midplane, as reported in previous studies. The recommended parameters for the time step (1×10–4 s) and residual level (1×10–4) provide sufficient accuracy of wake predictions to show good agreement with experiments. For the convective term of the momentum equation in IDDES, the bounded central difference discretization scheme is proposed to be adopted for discretization. Additionally, URANS cannot accurately capture this asymmetrical flow field. IDDES proves to be capable of predicting the wake flow field of this simplified heavy vehicle with high accuracy. All obtained conclusions can provide references for the aerodynamic drag reduction of the GTS.

Dynamics and bifurcations of laminar annular swirling and non-swirling jets

This paper presents bifurcation analyses characterising the nonlinear dynamics of fully developed laminar annular jets with respect to the centrebody diameter${ {d}}$, Reynolds number${ {Re}}$, and swirl ratio${ {S}}$. Similar flows appear in numerous applications and feature a vibrant range of topological and dynamical characteristics associated with phenomena including shear layer separation and vortex breakdown. Our results begin by describing the non-monotonic evolution of the axisymmetric jet's steady topology under varying${ {S}}$. In accord with earlier reports, the jet progresses through a sequence of wake, breakdown and wall jet regimes in a qualitatively similar manner across a wide span of${ {d}}$and${ {Re}}$values. In the wake regime, the non-swirling jet bifurcates to a plane-symmetric, but not axisymmetric, steady flow pattern beyond a${ {d}}$-dependent critical${ {Re}}$value. With further increase in${ {Re}}$, the steady non-swirling jet destabilises subsequently via multiple distinct Hopf bifurcations. Introducing${ {S}}>0$to the jet also induces unsteadiness by twisting the singly azimuthally periodic ($|m|=1$) asymmetric wake structure and causing it to precess periodically in time about the central axis. Intermediate swirl stabilises this unsteady dynamics and restores the jet's axisymmetry. This stabilising effect is then reversed in the breakdown regime at higher${ {S}}$, where a variety of different$|m|=1$and$|m|=2$instabilities bifurcate from the steady flow as${ {S}}$is increased. Several instances of hysteresis and subcritical behaviour are reported and discussed, including one that manifests precessing vortex core oscillations.

Numerical study on the flow-induced vibrations of two elastically mounted side-by-side cylinders at subcritical Reynolds numbers

Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) of an elastically mounted circular cylinder pair arranged in parallel are numerically investigated in a subcritical Reynolds number range of 1470–10320. The two cylinders are identical with mass ratios of m⁎ = 2.6 and mass-damping parameters of (m⁎ + Ca)ζ = 0.013. The transverse centre-to-centre spacing ratio (Sy/D) between them is varied from 4.0 to 10.0 with an increment of 2.0. The effect of Sy/D on the FIV responses, hydrodynamic features and wake patterns is evaluated. It is found that the response amplitudes of the two cylinders show similar variation trends and both drop to smaller values earlier than an isolated cylinder when Sy/D = 4.0, 6.0 and 10.0. Whereas, their response characteristics are different at Sy/D = 8.0. Cylinder #1 reaches its peak in-line (IL) and cross-flow (CF) amplitudes equivalent to those of the single cylinder, while the vibration amplitudes of Cylinder #2 experience decreases at Vr = 8.0. Moreover, the results suggest that the interference between the two cylinders is nonnegligible for all the Sy/D values considered in the present study. Six wake patterns are identified including the asymmetric long period flip-flopping (ALFF), asymmetric shear layer (ASL), biased in-phase synchronised (BIS), asymmetric shedding (A-Shed), in-phase synchronised (IS) and anti-phase synchronised (AS) patterns. The asymmetric wake patterns give rise to the distinct vibration modes of the two cylinders.

Region-based convolutional neural network for wind turbine wake characterization from scanning lidars

A convolutional neural network is applied to lidar scan images from three experimental campaigns to identify and characterize wind turbine wakes. Initially developed as a proof-of-concept model and applied to a single data set in complex terrain, the model is now improved and generalized and applied to two other unique lidar data sets, one located near an escarpment and one located offshore. The model, initially developed using lidar scans collected in predominantly westerly flow, exhibits sensitivity to wind flow direction. The model is thus successfully generalized through implementing a standard rotation process to scan images before input into the convolutional neural network to ensure the flow is westerly. The sample size of lidar scans used to train the model is increased, and along with the generalization process, these changes to the model are shown to enhance accuracy and robustness when characterizing dissipating and asymmetric wakes. Applied to the offshore data set in which nearly 20 wind turbine wakes are included per scan, the improved model exhibits a 95% success rate in characterizing wakes and a 74% success rate in characterizing dissipating wake fragments. The improved model is shown to generalize well to the two new data sets, although an increase in wake characterization accuracy is offset by an increase in model sensitivity and false positive wake identifications.

Floor motion's influence on wake asymmetry of a notchback bluff body

Large eddy simulations are used to explore the influence of floor motions on asymmetric flows around a notchback bluff body. The focus of this study is on the aerodynamic forces and the extent of natural wake asymmetry presented under moving and stationary ground conditions. The different ground condition has a notable influence on the aerodynamic force and the surrounding pressure distribution of the body. On the other hand, the wake asymmetry, known to be a sensitive phenomenon, is not evidently affected by the floor motion. However, quantitative analysis of the averaged and the statistic flow still suggests slight differences in the degree of wake asymmetry between the two ground conditions. Modal analysis applying proper orthogonal decomposition confirms that the asymmetric wake dynamics and the wake shedding frequency are not sensitive to the floor motion. The accuracy of the numerical simulation is established by a grid-independence study.

Three-dimensional flow past a circular cylinder in proximity to a stationary wall

In this paper, we present direct numerical simulations (DNS) of the three-dimensional flow around a circular cylinder near a stationary wall at the Reynolds number of 500. The gap (G) between the cylinder surface and the stationary wall varies in the range of 0–3.0D where D is the cylinder diameter. We observe that the proximity wall significantly affects the flow topology around the cylinder, which is characterized by the asymmetric wake, upward gap flow, and strong interactions of the cylinder vortices with the wall-generated boundary layer. Three flow regimes are identified with variations of the fluid forces and vortex dynamics. (i) Steady regime: at G/D < 0.3, vortex shedding is suppressed in the near wake, and scattered streamwise vortices form in the far wake where the upper side shear layer meets the stationary wall. No fluctuating forces act on the cylinder. (ii) Biased unsteady regime: at 0.3 ≤ G/D < 1.5, the gap flow deflects upward and the vortices shed from the gap side are significantly suppressed. The cylinder has enlarged fluctuating drag and lift forces with identical dominant frequencies. (iii) Parallel unsteady regime: at G/D ≥ 1.5, vortices shed from both sides of the cylinder are of almost identical intensities while the gap flow is approximately parallel to the wall. The vortex dynamics approaches that of an isolated circular cylinder in unconfined flows. Flow features of each regime are illuminated through the flow fields, vorticity contours, statistics of the enstrophies and gap flow, and pressure distribution on the cylinder surface. Finally, we investigate the critical gap ratio for the onset of the vortex-shedding of the upper shear layer and discuss the underlying physics. Moreover, we observe that the occurrence of the second harmonic lift and fundamental drag frequencies are resulted from the asymmetric wake because of the proximity of the stationary wall.

Wind Forces and Flow Patterns of Three Tandem Prisms with a Small Height–Width Ratio

Wind tunnel tests and large eddy simulations were conducted to investigate the dependency of wind forces and flow patterns on the spacing (S) for three tandem prisms with a small height–width ratio H/W = 0.4. At the spacing ratio S/W = 0.7, mean and root-mean-square drag of downstream prisms have large local peaks, and their magnitudes are larger than those at adjacent spacing ratios; these should be noted to ensure the safety and economy of the wind-resistant design of prism-like low-rise buildings. These phenomena are different from that of a small group of tandem prisms with a large H/W and a large group of tandem prisms with a small H/W. At S/W = 0.7, tap pressure time histories of downstream prisms are non-stationary with abrupt changes, but wind force time histories of downstream prisms are stationary, unlike a small group of tandem prisms with a large H/W, where both tap pressure and win d force time histories are non-stationary. Above phenomena at S/W = 0.7 are attributed to a special asymmetric time-averaged wake regime, which has two modes with symmetric wake flow directions and they irregularly switch. The duration of each mode is ruleless. This special wake regime was not observed in previous studies on tandem prisms.

Numerical investigations of the wake behind a confined flat plate

The two-dimensional flow around a confined flat plate is simulated with the spectral element code, Nek5000. Direct numerical simulations were carried out at low Reynolds numbers Re (between 10⩽Re⩽200) and various blockage ratios β (between 0.1⩽β⩽0.9) and compared with the confined two-dimensional circular cylinder flow previously reported by Sahin and Owens (2004). Four distinct flow regimes are observed for the flow over a confined flat plate. The first is a steady symmetric wake where the vortices are evenly distributed along the centerline of the channel. The second is an unsteady symmetric regime which upon time-averaging the instantaneous flow field, the wake profile is symmetric. The third is an asymmetric steady wake where the flow is steady but the vortices in the wake are skewed towards one of the channel walls. The first three have been reported for the confined flow over a circular cylinder. However, a fourth flow regime defined as unsteady asymmetric wake is found for a flat plate at β = 0.8. This flow regime was not reported in prior studies on the confined flow over a confined cylinder. Analysis using linear stability analysis is also reported in this paper which confirms the trends reported in this paper. Effects of the confinement on the wake of a flat plate on the hydrodynamic forces such as the mean drag coefficient and Strouhal number have also been documented for the same range of Re and β and compared with the flow over a confined cylinder.

Transient Thrust Analysis of Rigid Rotors in Forward Flight

The purpose of this study was to investigate and quantify the transient thrust response of two small rigid rotors in forward flight. This was accomplished using a distributed doublet-based potential flow method, which was validated against wind-tunnel experimentation and a transient CFD analysis. The investigation showed that for both rotors, advancing and retreating blade effects were predicted to contribute to transient thrust amplitudes of 5–30% of the mean rotor thrust. The thrust output amplitudes of individual rotors blades were observed to be 15–45% of the mean rotor thrust, indicating that it is not uncommon for the thrust output variation of an individual rotor blade to approach the same value as the mean thrust output of the rotor itself. In addition to this, the theoretical analysis also illustrated that higher blade thrust oscillations resulted in pronounced asymmetric rotor wake structures.

Intermittent swimming of two self-propelled flapping plates in tandem configuration

Intermittent swimming and schooling individually offer the possibility of energy economy for fish. To study the role of the simultaneous use of both behaviors, the intermittent swimming of two self-propelled plates in tandem configuration is investigated numerically. Two intermittent swimming modes, i.e., the multiple-tail beat (MT) mode and the half-tail beat (HT) mode, are considered. For solitary plate swimming intermittently while maintaining fixed bout period, the propulsion velocity and energy consumption decrease monotonically as the duty cycle increases, consistent with the prediction of the reduced-order model. A pair of plates swimming with independent duty cycle can form orderly configurations, without separating or colliding, when their duty cycles are similar. For the MT mode, the asymmetric wake of the leader enhances the drag on the following plate by inducing an additional oncoming flow against it, making the follower harder to follow. For the HT mode, the symmetric wake of the leader reduces the drag on the follower, making it easier to follow. No significant difference was found in the propulsive performance of intermittent swimming between the leading plate in orderly configurations and solitary plate. The results of efficiency indicate that the HT mode is more economical than the MT mode for the follower. Usually, the smaller the equilibrium gap spacing is, the more efficient the follower is. The results of the cost of transport show that the follower achieves better energy economy for higher propulsion velocity. The results provide some insight into the collective intermittent swimming of fish and are helpful for bionic design.

Blockage influence on bi-stable flows of a notchback bluff body

The expected flow asymmetry behind a three-dimensional notchback Ahmed body is numerically investigated using large-eddy simulations with different blockage ratios of 0%, 5%, 10%, and 20%. The focus of the study is on the natural bi-stable flow influenced by the blockage ratio. Although the wake asymmetry can be observed under the blockage ratio within 0%−10%, the significant blockage influence on the sensitive bi-stability is indicated by the wake structures, pressure gradients, and wake dynamics achieved with the proper orthogonal decomposition. The higher blockage ratio increases the turbulence kinetic energy, velocity, and negative pressure in the near-wake region, resulting in the decrease in the asymmetry degree. The consistency of the asymmetric wake is found with blockage ratios between 0% and 5%. However, a 20% blockage ratio symmetrizes the bi-stable wake. Several existing drag corrections for the blockage influence are discussed. The wind tunnel experiment verifies the bi-stable flow with low blockage ratios and the wake symmetrization with a 20% blockage ratio.

Flow past a rotationally oscillating cylinder with an attached flexible filament

Experimental studies are conducted on a rotationally oscillating cylinder with an attached flexible filament at a Reynolds number of 150. Parametric studies are carried out to investigate the effect of cylinder forcing parameters and filament stiffness on the resultant wake structure. The diagnostics are flow visualization using the laser-induced fluorescence technique, frequency measurement using a hot film, and characterization of the velocity and vorticity field using planar particle image velocimetry. The streamwise force and power are estimated through control volume analysis, using a modified formulation, which considers the streamwise and transverse velocity fluctuations in the wake. These terms become important in a flow field where asymmetric wakes are observed. An attached filament significantly modifies the flow past a rotationally oscillating cylinder from a Bénard–Kármán vortex street to a reverse Bénard–Kármán vortex street, albeit over a certain range of Strouhal number, $St_{A} \sim 0.25\text {--}0.5$ , encountered in nature in flapping flight/fish locomotion and in the flow past pitching airfoils. The transition from a Kármán vortex street to a reverse Kármán vortex street precedes the drag-to-thrust transition. The mechanism of unsteady thrust generation is discussed. Maximum thrust is generated at the instants when vortices are shed in the wake from the filament tip. At $St_{A} &gt; 0.4$ , a deflected wake associated with the shedding of an asymmetric vortex street is observed. Filament flexibility delays the formation of an asymmetric wake. Wake symmetry is governed by the time instant at which a vortex pair is shed in the wake from the filament tip.

Effect of superhydrophobicity on the wake of a pitching foil across various Strouhal numbers

Particle image velocimetry-based measurements have been performed to study the flow over a pitching superhydrophobic NACA—National Advisory Committee for Aeronautics—0012 foil (SphNACA0012 foil) and to compare the same with NACA0012 foil. This is perhaps the first experimental study on a pitching SphNACA0012 foil. The objective is to understand the effects of superhydrophobicity on NACA0012 foil pitching about its leading edge at various Strouhal numbers, St = 0.08–0.65, with a constant pitching amplitude, θ0 = 4°, and Reynolds number, Re = 2400. Superhydrophobicity is found to significantly affect three different flow regimes: 2S von-Ka´rma´n wake, symmetric wake, and asymmetric wake regimes at smaller, intermediate, and larger values of St. In the 2S von-Ka´rma´n wake regime, although the wake structures of both the foils are quite comparable, a reduction in the shear layer strength and early rolling-up of vortices are observed for SphNACA0012 foil due to a partial slip effect. With a further increase in St, a transition to the symmetric wake regime is observed for both the foils and another transition that leads to a symmetry breaking of the vortex street is found to be earlier for SphNACA0012 foil, which results in the onset of lift generation at lower St than that of NACA0012 foil. The shear layer strength is weaker for the SphNACA0012 foil except at St = 0.24, which is a critical St for the jet deflection point and results in a 13% larger thrust coefficient for SphNACA0012 foils as compared to NACA0012 foils. These results on the larger lift as well as thrust coefficient at low St suggest improved maneuverability with high propulsive efficiency when superhydrophobicity is employed on the propulsor of underwater vehicles.

The influence of background turbulence on Ahmed-body wake bistability

The discovery of wake bistability has generated an upsurge in experimental investigations into the wakes of simplified vehicle geometries. Particular focus has centred on the probabilistic switching between two asymmetrical bistable wake states of a square-back Ahmed body; however, the majority of this research has been undertaken in wind tunnels with turbulence intensities of less than$1\,\%$, considerably lower than typical atmospheric levels. To better simulate bistability under on-road conditions, in which turbulence intensities can easily reach levels of$10\,\%$or more, this experimental study investigates the effects of free-stream turbulence on the bistability characteristics of the square-back Ahmed body. Through passive generation and quantification of the free-stream turbulent conditions, a monotonic correlation was found between the switching rate and free-stream turbulence intensity.