Flow Structure Research Articles

Numerical study of particle dispersion in the wake of a static and rotating cylinder at Re = 140 000

In this study, the particle-laden flow in the wake of a static and a rotating cylinder at Reynolds number of 140 000 was investigated using the Reynolds Averaged Navier–Stokes numerical approach. Three turbulence models such as k–ω shear stress transport, Reynolds stress model, and local-correlation transition model (LCTM) were selected to predict the flow topology. Lagrangian approach with one-way coupling was used to track solid spherical particles of different sizes (0.01, 0.1, 2.5, 10, and 50 μm). The study reveals that LCTM is the most accurate to predict the flow topology in both cases. Cylinder's rotation generates different effects on flow structure. It breaks the wake's symmetry and reduces its width, and increases the frequency of vortex shedding and the size of the recirculation zone. Particle transport analysis has revealed that particles' response to the flow depends on their Stokes number and wake flow topology. Particles of 0.01, 0.1, and 2.5 μm distribute in and around vortex cores, while particles of 10 and 50 μm do not penetrate vortex cores. Instead, 10 μm particles accumulate mainly around the periphery of vortices, while 50 μm particles skip the vortex street to the thin shear flow region between vortices to be transported by the mainstream flow. Finally, cylinder rotation reduces the particle spread in the vertical direction and shifts all particle distributions in the cylinder's rotation direction. Analysis of particle dispersion functions showed that cylinder's rotation reduces differences in dispersion extent depending on particle size.

Holistic characterization of an under-expanded high-enthalpy jet under uncertainty

Elaborate methodologies have been developed to study the thermo-chemical response of materials in high-enthalpy flows. To reach the high magnitudes of heat flux encountered in some hypersonic applications, one can resort to supersonic jets. They involve several physical effects, such as detached shocks ahead of probes. Because of these features, characterizing supersonic flows is a challenging task, especially when one accounts for experimental and modeling uncertainties. Building on the development of stochastic approaches, we propose a holistic methodology to determine the quantities of interest in an optimal manner for an under-expanded high-enthalpy jet, using both experimental measurements and high-fidelity flow simulations. Given the high computational cost of the high-fidelity simulations needed to describe the flow, we built an adaptive/multi-fidelity surrogate model to replace the estimation of the costly computer solver. A Bayesian inference method then allowed for characterizing an experiment carried out in the von Karman Institute's Plasmatron facility, for which no robust methodology currently exists. We show that the reservoir pressure and temperature and the nitrogen catalytic recombination coefficient of the copper probes can be accurately determined from the available measurements. Contrarily, the test conditions do not allow us to estimate the oxygen catalytic recombination coefficient. Finally, the characterized uncertainties are propagated through the numerical solver, yielding an uncertainty-based high-fidelity representation of the hypersonic flow's structure variability.

Characterizing turbulence structures in convective and neutral atmospheric boundary layers via Koopman mode decomposition and unsupervised clustering

The atmospheric boundary layer (ABL) is a highly turbulent geophysical flow, which has chaotic and often too complex dynamics to unravel from limited data. Characterizing coherent turbulence structures in complex ABL flows under various atmospheric regimes is not systematically well established yet. This study aims to bridge this gap using large eddy simulations (LESs), Koopman theory, and unsupervised classification techniques. To this end, eight LESs of different convective, neutral, and unsteady ABLs are conducted. As the ratio of buoyancy to shear production increases, the turbulence structures change from roll vortices to convective cells. The quadrant analysis indicated that as this ratio increases, the sweep and ejection events decrease, and inward/outward interactions increase. The Koopman mode decomposition (KMD) is then used to characterize their turbulence structures. Our results showed that KMD can reveal non-trivial modes of highly turbulent ABL flows (e.g., transverse to the mean flow direction) and can reconstruct the primary dynamics of ABLs even under unsteady conditions with only ∼5% of the modes. We attributed the detected modes to the imposed pressure gradient (shear), Coriolis (inertial oscillations), and buoyancy (convection) forces by conducting novel timescale and quadrant analyses. We then applied the convolutional neural network combined with the K-means clustering to group the Koopman modes. This approach is displacement and rotation invariant, which allows efficiently reducing the number of modes that describe the overall ABL dynamics. Our results provide new insights into the dynamics of ABLs and present a systematic data-driven method to characterize their complex spatiotemporal patterns.

Variations of the shock and secondary flow structure in a transonic compressor cascade with outlet back pressure

The effects of back pressure on the transonic cascade operating state are crucial and can determine the structure of internal shock waves and secondary flows. In this paper, numerical methods validated by experiments were employed to investigate the evolution mechanisms of the inlet flow field, shock structure, secondary flow structure, and cascade performance under different back pressures. Analysis revealed that transonic cascade exhibited unique incidence characteristics in the inlet flow field under both subsonic and supersonic regimes, although these two regimes involved different physical mechanisms. The results revealed that the operating state of the transonic compressor cascade under the unique incidence condition was influenced by the outlet back pressure, and there existed a critical static pressure ratio. The critical static pressure ratio shifted from 1.61 for two-dimensional flow to 1.37 for three-dimensional (3D) flow at M1 = 1.1, due to the corner separation and the characteristics of 3D shocks. The 3D shock structure exhibited a non-uniform distribution along the spanwise direction due to the influence of back pressure and the separated boundary layer. The vortex structures analysis revealed that the secondary flow structure on the sidewalls of the transonic compressor cascade was primarily dominated by corner vortices, whose formation mechanism was related to the interaction between the shock wave and the sidewall boundary layer. Additionally, this interaction also led to the formation of detached shock and lip shock vortex structures. Finally, loss analysis indicated that the wake region of the transonic cascade primarily includes six types of loss, and the total loss of the cascade decreased with the rise in back pressure.

Теоретические основы оценки аэродинамического воздействия ветровых потоков на сооружения завода по подготовке и сжижению природного газа

Leaks (spills) of liquefied gases evaporate rapidly on the ground (water) and initially generate a cold plume of heavy vapors. The plume spreads fast downwind, heats up with time, and can become positively volatile in case the concentration of interest for the study (above the lower flammability limit) is reached; therefore, the plume can rise and transform into a vapor cloud. The plume or the vapor cloud can ignite in the flash form. Such situations are possible at liquefied natural gas production plants or regasification units where large amounts of explosive substances are handled involving changes in their aggregate state. The article analyses the significance of the wind impact on the facilities of natural gas liquefaction plants for regular operation and the potential consequences of emergencies. In order to assess the wind impact, the direct numerical modeling of the structure of local wind flows generated at the airflow around the plant facilities by vertical method is suggested. An example of numerical modeling for a natural gas liquefaction plant based on the modular constructions of the process line is provided.

Large-Eddy Simulations of Flow over a Backward-Facing Ramp with a Wall-Mounted Cube

Passive flow control devices, such as vortex generators (VGs), can effectively modulate the turbulent boundary layer flow near regions of adverse pressure gradients, but the interactions between the salient flow structures produced by VGs and those of the separated flow are not fully understood. In this study, a spatially evolving turbulent boundary layer interacting with a wall-mounted cube ahead of a backward-facing ramp is investigated using wall-resolved large-eddy simulations for a Reynolds number of 19,600, based on the inlet boundary layer thickness and freestream velocity. Different cube configurations are examined to isolate the effects of cube height and streamwise position. The large counter-rotating flow produced by the larger cubes generated more turbulent kinetic energy, thereby resulting in smaller separated regions over the ramp. Although significantly lower levels of turbulent kinetic energy dissipation than production are observed in the outer flow regions of the horseshoe vortex and in the induced counter-rotating flow, the spatial distribution of dissipation is similar to that of the turbulent kinetic energy. When the upstream position of an isolated single cube, relative to the leading ramp edge, is more than three cube heights, the streamwise decay of the counter-rotating flow results in lower levels of turbulent kinetic energy.

Unsteady flow behaviors and flow-induced noise characteristics in a closed branch T-junction

In the present study, dynamic delayed detached eddy simulation is utilized to explore turbulent flow in T-junctions at a Reynolds number of ReD = 2.0 × 104. Three systems with varying corner cavity depth-to-diameter ratios (Ld/D = 1, 2, and 4) are examined to elucidate the interplay between unsteady flow and flow-induced noise. The analysis employs Lighthill's acoustic analogy to scrutinize surface dipole acoustic sources and their noise propagation characteristics. Coherent flow structures, characterized as wavepackets, are identified through spectral proper orthogonal decomposition, demonstrating consistent dominance in modes and dipole distributions across the systems. In the system with Ld/D = 1, wavepackets originating from the downstream region of the junction exhibit a pronounced flapping behavior attributed to the Kelvin–Helmholtz instability. Most dissipate with the mainstream flow, whereas a portion interacts with the wall, forming dipole acoustic sources. For systems with Ld/D = 2 and 4, the dominant mode transitions to the junction adjacent to the corner cavity, expanding continuously after separation until obliquely colliding with the wall, resulting in expanded dipole distributions. Mechanisms underlying flow-induced noise generation are unveiled by extracting transient vorticity fields within oscillation cycles. For shallow corner cavity depths (Ld/D = 1), periodic oscillatory vorticity shedding from the junction's sidewall significantly contributes to far-field sound pressure. As the cavity is deep enough to support one or more full recirculations of the fluid (Ld/D = 2 and 4), periodic vorticity shedding from the trailing edge directly impacts the wall above the junction, simultaneously suppressing flapping behavior at the leading edge and weakening overall dipole acoustic source intensity.

Spatial distribution of rigid vorticity in pump-turbine under turbine mode with different guide vane openings

Abstract Under non-design operating conditions, pump-turbines often exhibit notable instabilities within their runner regions. This study endeavors to investigate the spatial distribution patterns of vortex structures occurring between runner blade channels, focusing on different guide vane opening conditions in the turbine mode of a model pump-turbine. Based on rigid vorticity vectors, the large-scale vortex structures in the channels were analysed. Additionally, this study proposes a novel approach that utilizes the relative streamline coordinates of the blade skeleton to conduct flow analysis. This method offers a quantitative description of the spatial distribution of rigid vortices and associated physical quantities within the blade channels along the streamwise, circumferential, and spanwise directions. Finally, the causes of rigid vortices were analysed. The paper presents a pioneering and advanced theoretical tool and research methodology, serving as a valuable resource for the analysis and understanding of unstable flow structures within pump-turbines.

Numerical study of flow past two square cylinders with horizontal detached control rod through passive control method

A two dimensional (2-D) numerical study is conducted through the lattice Boltzmann method for flow past two square cylinders with a detached control rod placed in the horizontal position of the channel. The range of Reynolds number (Re) is fixed at Re = 150, with the length (l) of the control rod varying from l = 0.1d–21d. First, we check the accuracy of grid points and the validity of the code for present problems by comparing the results with already available data in the literature. After that, we discussed the obtained results in terms of vorticity contour, drag and lift coefficients, and force statistics. In our study of flow structure mechanisms, we examined four types of flow regimes: a small length control rod, a small and moderate length control rod, a moderate length control rod, and a larger length control rod according to flow behavior. In force statistics, we calculated the values of CDmean, CDrms, CLrms, CDamp, CLamp, and St, respectively. The mean drag coefficient contains the smallest values at the largest length, i.e., l = 19 and 21d. The maximum value of CDmean is examined at the first cylinder (C1) as compared to the second cylinder (C2) at l = 2.25d, and it is 1.2789. The values of CDmean for C2 at the length of the control rod, l = 0.1d–1.25d, and at l = 21d are negative due to the effect of thrust. The value of the Strouhal number is the same for both cylinders C1 and C2, and its highest value is 0.1036. The pressure amplitude of the drag coefficient is maximum for C1, while the pressure amplitude of the lift coefficient is maximum for C2, and its value is 2.1569.

Validation of the stochastic inversion algorithm for acoustic travel-time tomography: a large eddy simulation study

Acoustic tomography (AT) is explored as a remote sensing technique to obtain instantaneous snapshots of temperature and velocity fluctuations for wind energy applications. This study integrates Large Eddy Simulation (LES) with the Stochastic Inversion (SI) method to validate the algorithm’s capacity for accurate reconstruction of atmospheric fluctuations. The initial findings demonstrate the efficacy of the method in accurately capturing the predominant flow structures. Normalized L2 error evaluations further inform the algorithm’s precision, with errors accentuated in less sampled peripheral regions. The results underscore the method’s promise as a non-intrusive observational tool, with ongoing development poised to improve its precision and reliability.

Effect of a fixed downstream cylinder on the flow-induced vibration of an elastically supported primary cylinder

This paper numerically investigates the influence of a fixed downstream control cylinder on the flow-induced vibration of an elastically supported primary cylinder. These two cylinders are situated in a tandem arrangement with small dimensionless center-to-center spacing (L/D, L is the intermediate spacing and D is the cylinder diameter). The present two-dimensional (2D) simulations are carried out in the low Reynolds number (Re) regime. The primary focus of this study is to reveal the underlying flow physics behind the transition from vortex-induced vibration to galloping in the response of the primary cylinder due to the presence of another fixed downstream cylinder. Two distinct flow field regimes, namely, steady flow and alternate attachment regimes, are observed for different L/D and Re values. Depending on the evolution of the near-field flow structures, four different wake patterns, “2S,” “2P,” “2C,” and “aperiodic,” are observed. The corresponding vibration response of the upstream cylinder is characterized as interference galloping and extended vortex-induced vibration. As the L/D ratio increases, the lift enhancement due to flow-induced vibration is seen to be weakened. The detailed correlation between the force generation and the near-wake interactions is investigated. The present findings will augment our understanding of vibration reduction or flow-induced energy harvesting of tandem cylindrical structures.

Estimating Uncertainties from Dual-Doppler Radar Measurements of Onshore Wind Plants Using LES

Towards the ongoing work of improving the capability of flow modeling within and around wind plants, an onshore model validation benchmark campaign is underway based on a field experiment involving multiple wind plants in Oklahoma, U.S.A. Dual-Doppler radar is being leveraged to provide flowfield information for the benchmarking owing to the unparalleled capability of such radar to capture minute-by-minute horizontal wind fields over a scale of tens of kilometers. However, dual-Doppler radar exhibits sampling artifacts that must be considered during model validation, and these are due to probe-volume averaging, coarse azimuthal/elevational resolution, non-ideal stereo angles, and coarse temporal sampling. Such sources of error in radar-reconstructed flowfields can be quantified using virtual radar sampling in the high-fidelity simulation environment (i.e., large-eddy simulation (LES)) where the true velocity field is known with confidence, and this is the uncertainty quantification approach adopted in this article. We leverage a virtual radar tool designed to replicate the specific sampling strategy of the X-band dual-Doppler instrument installed in the field campaign. This tool is featured in LES of an expansive 100 km by 100 km region of Oklahoma including hundreds of wind turbines modeled as actuator disks. In agreement with the sampling principles of radar, the results show that large-scale flow structures are qualitatively well-resolved by the instrument, though more simulation time and analysis are needed to determine the accuracy of the radar’s integral lengthscale estimates. At the turbine scale, the radar struggles to capture all of the features of the turbine wakes. The process of probe-volume averaging, as well as the subsequent interpolation to a Cartesian grid, biases the reconstruction of the peak near-wake deficit by an average of 2 m/s, or around 20% of the freestream velocity. Errors in this quantity of interest, as well as one characterizing the magnitude of the free-flow wind speed around the wakes, are found to be sensitive to the radar beam-crossing angle and beam range.

Fluid flow reconstruction around a free-swimming sperm in 3D.

We investigate the dynamics and hydrodynamics of a human spermatozoa swimming freely in 3D. We simultaneously track the sperm flagellum and the sperm head orientation in the laboratory frame of reference via high-speed high-resolution 4D (3D+t) microscopy, and extract the flagellar waveform relative to the body frame of reference, as seen from a frame of reference that translates and rotates with the sperm in 3D. Numerical fluid flow reconstructions of sperm motility are performed utilizing the experimental 3D waveforms, with excellent accordance between predicted and observed 3D sperm kinematics. The reconstruction accuracy is validated by directly comparing the three linear and three angular sperm velocities with experimental measurements. Our microhydrodynamic analysis reveals a novel fluid flow pattern, characterized by a pair of vortices that circulate in opposition to each other along the sperm cell. Finally, we show that the observed sperm counter-vortices are not unique to the experimental beat, and can be reproduced by idealised waveform models, thus suggesting a fundamental flow structure for free-swimming sperm propelled by a 3D beating flagellum.

Time-resolved tomographic particle image velocimetry of flow structures in non-circular orifice impinging jets

In this study, time-resolved tomographic particle image velocimetry (Tomo-PIV) was implemented on two different non-circular orifice impinging jets, i.e., elliptical and square orifices, and the circular one was employed as a reference for comparison, with the same equivalent diameter De=20 mm, impinging distance-to-diameter H/D = 3.0, and the Reynolds number (Re) at 1.6×103. A particular concern was placed on examining the coherent structure dynamics and turbulence dissipation of these impinging jets. The dominant Strouhal number (St) of all three jets has the component of 0.53, representing the large-scale Kelvin–Helmholtz (K–H) vortex ring, particularly for the square orifice, the dominant St is 0.70 at the central axis and 0.18 at the diagonal axis near the impinging surface. In free jet region, the streamwise velocity profile of the square orifice jet always maintains a rhombic development with a 45° difference relative to the outlet shape. In the impingement region, the circular orifice jet has the strongest K–H structure, with two opposite wall jets generated inside and outside, while in elliptical jet impinging, the upturned short axis of the vortex ring after axis-switching invariably contacts the impinging surface first, and then the wall jet vortex ring re-stretches to a circular shape due to the higher velocity of the wall jets generated from the upturned short axis, and the square orifice impinging jet contains no obvious wall K–H vortex rings but undergoes an irregular merging with the vortex ring downstream and stagnation. The time-averaged flow field statistics show that the circular orifice impinging jets have stronger wall jets, while the square orifice is the weakest, due to the strongest turbulent dissipation generated by the more fragmented flow upstream.

Study on the evolution stages of the flow field induced by an alternating current sliding discharge plasma actuator in different actuation modes

The present study investigates the discharge and flow characteristics of a sliding discharge (SD) driven by alternating current (AC) and negative direct current (DC) high voltage in continuous operation and burst-mode actuation in quiescent air. The burst frequency f is set at 20, 40, 50, and 100 Hz with a duty cycle τ fixed at 50%. Different actuation cases exhibit similar discharge morphologies and electrical properties. The results indicate that the flow induced by the horizontal body force generated by the SD undergoes the following stages: formation, intensification, accumulation, and stabilization. Based on the effects of the body force, the evolution of the induced flow field can be divided into three stages: the initial stage (starting-vortex stage), the transition stage, and the final stage. In continuous operation, the transition stage is marked by a complex flow structure, while the final stage is distinguished by a deflecting jet. When the burst frequency f ≤ 50 Hz, the duration of the transition stage increases with the burst frequency, and it becomes transient at f = 100 Hz due to the short voltage input time. Phase-averaged particle image velocimetry results indicate that the final stage of the burst-mode actuation can be categorized into three types mostly based on the interaction of the vortices from the AC and DC electrodes. Compared to the continuous operation, the application of the burst-mode actuation in this study has a shorter transition stage duration, resulting in a more rapid realization of flow control.

The maintenance of coherent vortex topology by Lagrangian chaos in drift-Rossby wave turbulence

This work introduces the “potential vorticity bucket brigade,” a mechanism for explaining the resilience of vortex structures in magnetically confined fusion plasmas and geophysical flows. Drawing parallels with zonal jet formation, we show how inhomogeneous patterns of mixing can reinforce, rather than destroy non-zonal flow structure. We accomplish this through an exact stochastic Lagrangian representation of vorticity transport, together with a near-integrability property, which relates coherent flow topology to fluid relabeling symmetries. We demonstrate these ideas in the context of gradient-driven magnetized plasma turbulence, though the tools we develop here are model-agnostic and applicable beyond the system studied here.

In-cylinder flow evolution in the horizontal plane of a motoring compression ignition engine

This study used the two-dimensional particle image velocimetry technique to quantify the in-cylinder horizontal plane velocity field evolution in a swirl-supported light-duty single-cylinder diesel engine. The data were acquired at a constant engine speed of 1600 revolutions per minute. For each case, the distance of the laser sheet from the fire deck was varied (z = 5, 10, and 20 mm) to investigate the axial variations in the flow field during the flow evolution in the compression stroke. A vortex identification algorithm was used to detect the swirl center and its deviation from the rigid body rotation. A Bessel fit was obtained using the experimental data. The result revealed that the in-cylinder flow was not axisymmetric. The swirl center approached the geometrical center as the piston approached the top dead center. The flow evolved at the farthest plane from the fire deck. The axial diffusion of angular momentum resulted in the formation of the swirl flow structure in the plane closer to the fire deck. Angular momentum analysis of a simplified geometry has been presented to explain the swirl amplification. The estimated results were compared with the experimental results to show the momentum stratification in the engine cylinder later in the compression stroke.

Eddy–Internal Wave Interactions: Stimulated Cascades in Cross-Scale Kinetic Energy and Enstrophy Fluxes

Abstract The interactions between oceanic mesoscale eddies, submesoscale currents, and internal gravity waves (IWs) are investigated in submesoscale-resolving realistic simulations in the North Atlantic Ocean. Using a novel analysis framework that couples the coarse-graining method in space with temporal filtering and a Helmholtz decomposition, we quantify the effects of the interactions on the cross-scale kinetic energy (KE) and enstrophy fluxes. By systematically comparing solutions with and without IW forcing, we show that externally forced IWs stimulate a reduction in the KE inverse cascade associated with mesoscale rotational motions and an enhancement in the KE forward cascade associated with divergent submesoscale currents, i.e., a “stimulated cascade” process. The corresponding IW effects on the enstrophy fluxes are seasonally dependent, with a stimulated reduction (enhancement) in the forward enstrophy cascade during summer (winter). Direct KE and enstrophy transfers from currents to IWs are also found, albeit with weaker magnitudes compared with the stimulated cascades. We further find that the forward KE and enstrophy fluxes associated with IW motions are almost entirely driven by the scattering of the waves by the rotational eddy field, rather than by wave–wave interactions. This process is investigated in detail in a companion manuscript. Finally, we demonstrate that the stimulated cascades are spatially localized in coherent structures. Specifically, the magnitude and direction of the bidirectional KE fluxes at submesoscales are highly correlated with, and inversely proportional to, divergence-dominated circulations, and the inverse KE fluxes at mesoscales are highly correlated with strain-dominated circulations. The predominantly forward enstrophy fluxes in both seasons are also correlated with strain-dominated flow structures.

Assessing the effect of turbine size on the coherent structures in the wake using DMD

The aim of this study is to evaluate and quantify the effect of the incoming flow on the coherent structures characterizing the wake of two NREL reference wind turbines with different dimensions: the NREL 5-MW and the NREL 15-MW. The Dynamic Mode Decomposition (DMD) approach has been used to detect dynamically-relevant flow structures. We employ the Sparsity-Promoting version of the DMD (SPDMD) algorithm for ranking the most relevant modes, in order to extract a limited subset of relevant flow features that optimally approximate the original data sequence. The dataset on which the SPDMD is based consists of ordered snapshots obtained by Large Eddy Simulations (LES), where the Actuator Line Method (ALM) simulates the rotor and the Immersed Boundary Method (IBM) models the tower and nacelle. To ensure a realistic comparison, the two turbines are subjected to two turbulent inflows with the same mean Atmospheric Boundary Layer (ABL) obtained through a precursor simulation. The results reveal significant differences in the dependence of the absolute value of the DMD amplitudes on the angular frequency for the two turbines. However, the coherent structures appear to have the same shape for the main modes, although the tip vortex structures have a higher dynamic relevance for the NREL 15-MW turbine. This is due to the larger length scales imposed by the rotor and the lower turbulence intensity at the taller rotor height.

Vortex-shedding and bistability in cylinder-flexible plate assembly in a channel

This study numerically investigates the fluid–structure interaction dynamics of a stationary circular cylinder with an attached flexible splitter plate in a confined fluid domain. We explore how variations in Reynolds number (Re), plate length, offset from the channel centerline, and blockage ratio influence the vortex-shedding and oscillatory behavior of the plates in laminar flow. Results indicate that at low Reynolds numbers (Re = 100), there are no vortex shedding or oscillations, while at higher Reynolds (Re = 200 to 300), the shorter plate exhibits first-mode oscillations and symmetry breaking, whereas the longer plate shows only transient second-mode oscillations at Re = 300 that diminish in amplitude, suggesting that increased plate length reduces vortex-induced forces. Dynamic Mode Decomposition (DMD) analysis confirms consistent primary flow structures across different Reynolds numbers, with initial modes encapsulating the majority of the system’s dynamics. In addition to determining the critical Re for vortex-shedding, vortex-induced oscillations and bistability, the study also examines the critical blockage ratios on the symmetry breaking phenomenon, and also shows that plate stability is influenced by domain asymmetry. These insights enhance understanding of the biomechanics of fish-like robots and inform the design and control of bioinspired flexible structures in fluid flows.