The paper presents a systematic investigation of vortex-induced vibrations (VIV) of a D-section prism at subcritical Reynolds numbers (Re) through direct numerical simulation. To this end, we first report the critical $\text{Re}$ values for flow over a stationary and an elastically supported D-section prism within the angle of attack $\alpha =0^{\circ }–{180}^{\circ }$. We then focus on the VIV response and vortex dynamics across eight recognized regimes, classified based on the vibration amplitude and frequency responses, at subcritical $\text{Re}$. Further, the physical mechanisms for the excitation and sustenance of the VIV response are imparted, using the force partitioning method that allows for load estimation by different generation origins. It is found that the VIV response of the D-section prism can be excited and sustained by the viscous and/or pressure lift coefficient in phase with the prism velocity. Finally, we check the critical $\text{Re}$ for the galloping onset and verify the absence of galloping in subcritical flow. The reasons behind the absence and occurrence of galloping are unraveled. It is found that galloping is excited and sustained by the motion-induced asymmetric pressure lift with a frequency identical to the dominant vibration frequency. The viscous lift is entirely low-frequency and motion-related but negative to galloping. The analysis of mode conditions indicates that galloping requires an unstable structural mode with a frequency close to the natural frequency of the prism and flow mode with the natural vortex shedding frequency. The flow mode should be sufficiently strong to guarantee galloping at infinite reduced velocity.

Understanding the dynamics of fluid transport and trapping within microscale cavities is important for a range of environmental, industrial, and research applications. Using PDMS microfluidic channels, we explore the displacement and retention of (wetting) oil by an invading flow of (nonwetting) water at low Reynolds number $(\mathrm{Re}\ll 1)$ in noncontiguous pores, and examine the influence of trapping velocity, viscosity ratio, and pore aspect ratio. We find that increasing capillary numbers lead to a greater amount of oil trapped per cavity. This is contrary to findings for interconnected porous media in which the availability of multiple pathways for fluid flow leads to more displacement with increased flow rates. This result can be attributed to a dynamic transition from a meniscus displacement to a viscous fingering displacement, by which the advancing water front shifts from a discrete triple contact line at channel walls to a continuous layer of oil enveloping the water. Data from all pore geometries can be collapsed onto a single trend by subtracting the amount of oil captured in the zero capillary number limit, indicating that increased oil retention at higher values of capillary number is not dependent on pore geometry. A model for steady-state, three-dimensional flow based on the long-wave approximation was developed to analyze the amount of fluid retained as a function of capillary number and viscosity ratio. Model predictions are qualitatively consistent with several experimental observations, including the shape of the interface of the trapped oil and the trend that increasing capillary number leads to greater oil trapping per pore. Our results highlight the need to quantitatively investigate the transient dynamics of fluid invasion in multiphase systems that exhibit localized entrapment.

Using statistical analysis and complex networks, we study the role of inverse Rossby deformation radius, $\lambda$, on freely decaying quasi-geostrophic turbulence dynamics. We find that the area fraction occupied by vortices remains constant over an extended duration for all values of $\lambda$. We establish an energy spectrum scaling based on a self-similar distribution of vortices of area $A$ during this period. Our findings suggest that the vortex number density follows the relationship $n\left(A\right)\sim N_v{A}^{-p}$, and the inertial range energy spectra scales as $k^{-7+2p}$, where $N_v$ represents the number of vortices and $p$ depends on $\lambda$. To investigate vortical interactions, we construct a spatiotemporal weighted network. Our analysis uncovers two distinct strength distributions: (1) a briefly observed scale-free distribution resulting from nonlocal interactions when $\lambda \ll k_0$, and (2) a truncated scale-free distribution due to local interactions over an extended period when $\lambda \gg k_0$, where $k_0$ denotes the initial characteristic wave number at which the total energy is at its maximum. Both networks are robust against random disturbances but are vulnerable to targeted attacks on their hubs. Additionally, we found that these network hubs contribute to the large-scale energy spectra, which can be reconstructed using only $1\%$ of the total degrees of freedom in a quasi-geostrophic turbulent field.

Rare but extreme dissipation events are dynamically important, but their numerical simulation represents a formidable computational challenge given the scale separation of high Reynolds number turbulence. Here, we explore the potential of a reduced dimensionality model, namely, the one-dimensional turbulence (ODT) approach, to represent the structure and evolution of forced homogeneous isotropic turbulence (HIT). We extend the classical ODT formulation to an Eulerian framework by solving the fully compressible equations (solved at low turbulent Mach numbers) including the modeling of all three velocity components. We computed temporally and spatially resolved simulations of forced HIT at Reynolds numbers up to ${\mathrm{Re}}_{\lambda }=5428$ and validated against theoretical and numerical published results. More specifically, we show that the developed compressible formulation of ODT can capture many of the quantitative characteristics of HIT such as the turbulent spectrum, the normalized dissipation rate, the skewness, energy flux, and intermittency, among others, although accompanied by strong compressible effects inherent in the turbulence forcing formulation of the model. The computational tractability of ODT enables a detailed study of the generation of extreme localized dissipation in turbulence. Conditional sampling reveals that occurrence of extreme events is positively correlated with a high frequency of eddies at a specific spatial location and within a short time window.

Large-scale circulation (LSC) quasistably emerges in the turbulent Rayleigh-Bénard convection, and intermittently reverses its rotational direction in two-dimensional turbulent convection. In this paper, direct numerical simulations of the intermittent reversals of the LSC in a two-dimensional square domain are performed, and the time series of the total angular momentum indicating the rotational direction of the LSC is predicted by reservoir computing whose input consists of the shear rates and temperatures at six locations on the sidewalls. The total angular momentum in the simulation after times shorter than half the typical duration of the quasistable states is successfully reproduced by the locally-measurable quantities on the sidewalls because the secondary rolls accompanied by the boundary flow characterize the reversal of the LSC. The successful prediction by such sparse input derived from local measurements on the sidewalls demonstrates that the reservoir computing prediction of the reversal is feasible in laboratory experiments and industrial applications. On the other hand, long-term prediction often provides the total angular momentum opposite in sign to the one in the simulations in the late parts of long quasistable states. The statistical independence of each reversal implies that the prediction after the reversal is difficult or even impossible, and the training data in the late parts in the long quasistable states, which rarely appear, is contaminated by the statistically-independent angular momentum in the subsequent quasistable states.

Plant leaves vibrate in response to raindrop impacts. When the resulting inertial forces are sufficient, residual rainwater at the leaf surface may be dislodged and ejected in the form of droplets. These droplets participate to the transport of pathogenic spores, including in the upward direction. The present experimental work aims at exploring the limits of this mechanism, in the simpler case of a single drop impacting an initially dry artificial leaf. The transfer of momentum from the impacting drop to the leaf is rationalized. The conditions of droplet ejection are identified, and these droplets are shown to inherit from the velocity of the leaf. Finally, these results are extrapolated to estimate the frequency of upward transport events as a function of rainfall intensity for a distribution of raindrop sizes.

Motivated by the need to improve fundamental understanding of multilayer coating on discrete objects, a model problem involving the flow of bilayer thin liquid films on rotating cylinders is considered here. The layers are assumed to be immiscible, and the lubrication approximation is applied to derive two coupled nonlinear evolution equations describing the heights of the two layers as a function of time and the angular coordinate. In the limit of rapidly rotating cylinders, gravitational effects are negligible, and linear stability analysis and nonlinear simulations demonstrate that a more viscous, thicker inner film or higher liquid-liquid interfacial tension suppresses instabilities driven by centrifugal forces for fixed properties of the outer layer. When gravitational effects are significant, a parametric study reveals that the critical rotation rate required to cause motion of liquid lobes that form due to gravitational drainage is lowered for a more viscous and thicker inner film due to an increase in viscous forces. These properties of the inner layer also lead to a reduction in the amplitude of temporal oscillations in the film thickness. In contrast, the stabilizing effects of liquid-liquid interfacial tension are negligible near the critical rotation rate due to the largely uniform curvature of the inner film. Results from the lubrication-theory-based model are complemented by finite-element simulations of the full two-dimensional equations, which reveal that the lubrication model works well for thicker films provided that gravitational effects are sufficiently small. In addition to advancing fundamental understanding, the results reported here suggest strategies for improving the uniformity of coatings on discrete objects.

We carry out linear stability analysis of both inertialess and inertial viscoelastic plane Couette flow using the Giesekus model augmented with stress diffusion. Recent work [Beneitez et al., Phys. Rev. Fluids 8, L101901 (2023)] has shown that plane Couette and Poiseuille flows of an Oldroyd-B fluid are linearly unstable if polymer stress diffusion is included. The unstable mode, termed “polymer diffusive instability” (PDI), however, has wavelengths of the order of the size of the polymer for realistic values of polymer diffusivity, thereby raising a question on the applicability of the Oldroyd-B model, which is valid on length scales large compared to the size of the polymer molecule. To address this issue, in the present study we examine the role of anisotropic mobility of the polymer molecule on the PDI within the framework of the Giesekus model. The stability is governed by the Weissenberg number $\text{Wi}=\lambda V/H$, Reynolds number $\text{Re}$ (or the elasticity number $E=\text{Wi}/\text{Re}$), the anisotropy parameter of the Giesekus model $\alpha$, and a dimensionless polymer diffusivity $\mathcal{D}=\lambda D/H^2$. Here $\lambda$ is the polymer relaxation time, $V$ is the plate velocity, and $H$ is the channel half-width. The conventional (nondiffusive) Giesekus model predicts plane Couette flow to be linearly stable when the constitutive curve is monotonic. For the diffusive Giesekus model, following earlier studies, we employ two different boundary conditions for the polymeric stress tensor: no-flux of the stress tensor and no-diffusion at the walls. Our numerical results reveal that in both the inertialess and inertial regimes, and for both boundary conditions, the PDI is rapidly stabilized as $\alpha$ is increased, resulting in an increase in the critical Weissenberg number (${\text{Wi}}_c$). This is also accompanied by a concomitant shrinking of the neutral curves in the $\text{Wi}\text{−}k$ plane ($k$ is the streamwise wave number), and an eventual disappearance of the unstable region beyond a threshold $\alpha$. The critical Weissenberg number diverges with increasing $\alpha$ for all $\mathcal{D}$'s considered. In the dilute limit, with the solvent-to-solution viscosity ratio $\beta \sim 0.9$, PDI stabilizes rapidly at negligibly small values of $\alpha$ ($\sim {10}^{-5}$). For concentrated polymer solutions ($\beta \sim 0.1$), the PDI is fully stabilized at a slightly higher $\alpha \sim {10}^{-3}$. The suppression of PDI due to anisotropy in the Giesekus model, even for extremely small $\alpha$'s, raises the question whether the PDI will be present when a more rigorous constitutive model (rooted in kinetic theory) is employed, one that accounts for anisotropic diffusion of polymer molecules at higher shear rates.

To study the feasibility of shear-stress-driven locomotion in the Reynolds number range of $O(10–{10}^2)$, we propose an aquatic swimming system characterized by an elongated barrel-shaped body with both ends open. The side wall of the body is enwraped within a flexible membrane, which circulates around the body similar to the tank treading motion of vesicles or erythrocytes (red blood cells). During the circulation, the membrane on the outer side of the barrel and the one on the inner side travel at opposite directions (one downstream and the other upstream), generating a net thrust force due to the inner-side versus outer-side asymmetry of the design. The performance of this system has been investigated numerically by using an immersed-boundary model. The results show that this device is able to achieve forward speeds that are comparable to the circulation speed of the membrane. Further study indicates that within the targeted Reynolds number range, when the membrane circulation speed is given the swimming speed is not sensitive to the Reynolds number, although it does depend on the diameter-to-length ratio of the body.

Incompressible fluids in microfluidic networks with nonrigid channels can exhibit flow rate oscillations analogous to electric current oscillations in RLC circuits. This is due to the elastic deformation of channel walls that can store and release fluid, as electric capacitors can store and release electric charges. This property is quantified through the compliance of the system, defined as the volume change relative to the pressure change. In systems with rigid walls and incompressible fluid, compliance vanishes, and no oscillations can occur through this mechanism. Here, we show that not only oscillations but also chaos can emerge in the flow-rate dynamics of noncompliant microfluidic networks with incompressible fluid. Notably, these dynamics emerge spontaneously, even under time-independent driving pressures. The underlying mechanism is governed by the effect of fluid inertia, which becomes relevant at moderate Reynolds numbers observed in microfluidic systems exhibiting complex flow patterns. The results are established using a combination of direct numerical simulations and a reduced model derived from modal analysis. This approach enables us to determine the onset of oscillations, the associated bifurcations, the oscillation frequencies and amplitudes, and their dependence on the driving pressures. These findings can inspire novel studies and applications of previously unexplored oscillatory and chaotic regimes in noncompliant microfluidic systems.

We introduce a toy model for shear flows, exploiting the spatial intermittency and the scale separation between large-scale flows and small-scale structures. The model is highly sparse, focusing exclusively on the most intense structures, which are represented by vortons—dynamically regularized quasisingularities that experience rapid distortion from the large-scale shear. The vortons, in turn, influence the large-scale flow through the subgrid stress tensor. Despite its simplicity, the model displays an interesting transition between two distinct regimes: (i) a laminar regime, where dissipation is entirely attributed to the large-scale flow and the vortons dynamics is essentially diffusive, and (ii) a turbulent regime, in which most of the dissipation arises from the vortons. These regimes correspond to different scalings of dissipation and the Grashof number as functions of the Reynolds number, with power-law relationships that resemble those observed in classical turbulence.

Recent studies based on simulations of the Boussinesq equations indicate that stratified turbulent flows can develop large-scale intermittency in the velocity and temperature fields, as detected in the atmosphere and oceans. In particular, emerging powerful vertical drafts were found to generate local turbulence, proving necessary for stratified flows to dissipate the energy as efficiently as homogeneous isotropic turbulent flows. The existence of regions characterized by enhanced turbulence and dissipation, as observed, for instance, in the ocean, requires appropriate tools to assess how energy is transferred across the scales and at the same time locally in the physical space. After refining a classical coarse-graining procedure, here we investigate the feedback of extreme vertical velocity drafts on energy transfer and exchanges in subdomains of simulations of stably stratified flows of geophysical interest. Our analysis shows that vertical drafts are indeed able to trigger upscale and downscale energy transfers, strengthening the coupling between kinetic and potential energies at certain scales, depending on the intensity of the local vertical velocity.

Experiments have demonstrated a nonlinear electrokinetic flow around a sharp charged dielectric corner in a microchannel. Since sharp corners are ubiquitous in microfluidic systems, this flow can play a significant role in manipulating liquids in microfluidic systems. In the past, induced-charge electro-osmosis (ICEO) was widely used to explain this observed flow. However, there are significantly qualitative differences between the experimental results and ICEO predictions. Here, we theoretically demonstrate that the concentration polarization-induced electro-osmosis (CPEO) caused by the double-layer polarization is the origin of the observed nonlinear electrokinetic flow around a charged dielectric corner because CPEO quantitatively captures both the frequency and salt-concentration dependences of the experimentally measured electrokinetic velocity. Our developed CPEO model can provide a theoretical guidance for the design of new flow control techniques for microfluidic systems.

We establish a number of results concerning conditions for minimum energy dissipation and advective travel time along path lines for potential flows in heterogeneous porous and fractured media, governed respectively by Darcy's law and the cubic law. First, we establish a pair of converse results concerning fluid motion along a streamline between two points of fixed head in porous media in arbitrary dimensions: the minimal advective time is achieved under conditions of constant energy dissipation, and minimal energy dissipation is achieved under conditions of constant velocity along the streamline (implying homogeneous conductivity in the vicinity of the streamline). We also show directly by means of variational methods that minimum advection time along a streamline in one dimension with a given average conductivity is achieved when the conductivity is constant. Next, we turn our attention to minimum advection time and energy dissipation in parallel and sequential fracture systems governed by the cubic law, for which fracture cross section and conductivity are intimately linked. We show that, as in porous domains, flow partitioning between different pathways always acts to minimize system energy dissipation. Finally, we consider minimum advection time as a function of aperture distribution in a sequence of fracture segments. We show that, for a fixed average aperture, a uniform-aperture system displays the shortest advection time. However, we also show that any sufficiently small perturbations in aperture away from uniformity always act to reduce advection time.

This study investigates the physical connection between turbulence statistics and the fragmentation cascade of droplets in incompressible nondecaying homogeneous isotropic turbulence. Using interface-resolved direct numerical simulation and based on the concept of vorticity transport across turbulent length scales, we analyze the spectral rate of enstrophy generation by two major production mechanisms: vortex stretching and surface tension. We demonstrate that these spectral rates always equate at a characteristic length scale, implying a balance between disruptive and resistant mechanisms in turbulent fragmentation. At this length scale, the droplet-laden energy cascade shows pivoting from its single-phase counterpart, and the size distribution of drops yields a drastic slope change, indicating where turbulent fragmentation stops. This observation holds for different Taylor-scale Reynolds numbers and provides a more deterministic interpretation of the largest stable droplet in turbulence, also known as the Kolmogorov-Hinze (K-H) scale. It is also observed that by increasing the surface tension coefficient, and consequently decreasing the Taylor-scale Weber number toward unity, the K-H scale is determined mainly by the spectral rate of surface tension contribution. The present study carries a direct implication for the size prediction of drop and/or bubble-laden turbulent flows.

In the present paper, we apply the framework of volume filtering, initially proposed by [T. B. Anderson and R. Jackson, Ind. Eng. Chem. Fundam. 6, 524 (1967)] for particle-laden flows, to large eddy simulations (LES) of wall-bounded flows leading to a new perspective on wall-modeled LES (WMLES) that we refer to as volume-filtered WMLES (VF-WMLES). In contrast to existing wall models, the VF-WMLES framework does not rely on temporal averaging, does not make a priori assumptions on the pressure gradient, and can be used with a uniform spatial filter, which avoids the appearance of commutation closures in spatial derivatives of the filtered momentum and continuity equation. Volume filtering is well defined, even close to the wall, and it is shown that a nonzero slip and penetration velocity at the wall is a direct consequence of volume filtering the flow. With the VF-WMLES concept, new wall models can be directly assessed in a priori and a posteriori studies by comparing the predicted slip and penetration velocities at the wall with the velocities from explicitly volume-filtered direct numerical simulations (DNS). Based on the VF-WMLES concept, we derive an LES modeling strategy that is based on the recently proposed physically consistent immersed boundary method [M. Hausmann et al., J. Comput. Phys. 519, 113448 (2024)], a modeling framework based on volume filtering allowing to couple the flow with arbitrarily shaped solid boundaries using relatively coarse Cartesian fluid meshes. The proposed VF-WMLES is validated with two cases, a turbulent channel flow and a turbulent flow over periodic hills, and we show it accurately predicts the wall-boundary conditions known from explicitly volume-filtered DNS.

The universality of small scales, a cornerstone of turbulence, has been nominally confirmed for low-order mean-field statistics, such as the energy spectrum. However, small scales exhibit strong intermittency, exemplified by formation of extreme events which deviate anomalously from a mean-field description. Here, we investigate the universality of small scales by analyzing extreme events of velocity gradients in different turbulent flows, viz., direct numerical simulations of homogeneous isotropic turbulence, inhomogeneous channel flow, and laboratory measurements in a von Kármán mixing tank. We demonstrate that the scaling exponents of velocity gradient moments, as function of Reynolds number ($\text{Re}$), are universal, in agreement with previous studies at lower $\text{Re}$, and further show that even proportionality constants are universal when considering one moment order as a function of another. Additionally, by comparing various unconditional and conditional statistics across different flows, we demonstrate that the structure of the velocity gradient tensor is also universal. Overall, our findings provide compelling evidence that even extreme events are universal, with profound implications for turbulence theory and modeling.

An immersed-boundary method-based incompressible flow solver was used to study the vertical diamond formation that occurs within fish schools and the resulting hydrodynamic performance enhancements and wake dynamics. The vertical spacing $H$ between the top and bottom fish within the diamond was varied to understand the impact of this spatial parameter on performance enhancements. At lower $H$ spacings, thrust enhancement and drag reduction were experienced by all four fish; these effects were maximized at $H$ = 0.27 body length. At this spacing, the follower obtains the largest benefits with a 15.5% drag reduction and 6.0% thrust increase compared to solitary swimming. The top and bottom fish extract a more than 6.0% thrust increase, while a less significant drag decrease is experienced. In contrast, the leader faces an increase in thrust and decrease in drag. Power consumption of the leader and follower are reduced as well; however, the top and bottom fish power consumption is increased by more than 6.0% in this formation. By examining the vortex dynamics, pressure distribution, and wake velocity patterns, mechanisms responsible for the performance enhancements in low $H$ vertical diamonds were identified. The leader benefits were obtained through body-body interactions with positive signed pressure ahead of the top and bottom fish. The top and bottom fish extracted anterior suction, and therefore drag reduction, from the leader's vortex rings. The caudal fins of the top and bottom fish generated strong leading-edge vortices (LEVs) in the interior of the diamond, therefore, enhancing thrust. These strengthened LEVs convected downstream forming coherent vortex legs within a complex pattern of vortex rings. The wake-body interaction between the top and bottom fish vortex rings and the follower fish (i) generated strong anterior suction pressure and (ii) produced a like-signed vortex ring and boundary layer vorticity interaction resulting in a reduction of drag. Finally, the follower's caudal fin extracted a wake-fin interaction and thrust increase from spanwise-compressed vortices generated by the top and bottom fish. A Reynolds number study confirmed enhancements in the lower $H$ diamond over a sparser diamond are obtained across a range of Re from 1000 to 8000. This study revealed the complex wake dynamics and body-body, wake-body, fin-fin, and wake-fin interactions that can be leveraged for performance benefits in vertical diamond fish schools. The findings provide insights into optimizing the configurations of fish-inspired robotic swarms for greater efficiency.

Hypersonic boundary layers exhibit diverse transition pathways, influenced by various flow conditions and environments. Nonmodal mechanisms, such as the lift-up effect, are recognized as pivotal contributors to transition, particularly over complex geometries like rough walls or blunt forebodies. The lift-up mechanism generates streaks that alter the baseflow, resulting in a modulated boundary-layer profile with stability properties significantly different from that of the original profile, such that new unstable modes may arise. In this numerical study we study the impact of streaks on a hypersonic boundary-layer at Mach 6 over an adiabatic wall. Streaks are introduced in the baseflow by optimal disturbances at the inlet of the computational domain. These baseflows serve as the foundation for investigating the linear dynamics supported by a streaky boundary layer evolving over an adiabatic flat plate at Mach number $M_{\infty }=6.0$. Our analysis involves linearized direct numerical simulations using white-noise forcing, and locally parallel stability analysis combined with dedicated postprocessing that we use to characterize the observed linear dynamics. The data processing involves an efficient SPOD extension based on Floquet theory in wave number space. The results reveal rich linear dynamics, quite different from the baseline case without streaks. Notably, low-frequency first-mode instabilities and streak-supported instabilities dominate the growth mechanisms. The results reveal and clarify a stabilization of the second Mack mode by streaks of low to medium amplitude; and a destabilization of the first mode. The study illustrates the rich linear dynamics that can arise due to the growth of streaks and how multiple paths are available for the transition to turbulence.

Suppression of $\mathrm{N}{\mathrm{O}}_{\mathrm{x}}$ and $\mathrm{C}{\mathrm{O}}_2$ emissions in gas turbines is an urgent challenge. While lean premixed combustion is a strategy for reducing $\mathrm{N}{\mathrm{O}}_{\mathrm{x}}$ production, the occurrence of thermoacoustic instability is a significant issue. In addition, while hydrogen is a promising fuel for replacing conventional hydrocarbon fuels and reducing $\mathrm{C}{\mathrm{O}}_2$ emissions, the unsteady flame-flow dynamics of hydrogen flames under thermoacoustic instabilities remain to be elucidated. Recently, low-swirl combustors have attracted attention since they can stabilize flames with a wide range of fuel compositions including pure hydrogen-air flames. In particular, the characteristics of hydrogen flames are expected to be significantly influenced by its Lewis number Le, where it is $\text{Le}<1$ for hydrogen-air flames in contrast to $\text{Le}\approx 1$ for methane-air flames. Therefore, this study experimentally analyzes the Lewis number effect in hydrogen and methane flames during thermoacoustic instability and discuss its influence on the local flame-flow interaction. The flames were stabilized in a low-swirl combustor with a geometric swirl number of 0.39. Pressure fluctuation measurements, OH* chemiluminescence imaging, and particle imaging velocimetry were performed simultaneously. It was found that the pressure fluctuation amplitude was nearly three times larger in the hydrogen flame than in the methane flame. To discuss the Lewis number effect, the instantaneous flame stretch rate and the chemiluminescence intensity were calculated at the local flame tip along the center axis. This analysis revealed that in the hydrogen flame ($\text{Le}<1$), the flame stretch rate fluctuation strongly correlated with the chemiluminescence intensity fluctuation, while the correlation between those in the methane flame ($\text{Le}\approx 1$) was found to be weaker. Therefore, it was concluded that, in the hydrogen flame, the Lewis number effect is responsible for the coupling between the heat release rate fluctuation and the flow fluctuation at the local flame tip during thermoacoustic instability.