The dynamics of a liquid drop impact on a liquid surface is studied experimentally. The drop diameter, the impact velocity, and the depth of the target liquid in the reservoir are parameters that are varied. The crown and the jet characteristics are mostly affected by the water depth and the size of the first secondary drop. The number of secondary drops strongly depends on the Weber number and the jet characteristics. The interplay between the inertia forces and surface tension forces during the expansion and contraction of the cavity determines the shape of the cavity. In shallow water, the cavity expansion and retraction is dominated by the surface tension forces, but in deep water the inertia forces and the gravity forces dominate the cavity dynamics. The crown evolution and the cavity evolution are almost simultaneous in deep water, but in the case of shallow water, it is not the same due to the hindrance caused by the reservoir bottom on the cavity retraction. Physical insights of the energy models for a drop impact on the deep pool are provided. These models incorporate the effects of surface tension, Bond number, and drop oscillations. The effects of the Weber number and the Froude number on the jet characteristics are found to be distinct on shallow and deep water. It is found that the jet velocity, Weber number, and water depth can form the boundary limits for the prediction of number of secondary drops. The expansion of cavity resembles a source of the potential flow below the surface of the liquid. Time resolved particle image velocimetry measurements enable estimates of time variation of the source strength. The source strength or the maximum discharge flow rate is found to be directly proportional to the momentum of the impacting drop and is negligible for low Froude numbers.

The present work investigates the fluid-structure interaction of a flexible cylindrical cantilever in a tandem configuration. A fully coupled fluid-structure solver based on the three-dimensional incompressible Navier-Stokes equations and Euler-Bernoulli beam equation is employed to numerically examine the coupled dynamics of the cantilever. We assess the extent to which such a flexible cylindrical structure could sustain oscillations in both subcritical and postcritical regimes of a Reynolds number ($\text{Re}$). Spatiotemporal power transfer patterns, response amplitudes, and vorticity dynamics are quantified and compared between isolated and tandem configurations. The results of our analysis indicate that the cantilever in tandem configuration is prone to sustained oscillations dependent on the Reynolds number and the reduced velocity parameter ($U^{*}$). In the subcritical $\text{Re}$ regime, the cantilever exhibits sustained oscillations with peak transverse oscillation amplitudes occurring within a specific range of $U^{*}$. Within this range, the transverse oscillations demonstrate lock-in behavior and synchronization with the vortex-shedding frequency. The vorticity dynamics in the subcritical $\text{Re}$ regime reveal that in the tandem configuration, the presence of the upstream cylinder significantly modifies the wake structure, delaying vortex formation and extending the near-wake region. In the postcritical regime of $\text{Re}$, the cantilever shows a wider range of sustained oscillations in terms of $U^{*}$, with single- and multifrequency response dynamics driven by vortex-body interactions. Power transfer analysis shows cyclic energy exchange patterns between the fluid and flexible structure, with significant variations in the hydrodynamic loading along the length of the cantilever. The findings of this work aim to broaden the understanding of sustained oscillations in flexible cantilevers and provide physical insights into the design of artificial cantilever flow sensors.

This work presents a feature-consistent field inversion and machine learning framework to enhance the capability of the Reynolds-averaged Navier-Stokes (RANS) turbulence model in predicting complex flows with separations. It effectively assimilates direct numerical simulation solutions and sparse experimental data, including velocity profiles, pressure distribution, and aerodynamic forces, into the improved k-ω shear stress transport (SST) closure model using the regularized ensemble Kalman inversion method. An artificial neural network (ANN) model is built to reconstruct the destruction term by considering local flow features. A modified analytical scheme with a prior mean-based regularization constraint is used to facilitate the model's exploration of the most influential regions for correction. The training process of the ANN model not only integrates the solution of the RANS equations but also minimizes the loss function by considering multiple flow conditions simultaneously so that feature inconsistency is avoided, resulting in a more effective model that delivers more accurate RANS results. Typical turbulent flow problems are simulated to validate the proposed method, including the separation flows over slopes and steps with low Reynolds numbers and the separation flows over airfoils with high Reynolds numbers. It is demonstrated that the proposed framework is capable of training a robust and consistent ANN-improved k-ω SST turbulence model for predicting turbulent flows with separations at both low and high Reynolds numbers. It also shows that the present ANN-improved k-ω SST turbulence model achieves generalization for separated flows with unforeseen geometries and Reynolds numbers.

This Letter presents nontrivial stochastic identities for random isotropic second-rank tensor fields. They can be considered as markers of statistical isotropy in turbulent flows of any nature. The case of axial symmetry is also considered. We confirm the validity of the identities using different direct numerical simulations of turbulent flows.

We revisit the mesoscopic hydrodynamic description of the dynamics of sessile partially wetting compound drops, i.e., of drops that consist of two immiscible nonvolatile partially wetting liquids and are situated on a smooth rigid solid substrate. We briefly discuss and complete existing dynamic models employing a gradient dynamics approach. Thereby, the underlying energy features capillarity and wettability contributions for all relevant interfaces in full-curvature formulation. Establishing transparent consistency relations between macroscopic and mesoscopic parameters, we obtain mesoscopic Neumann and Young laws that are also fully consistent with the macroscopic ones. In particular, we discuss the minimal requirements for the wetting energy that ensure the full spectrum of macroscopic parameters for partially wetting cases is addressed by the mesoscopic model. Subsequently, we distinguish long-wave and full-curvature variants of the dynamical model based on properties of the energy, and employ the latter to illustrate the usage of the mesoscopic model. As examples, we chose the spreading of individual compound drops on one-dimensional horizontal substrates, sliding compound drops on one-dimensional inclined substrates, and the coarsening of drop ensembles on one- and two-dimensional horizontal substrates. In each case, the discussion emphasizes occurring qualitative changes in the drop configurations.

We study the three-dimensional shear layer response of an overexpanded rectangular jet to small-perturbation-based control and associated impact on its noise field using linear analysis and implicit large-eddy simulations (ILES). Using the most receptive frequency, the rectangular shear layer is forced to excite specific circumferential vortical structures by gradually increasing the phase difference between consecutive actuators, thereby augmenting the three-dimensional characteristics of the shear layer. Upon adopting this active control strategy, the jet exhibits increased shear-layer spreading rate, shortened potential core, and smaller shock-expansion cells. While downstream noise reduction is achieved, the resulting tonal response of the overexpanded jet is higher than a perfectly expanded jet particularly in the upstream direction, due to additional shock-vortex interactions. Turbulent and acoustic signatures reveal that forcing at the third azimuthal mode of the corresponding circular jet, termed M3, has the most desirable noise impact, consistent with prior experimental observations. As identified from linear global modes and ILES, M3 forcing minimizes the tonal response of actuation, while concurrently reducing the radiative efficiency of the jet by attenuating acoustic energy in the supersonic phase-speed regime, and turbulent kinetic energy levels in the shear layer. Further, M3 forcing weakens the coherent-structure/shock interactions and curtails upstream propagating guided acoustic modes and plume flapping, thus effectively mitigating shock-associated noise and screech, respectively. The study highlights the control authority of small-perturbation actuation on the hydrodynamic and acoustic components of shocked jets, while incurring a relatively small thrust penalty of approximately one percent.

In turbulent flows, the fluid element gets deformed by chaotic motion due to the formation of sharp velocity gradients. A direct connection between the element of fluid stresses and the energy balance still remains elusive. In this Letter, an exact identity of incompressible turbulence is derived linking the velocity gradient norm across the scales with the mean kinetic energy. In the context of three-dimensional (3D) homogeneous turbulence, this relation can be specialized obtaining the expression of the mean kinetic energy decomposed either in terms of deformations due to strain motion or via the vorticity norm of the fluid element. Applied to data from direct numerical simulations (DNS) describing homogeneous and isotropic turbulence, the decomposition reveals that, beyond the scales dominated by the external forcing, extensional and contractile deformations account approximately for $40\%$ and $55\%$ of the kinetic energy of the associated scale while less than the remaining $5\%$ is carried by the indefinite-type stresses. From these two identities, one can derive an exact expression for the kinetic energy spectrum which is based solely on real space quantities providing a characterization of the Kolmogorov constant as well. Numerical evidences show that this formulation of the energy spectrum is consistent with the Kolmogorov power-law spectral scaling.

Fluid-rock reactions are of great interest in many engineered geological storage and disposal systems where the long term integrity of the system is key, and where fluid seepage through a permeable rock may lead to reaction and convective transport of material through the formation. If an unsaturated fluid displaces formation fluid in equilibrium with a reactive porous medium, a reaction front develops, across which the invading fluid becomes saturated with the soluble matrix material. Depending on the composition of the invading fluid, it may initially be less dense than the formation fluid, but following reaction it may become denser than the formation fluid. If the invading fluid displaces the formation fluid downwards through the porous layer, the reaction front may then be stabilized by buoyancy, but a Rayleigh-Taylor type instability can develop at the interface between the reacted fluid and the original formation fluid ahead of the reaction front. We present a series of new analog experiments of this process by injecting aqueous sugar solutions into a porous layer containing saturated salt solution, salt powder, and glass ballotini. As an analog of a reaction front, a dissolution front develops as the aqueous sugar solution dissolves the salt powder and becomes denser than the saturated salt solution. The buoyancy instability then leads to a growing finger interface. If the buoyancy speed of the fluid, $u_B$, is smaller than $u_F-u_R$, where the speed of the advancing fluid-fluid front is $u_F$ and the speed of the dissolution front is $u_R$ then the instability grows as if the system were unconfined. However, if $u_B>u_F-u_R$, then the supply of fluid at the dissolution front limits the growth of the instability. We present an idealised model for the speed of the non-linear buoyancy-driven fingers, and we consider the implications of our results for the long term integrity of a number of geological storage systems.

We investigate the flow of quasi-2D liquid foams, composed of a single monolayer of bubbles in close contact and confined between two glass plates in a Hele-Shaw cell, with a specific emphasis on understanding how bubble shapes evolve in response to varying flow speeds. Utilizing an experimental setup capable of displacing a substantial number of bubbles in the spanwise direction, while the bubble shapes remain stationary as the bubbles themselves are advected in a plug flow, we reveal an average bubble anisotropy characterized by elongated bubbles in the streamwise direction and curved bubble edges in a preferential orientation. Notably, these effects intensify with increasing flow speeds. While the bubble anisotropy is created at the entrance of the cell, our study establishes a clear connection between bubble edge curvature and orientation, confinement thickness, frictional forces with the plates, and the inherent anisotropy of the bubbles. We introduce a model that not only aligns with these observations but also demonstrates quantitative agreement with experimental data.

The coupling between mass transfer and hydrodynamic phenomena in two-phase flow is not straightforward due to the different effects that can be encountered. Its description is complex and requires particular efforts, especially in the modeling of the interface between phases. Here, we consider the case of a two-component droplet (one miscible and one immiscible in water) released in a 2D rectangular domain filled with water. Mass transfer occurs between the miscible element and the surrounding water, which leads to a density inversion that directly affects the droplet trajectory through buoyancy. We perform simulations using a ternary Cahn-Hilliard model to capture such coupled phenomena. The Boussinesq approximation for a multicomponent system is used to define the density law and an analytical chemical potential is proposed for the thermodynamic landscape. The effect of the mobility parameter on the flow is highlighted, the solutal Marangoni effect is discussed, and the results are found in good agreement with the dynamics described from an experimental study of the literature.

It is known that in an unbounded fluid, the inline configuration of a freely rising bubble pair is often unstable with respect to lateral disturbances. This work numerically examines the stability of this configuration in the presence of a nearby vertical wall. The focus is on moderately inertial regimes, where two bubbles rising initially in line typically separate laterally from each other under unbounded conditions. In the presence of the wall, our results indicate that while the path of the bubble pair predominantly separates laterally, the plane of separation largely depends on the wall-bubble interaction. This interaction involves a competition between two distinct effects, with the dominance determined by the ratios of buoyancy-to-viscous and buoyancy-to-capillary forces, which define the Galilei $\left(\text{Ga}\right)$ and Bond $\left(\text{Bo}\right)$ numbers, respectively. When $\text{Bo}$ is below a critical $\text{Ga}$-dependent threshold, irrotational effects dominate, initially stabilizing both bubbles near the wall until horizontal separation among them occurs in the wall-parallel plane. Conversely, at higher $\text{Bo}$, vortical effects dominate such that both bubbles migrate away from the wall. During the departure, asymmetric interactions cause the wall-normal velocities of the two bubbles to differ, leading to horizontal separation in the wall-normal plane. These two separation motions, both newly identified in the present study, are found to result from two distinct mechanisms: one associated with the shear flow generated in the gap separating the wall and the leading bubble, which attracts the trailing bubble toward the wall, and the other linked to vortex shedding from the leading bubble, which promotes the trailing bubble's faster escape from the wall. A slight angular deviation favors separation in the wall-parallel plane, promoting the formation of a near-wall, bubble-rich layer as observed in prior investigations of buoyancy-driven, bubble-laden flows.

The “fluid-mechanical sewing machine” creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the reported patterns are translated coiling, alternating loops, W pattern, and meander. A simplified theoretical model based on the geometry and local bending of the contact point can predict these patterns. We experimentally explore the patterns in this region by collecting data to compare with the model. Our review of the model's bifurcation diagram reveals additional patterns beyond the ones reported, although current experiments have not shown their existence. The W pattern, previously omitted in regime diagrams because of its small region, is now shown explicitly. We report on the consistent appearance of a period-doubled version of the W pattern, as well as rare appearances of resonant patterns. Comparing the theoretical model to experimental data, we find that the predicted phase diagram and the meander variation deviate from observations. These deviations hint at an unaccounted dynamics that merits further study.

This paper presents a comprehensive framework for addressing the challenges associated with turbulence linear forcing in incompressible two-phase flows. By examining existing literature on linear forcing techniques for single-phase flows, which typically yield constant turbulent production, kinetic energy, or dissipation rates, we derive a general method based on constant energetics. This method ensures that any constant power of kinetic energy multiplied by any constant power of dissipation rate remains unchanged over time. A linear stability analysis of this forcing method is performed, demonstrating its relevance and suitability in practical scenarios. Then, we investigate the linear forcing of turbulence in two-phase flows. Removing the mean contribution of the capillary forces prevents the exponential growth of kinetic energy reported in previous works. The paper also explores the impact of capillary forces on the energetics budgets and their implications for turbulent forcing. While the capillary power does not contribute significantly to the budget of kinetic energy, the capillary-related term prevails in the budget of dissipation rate. Including this term in the constant-energetics forcing method improves the control of the dissipation rate in the simulations. A further improvement is proposed by removing discretization errors in the computation of the energetics budgets, which provides a perfect control of the turbulent quantities. Turbulent modulation of the energy spectrum is also discussed showing that the proposed linear forcing method allows us to recover the expected modulation of the dispersed phase on the turbulent cascade. Indeed, the energy spectra compare well with previous works on turbulent emulsions, bubbly flows, and droplet/particle-laden flows.

We investigate the transition from pure Couette flow to Poiseuille flow at $\text{Re}\approx 2250$ with a focus on the observed disappearance of single-circle coherent structures occupying the whole channel height. According to the DNS study by Gandía-Barberá et al. [Phys. Fluids 30, 041702 (2018)], these are accompanied by a change of sign in the Reynolds stress tensor at sufficiently large pressure gradients, although from a deeper theoretical point of view the actual mechanisms for the disappearance of these structures remained completely uncovered. In order to investigate the behavior of these structures theoretically, we use resolvent and structured singular value analysis, with the aforementioned DNS serving as a data basis for comparison, hence simultaneously exploring the capabilities of resolvent and structured singular value analysis in capturing the characteristics of these structures. Through detailed parameter studies, we examine how the pressure gradient influences the length and width of streamwise elongated rolls, noting a shortening and narrowing effect as the flow becomes increasingly pressure driven, and compare these effects to the ones observed in the DNS work. Additional insights into the development of coherent structures are gained, as their wall-normal positions are successfully linked to the occurrence of critical layers within the flow, particularly through structured singular value analysis. The results show that the modified response modes from structured singular value analysis show the best agreement with the DNS observations, suggesting that these analytical approaches can effectively replicate the phenomena otherwise obtained only through costly DNS, and provide deeper insights into the underlying fluid dynamics.

The time-averaged and spectral characteristics of the scalar dissipation rate and a related turbulent burning velocity of premixed flames are investigated experimentally. The Karlovitz and turbulent Reynolds numbers are varied from about 0.1 to 34.5 and 62 to 1115, respectively. The hot-wire anemometry is performed to characterize the background turbulence. The Rayleigh scattering measurement is carried out to obtain the instantaneous two-dimensional temperature field, which is used to estimate the scalar dissipation rate and a related turbulent burning velocity. It is observed that, for lengthscales smaller than a few times the laminar flame thickness (yet larger than the resolving limit of the measurements), the power spectral densities of the scalar dissipation rate and the corresponding burning velocity collapse and decay following power-law relations. The slope of the decay is nearly independent of the background turbulence but depends on the examined fuel mixture. For lengthscales larger than a few times the laminar flame thickness, increasing the background turbulent Reynolds number generally increases the power spectral density of the scalar dissipation rate and the related turbulent burning velocity. This experimental study quantifies the role of intermediate- and large-scale turbulence in how fast premixed flames burn. The results suggest that quantifying the impact of large eddies on the turbulent burning velocity using merely the integral lengthscale may not be sufficient, and a range of lengthscales larger than two to four times the laminar flame thickness should be considered for studying such impact.

We investigate the intricate dynamics arising from the vibrations of a thin sheet in a compressible fluid medium. The system comprises a closed chamber that is filled with an ideal gas and is divided into two parts by a thin sheet. We develop an analytical model that combines the elasticity of thin sheets with the hydrodynamics of compressible fluids to analyze how the sheet's material properties and compression affect the system's lowest mode of vibration. We employ a linear stability analysis around three distinct solutions of the static equations and show that the lowest mode consists of either a vortexlike patterned flow that is localized around the area of the sheet or an extended, oscillating net flow. While these eigenmodes are influenced mainly by the ratio between the thermal energy of the fluid and the bending rigidity of the sheet, the frequency of the vibrations also depends on the mass ratio between the sheet and the fluid. Notably, our findings can provide guidelines for the design of technological applications that require precise control over elastohydrodynamic interactions.

Motivated by the aim of understanding the effect of media heterogeneity on the swimming dynamics of flagellated bacteria, we study the rotation and swimming of rigid helices in dilute suspensions experimentally and theoretically. We first measure the torque experienced by, and thrust force generated by, helices rotating without translating in suspensions of neutrally buoyant particles with varying concentrations and sizes. Using the ratio of thrust to drag forces ${\xi }_{F\mathrm{\Gamma }}$ as an empirical proxy for propulsion efficiency, our experiments indicate that ${\xi }_{F\mathrm{\Gamma }}$ increases with the concentration of particles in the fluid, with the enhancement depending strongly on the geometric parameters of the helix. To rationalize these experimental results, we then develop a dilute theoretical approach that accounts for the additional hydrodynamic stress generated by freely suspended spheres around the helical tail. We predict similar enhancements in the drag coefficient ratio and propulsion at a given angular speed in a suspension and study its dependence on the helix geometry and the spatial distribution of the suspended spheres. These results are further reinforced by experiments on freely swimming artificial swimmers, which propel faster in dilute suspensions, with speed increases over $60\%$ for optimal geometries. Our findings quantify how biological swimmers might benefit from the presence of suspended particles, and could inform the design of artificial self-propelled devices for biomedical applications.

This paper presents an analytical exploration of the two-dimensional concentration distribution of a solute under the influence of first-order bulk and wall chemical reactions in a viscous, couple stress fluid flowing between two parallel plates. The analytical expressions for mean and transverse concentration distributions up to third order are derived using Mei and Vernescu's multiscale homogenization technique. This paper meticulously investigates the impact of a couple stress parameter $\left(\alpha \right)$ and the chemical reaction parameters on Taylor dispersion through a reactive solute's dispersion coefficient, mean, and transverse concentration distributions. Results reveal that the effect of couple stress is most significant for smaller values of $\alpha$ (i.e., $20>\alpha \ge 1$), in which the dispersion increases and the tracer particle's mean concentration decreases. As $\alpha$ increases, there is a decreasing trend in dispersion, and for a large value of $\alpha$ a subtle decrease in dispersion is observed, which implies that the increment in viscosity impacts the dispersion coefficient. However, the negligible effect of couple stress $(\alpha \gg 20)$ results in a subtle increase in the mean concentration distribution. Increasing the value of the bulk chemical reaction parameter uniformly decreases the transverse concentration more effectively for smaller values of $\alpha$. Both couple stress and wall reactions significantly impact the concentration variation by inducing nonuniformity. Interestingly, at the center of the channel cross section, the bulk chemical reaction is more efficient in decreasing the transverse concentration profile when compared to wall chemical reactions, especially for smaller values of $\alpha$ where the couple stress is notably high. The results are effective as they are pivotal in advancing the design and performance of microfluidic devices, enhancing the separation of fluids and components, and improving fluid mixing efficiency.