In low-Reynolds-number flows, time reversibility makes it impossible for rigid particles to self-propel using reciprocal motions. When passive particles are freely suspended in a background flow that sinusoidally oscillates and is on average stationary, rigid particles are likewise stationary on average. However, as we demonstrate, an elastic particle in such a flow may experience net translation over each period of the flow oscillation. In this paper we analytically and numerically explore the dynamics of particles in steady and oscillatory shear flows. In particular, we study hinges, which we define as a particle consisting of two slender rigid rods joined at one of their ends at a hinge point. We focus on two classes of hinges: rigid hinges, where the two arms of the hinge are fixed relative to each other, and elastic hinges, where the two arms are allowed to rotate relative to each other with a restoring torque provided by a linear torsional spring. Hinges serve as qualitative analogs for curved fibers, which are an important class of particles in many biological and industrial flow applications. We first analyze the motion of elastic hinges in flow-free environments, providing an asymptotic theory to explain the emergence of symmetry breaking in the net translation between a hinge that is initially open versus one that is initially closed. We next turn to studying hinges in flows. In steady shear, both rigid and elastic hinges undergo periodic motions similar to Jeffery orbits with no steady cross-streamline motion. When the hinges are placed in a shear flow whose shear rate oscillates with time, the rigid hinge undergoes no net motion while an elastic hinge's motion is characterized by attracting cycles in the phase space, which undergo bifurcations as the geometric and flow parameters vary. These cycles lead to nonreciprocal translational motions of the hinge, related to the symmetry-breaking motion presented in the flow-free case, which vary in both magnitude and direction as a function of the controlling parameters. This raises the possibility of designing hinges with particular geometric parameters and then tuning the macroscopic flow properties to control and manipulate the particles while also aiding in particle separation, or, conversely, mixing.

We study a wave wake produced by a finite-size source uniformly moving on an ice plate overlying deep water. We describe the kinematic characteristics of source-generated flexural-gravity waves in terms of isophase patterns scaled by the minimum phase speed and show that the wave picture is determined by ad hoc defined Mach and Bond numbers. Then, we show that several bifurcations occur in the wave wake when the source speed increases. In particular, cusps appear in the wake patterns at certain speeds due to the merging at specific points of two or three wave characteristics (wave rays) which correspond to longitudinal (divergent), transverse, and fan waves. To describe the distribution of wave amplitudes in the wake accounting for the source size and shape, we use the reference solution approach. This approach agrees with the stationary phase method in the far-field zone and reproduces also specific wave dynamics at short and intermediate distances from the source. The effect of a source shape on the wave wake pattern is graphically illustrated for the elliptic source as the dependence on the dimensionless Bond number and the source length-to-beam ratio. The illustrations of the source speed and shape effects are given for low-speed regimes when wave patterns are conformed by single-ray solutions. Ways of the generalization of the suggested approach are outlined.

Data from fluid flow measurements are typically sparse, noisy, and heterogeneous, often from mixed pressure and velocity measurements, resulting in incomplete datasets. In this paper, we develop a physics-constrained convolutional neural network, which is a deterministic tool, to reconstruct the full flow field from incomplete data. We explore three loss functions, two of which are from machine learning literature and one designed by us: (i) the softly constrained loss, which allows the prediction to take any value; (ii) the snapshot-enforced loss, which constrains the prediction at the sensor locations; and (iii) the mean-enforced loss, which constrains the mean of the prediction at the sensor locations. The proposed methods do not require the full flow field during training, making it suitable for reconstruction from incomplete data. We apply the method to reconstruct a laminar wake of a bluff body and a turbulent Kolmogorov flow. First, we assume that measurements are not noisy and reconstruct both the laminar wake and the Kolmogorov flow from sensors located at fewer than 1% of all grid points. The snapshot-enforced loss reduces the reconstruction error of the Kolmogorov flow by $\sim 25\%$ compared to the softly constrained loss. Second, we assume that measurements are noisy and propose the mean-enforced loss to reconstruct the laminar wake and the Kolmogorov flow at three different signal-to-noise ratios. We find that, across the ratios tested, the loss functions with harder constraints are more robust to both the random initialization of the networks and the noise levels in the measurements. At high noise levels, the mean-enforced loss can recover the instantaneous snapshots accurately, making it the suitable choice when reconstructing flows from data corrupted with an unknown amount of noise. The proposed method opens opportunities for physical flow reconstruction from sparse, noisy data.

A low-friction-Reynolds-number (${\mathrm{Re}}_{\tau }\approx 400–480$) turbulent boundary layer perturbed by additional streamwise vortices is investigated using wall-resolved large-eddy simulation. To better understand how one might passively mimic and/or manipulate the formation of streamwise vortex pairs (SVPs) that naturally occur as part of the near-wall cycle, SVPs are artificially produced by small vortex generators (of height $h^{+}=30$) within the near-wall region. Thus, the present study contrasts the more typical large vortex generators used in turbulent boundary layer manipulation and separation control. Analyses employing a triple decomposition of velocity and pressure and its extension to the incompressible Navier-Stokes equation is used to better understand the coherent and turbulence fields associated with the synthetic and naturally occurring SVPs. Overall, it is observed that the near-wall synthetic and natural streamwise vortices have similar interactions with the surrounding turbulent field, and exhibit similarities in statistical structure. In particular, it is found that the synthetic SVPs exhibit a remarkably similar signature of kinetic energy transport with their natural counterparts. Through the comparisons with the ensemble-averaged natural SVPs, it is found that the natural and synthetic SVPs are identified to own similar spatial scales and evolution characteristics such that when they are inner scaled they exhibit similar magnitudes at comparable streamwise stations. This indicates that the wall response to SVPs may in fact constitute a generic mechanism underlying turbulent transport near the wall. These similarities suggest that embedded small synthetic streamwise vortices are self-contained in the near-wall region and directly interact with the structures in this area to influence the associated turbulent transport.

V-notched round jets at a Reynolds number of 2200 were subjected to strong forcing and were experimentally investigated at forcing frequencies corresponding to Strouhal numbers of 0, 0.25, 0.5, 0.75, and 1. Time-resolved particle image velocimetry results are presented, and the fundamental differences in the near-field vortex dynamics of the jet flow at the peak and trough planes of the V-notched nozzles are discussed. The flow phenomena, side jets, are of particular interest as they drastically increase the jet spread rate and mixing, and were observed to form in different nozzle planes depending on the forcing frequency. Forcing at the lowest frequency resulted in strong amplification of mechanical disturbances for the V-notched jets. This led to the suppression of the breakdown of the primary vortex ring and the formation of large-scale, symmetrical coherent flow structures near the jet centerline. Additional smaller-scale flow structures and side jets are also observed along the nozzle peak plane leading to significant enhancements of the jet spread rate. Flow bifurcation and forking of the vorticity branches were attributed to the formation of streamwise vortices that formed because of the heightened azimuthal instabilities incurred by the primary vortex ring. As the forcing frequency increases, the flow structures are observed to be increasingly destabilized with reductions in their length scales. Flow bifurcation in the peak plane would cease to exist and side jets appear along the trough planes instead. The formation of these side jets results from the jet fluid seeking to achieve pressure equilibrium with the ambient fluid due to the significant perturbations induced by the strong forcing. Based on the two V-notched aspect ratio nozzles studied, the sharper V-notched nozzle is more destabilizing to the primary vortex ring, which led to earlier breakdown of large-scale coherent structures.

Over the past four decades, significant advances have been made in the noninvasive imaging of intracardiac blood flow, primarily through the development of echocardiography (echo) and cardiac magnetic resonance (CMR) imaging. These technologies have helped expand our understanding of the complex fluid dynamics within the heart's chambers, offering new insights into cardiac function in healthy and diseased states. However, despite these advancements, much of the knowledge gained has yet to be fully translated into clinical practice. This manuscript explores the critical role of fluid mechanics in intracardiac flow analysis, emphasizing the contributions of in vitro experiments and in vivo imaging in measuring and visualizing blood flow. Key hydrodynamic parameters such as vorticity, pressure, and kinetic energy are discussed, highlighting their relevance in assessing cardiac function and diagnosing diseases such as heart failure. The strengths and limitations of current imaging modalities are discussed, and the spatial and temporal resolutions, measurement accuracy, and clinical applicability of echo and CMR are compared. Emerging trends in the field include a shift from pressure-based assessments to more detailed analyses of flow energy and vortex dynamics facilitated by higher-resolution imaging techniques. The integration of artificial intelligence and machine learning is also gaining traction, with applications ranging from image reconstruction to advanced flow analysis. However, challenges remain, particularly in the reproducibility and standardization of these techniques across different clinical settings. Finally, critical research needs are identified, including validating fluid mechanics measurements through large multicenter trials and developing a unified framework for intracardiac flow analysis. Addressing these gaps will be essential for the broader clinical adoption of these advanced diagnostic tools, ultimately improving patient outcomes in cardiovascular care.

In the present study, we investigate the interphasial momentum and thermal interactions between the fluid and particles in compressible turbulent boundary layers by exploiting direct numerical simulation databases at the free-stream Mach number of 2.0 laden with zero, finite, and infinite thermal inertia particles. Results show that the particle thermal inertia modulates the turbulent statistics and coherent structures significantly, with the most profound effects manifested in the cases with infinite thermal inertia particles that constantly absorb heat from or release heat to the fluid. Besides the variation of the mean fluid temperature due to the presence of these endothermic or exothermic particles, turbulence suppression by the hot particles and augmentation by the cold particles (compared with the zero thermal inertia particles) are also identified by the variation of the morphology of the velocity streaks, the intensity of the vortical motions, the Reynolds shear stress, and the skin friction. From the perspective of the near-wall coherent structures, we found that the particle feedback force inhibits the wall-normal turbulent fluctuations, with the positive and negative particle feedback heat aligning primarily with the ejection and sweeping events, respectively.

We experimentally observe the Faraday instability transition of a three-layer fluid system from zigzag mode to B-interface instability mode in a Hele-Shaw cell by changing the excitation, the thickness of the liquid layer, and the fluid properties. Floquet analysis shows that the transitions strongly depend on the interfacial coupling in the system. For a more detailed explanation of the mode transition process, the relationship between the interface coupling and the amplitude ratio ${\xi }_A/{\xi }_B$ of two interfaces is established. Considering the zero-order interface coupling effect, we identify that the mode transition can be promoted by increasing the wave number and thickness of the middle layer liquid. Furthermore, by including the effect of first-order interface coupling, it is evident that a decrease in vibration acceleration and an increase in viscosity can promote mode transition from the dispersion relation. However, the interface tends to stabilize as the viscosity is further increased.

Deep learning is increasingly becoming a promising pathway to improving the accuracy of subgrid scale (SGS) turbulence closure models for large-eddy simulations (LESs). We leverage the concept of differentiable turbulence, whereby an end-to-end differentiable solver is used in combination with physics-inspired choices of deep learning architectures to learn highly effective and versatile SGS models for two-dimensional turbulent flow. We perform an in-depth analysis of the inductive biases in the chosen architectures, finding that the inclusion of small-scale nonlocal features is most critical to effective SGS modeling, while large-scale features can improve pointwise accuracy of the a posteriori solution field. The velocity gradient tensor on the LES grid can be mapped directly to the SGS stress via decomposition of the inputs and outputs into isotropic, deviatoric, and antisymmetric components. We see that the model can generalize to a variety of flow configurations, including higher and lower Reynolds numbers and different forcing conditions. We also demonstrate the use of ensemble uncertainty quantification for characterizing the impact of data-driven closures on time-evolving resolved flow fields. We show that the differentiable physics paradigm is more successful than offline, a priori learning, and that hybrid solver-in-the-loop approaches to deep learning offer an ideal balance between computational efficiency, accuracy, and generalization. Our experiments provide physics-based recommendations for deep-learning-based SGS modeling for generalizable closure modeling of turbulence.

Surrogate modeling methods based on polynomial chaos expansion (PCE) and bifidelity (BF) approaches are investigated in the context of two-dimensional flow past two square cylinders. The overall wake behavior of this flow has been shown by Ma et al. [Phys. Fluids 29, 033604 (2017)] to give rise to multiple flow regimes with various vortex shedding patterns depending on the cylinder gap spacing, $g^{*}$, and oncoming flow Reynolds number, Re. Within the scope of surrogate modeling, the possibility of multiple flow regimes occurring with varying input parameters forms an intriguing challenge, hence, the attempt in the present work to construct a model that will accurately reproduce the statistical quantities of the underlying physical flow regimes provides a distinction with typical reduced order models. We evaluate these surrogate models through statistical measures of their output with the ground-truth data collected from 200 Monte Carlo samples. Using the PCE-based methods, we are able to obtain highly accurate statistics and well-defined probability density functions (PDFs) but at a high overall cost in accordance with the findings reported in the preceding literature. Bifidelity approaches, by contrast, generate approximations to a large high-fidelity data-set by correcting low-fidelity (LF) solutions through a limited number of high-fidelity (HF) solutions. In this paper, LF models are constructed by using a dramatically reduced number of simulation grid points where the cost ratio of LF to HF simulation is $\mathcal{O}\left({10}^{-3}\right)$. We begin by using a multiplicative correction method where the mapping between low and high fidelity is achieved through a correction at randomized sample points. However, unreliable and inaccurate solutions are obtained, which provides a motivation to employ rank-revealing interpolative decomposition (ID) within the BF framework. More than just accurately approximating the high-fidelity data, our results show that ID can correctly classify physics in the solution space and identify the transition boundaries between flow regimes. By investigating multiple low-fidelity models, we find that increasing mesh resolution lowers the rank in our interpolative decomposition procedure and also the reconstruction error of the original LF matrix. We suggest that ID would allow purposeful and efficient uncertainty quantification methods, sensitivity analysis, and optimization for problems involving multiple modes of outcome or high-dimensional uncertainties.

The dynamics of a conductive liquid jet in an electromagnetic field are investigated experimentally. Steady jets under a constant Lorentz force and oscillating jets under a periodic Lorentz force are analyzed by varying the input current, magnetic flux density, and parameters related to the jet, namely the jet velocity and nozzle diameter. First, a model for predicting the trajectory of the steady jet is established from mass and momentum conservation, incorporating the velocity distribution of the crossflow generated by the Lorentz force. Despite the small magnitude of the Lorentz force, the continuous momentum transfer from the crossflow to the jet is sufficient to deflect the jet. Oscillating jets with nonzero forcing frequencies are classified into quasisteady, bifurcating, and asymptotic jet regimes, based on the characteristics of the jet structure. The boundaries between the three regimes primarily depend on the Strouhal number, which is proportional to the forcing frequency of the input current. The behaviors of the quasisteady jet can be predicted by considering temporal changes in the crossflow velocity based on the trajectory model of the steady jet. In the bifurcating jet regime with a higher Strouhal number, the jet splits into two distinct streams under the periodic vortex breakup induced by the crossflow near the nozzle exit. As the Strouhal number increases further, the jet reaches the asymptotic regime and exhibits minor deflection, although it spreads more broadly far from the nozzle exit than ordinary jets.

This work investigates efficient routes to turbulence in quasi-two-dimensional shear flows. Two-dimensional disturbances require high Reynolds numbers to incite transition from a steady base flow, as transient growth is modest. With the addition of an oscillatory base flow component, this work shows that the transient growth experienced by two-dimensional initial perturbations is often well above that provided by the steady component. However, as has been shown for three-dimensional flows [B. Pier and P. J. Schmid, J. Fluid Mech. 926, A11 (2021)], the transient growth is almost entirely composed of modal intracyclic growth, rather than a transient mechanism which takes advantage of non-normality. This lack of transient growth, relative to the severe decay induced by the favorable pressure gradient during the acceleration phase of the oscillatory base flow, only ever delays the transition to sustained turbulence. Thus, a nonoscillatory driving force remains the most efficient strategy for sustained turbulence in quasi-two-dimensional shear flows. The only benefit provided by pulsatility is that the amplitude of the initial condition required to trigger intermittent turbulence is orders of magnitude smaller.

A microscale lubrication flow of a gas between rotating eccentric circular cylinders is studied on the basis of kinetic theory. The dimensionless curvature, defined as the mean clearance divided by the radius of the inner cylinder, is small, the circumferential speeds of the cylinders are small, and the Knudsen number based on the mean clearance is arbitrary. The Boltzmann equation is studied analytically using the slowly varying approximation. A macroscopic lubrication equation is derived, extending the author's previous work [J. Fluid Mech. 974, A13 (2023)] to include rotation of both cylinders. A direct numerical analysis using the Bhatnagar–Gross–Krook–Welander kinetic model of the Boltzmann equation is conducted to provide a reference solution evaluating the lubrication equation. Two typical problems are examined: (i) comparing the flow of a rotating inner cylinder with that of a rotating outer cylinder at the same speed, and (ii) simultaneous rotation of both cylinders in opposite directions at the same speed. In (i), the difference in the eccentric force between the two flows is small at small Knudsen numbers but becomes significant as the Knudsen number increases. In (ii), the eccentric force nearly vanishes at small Knudsen numbers because of the cancellation of the wedge action due to the opposing rotation; however, considerable eccentric force emerges as the Knudsen number increases. The lubrication equation clarifies these phenomena, attributing them to noncontinuum and curvature effects.

Seawater cavitation, an intricate liquid-vapor phase transition caused by overstretching, is influenced by soluble salts such as chloride (${\mathrm{Cl}}^{-}$), sodium (${\mathrm{Na}}^{+}$), sulfate (${\mathrm{SO}}_4^{2-}$), and magnesium (${\mathrm{Mg}}^{2+}$). However, the super-stability and lifespan elongation of nanobubbles in electrolyte solutions have been extensively reported without considering the nonequilibrium cavitation inception. Cavitation, aroused and further exacerbated by transient pressure fluctuations, leads to hydraulic damage and inaccurate inception predictions. This study therefore performs a nanoscopic investigation on cavitation inception under transient pressure fluctuations in electrolyte solutions via molecular dynamics (MD) simulations. We examine the effects of ionic specificity and concentration on bulk vapor bubble nucleation and nanobubble expansion at the early stage of cavitation. Our findings show that ${\mathrm{MgSO}}_4$ promotes more bulk liquid ruptures to nucleate more bulk vapor cavities than NaCl, facilitating nanobubble growth. Interestingly, surface tension obeys a linear positive correlation against ionic strength irrespective of ionic type, delaying the nanobubble shrinkage in ionic environments. Although NaCl accumulates much at the nanobubble interface, its effect on surface tension increase is less significant than ${\mathrm{MgSO}}_4$ which features a higher polarity.

In a dense droplet environment, droplets influence each other's motion, deformation, and breakup behavior. The tandem droplet is a particularly relevant case for the study of its unsteady dynamic behavior. A three-dimensional numerical simulation study was conducted to investigate the deformation process of tandem droplets under different conditions. The input parameters included Reynolds numbers (150–1500), liquid/gas density ratios (100–1000), Weber numbers (30–90), and initial relative distances (4–12). The volume of fluid method was employed on an adaptive octree grid combined with the dynamic Smagorinsky turbulence model. This method has passed validity verification and grid independence verification, and it requires significantly fewer computational resources than the direct numerical simulation method when droplet breakup is not considered. The results of the research show that under conditions of high density ratio and a significant Reynolds number, the edge morphological characteristics of droplets are predominantly influenced by the Rayleigh-Taylor instability. In the case of low density ratios, the pressure drag force on the leeward side exerts a dominant influence on the accelerated motion of the leading droplet. The shape of the droplet is significantly influenced by the vortex ring present in the recirculation region. The perturbation of the liquid edge induces the vortex ring to split into secondary vortex rings, which act back on the droplet, thereby affecting its morphological characteristics. The trailing droplet is subject to a reduction in cross-flow radius, drag coefficient, minimum length, and expansion speed of the liquid bag due to the influence of the wake of the leading droplet. The decrease in Reynolds number and relative distance leads to a stronger suppression effect, while the decrease in density ratio shortens the length of the recirculation region, thereby weakening the suppression of trailing droplets. Finally, a predictive model was proposed to describe the time evolution of the radius of tandem droplets.

We employ a four-way coupled numerical approach to investigate the dynamics of suspended cohesive particles in Rayleigh-Bénard turbulence. The Stokes drag, cohesive, and direct contact forces between primary particles are captured in detail, yielding the phenomena of flocs' aggregation, breakage, and deformation. The momentum and thermal exchange between primary particles and the fluid are considered based on the Source-in-Cell method. We found that the initial increase of the average floc size indicates a temporary flocculation phase, which is followed by an equilibrium phase where the average floc size becomes stable, reflecting the balance between aggregation and breakage. Different from the traditional perspective, which attributed the local accumulation of particles to their gravity, we found that the suspended particles still tend to accumulate in the bottom hot boundary layer region. This accumulation is primarily driven by the temperature-induced variation in aggregation strength and the nonuniform spatial distribution of floc inertia. Additionally, the stronger cohesion yields a reduction in momentum intensity of the thermal plumes, primarily due to the more pronounced weakening of fluid momentum by the larger flocs.

The dynamics of thin liquid films flowing over a spinning disk is studied through a combination of experiments and direct numerical simulations. We consider a comprehensive range of interfacial flow regimes from waveless to three-dimensional (3D) waves, and for previously unexplored inertia-dominated conditions that have practical relevance. The transition between these regimes is categorized within a phase map based on two governing parameters that correspond to modified inverse Weber ($\lambda$) and Ekman numbers ($r_{\text{disk}}$). Our findings show that stationary two-dimensional (2D) spiral waves, which unfold in the direction of rotation from the Coriolis effect, transition to 3D waves with the emergence of small perturbations on the wavefronts. These nonstationary structures grow asymmetrically in the 2D-3D transitional region, and detach from the parent spiral wave to form wavelets or so-called $\mathrm{\Lambda }$ solitons. We show that during and after this wave formation process, flow circulations unique to the spinning disk arrangement are present within the main wave hump. Furthermore, when combined with observations of wall strain rates and topology within the film, these findings elucidate the mechanisms that underpin the apparent wave-induced interfacial turbulence effects observed for spinning disk flows.

We study the design of chiral particle shapes that couple translation to rotation in viscous fluid flow. We identify helical ribbons as particles with strong coupling whose symmetry ensures that the centers of mass, buoyancy, resistance, and mobility coincide. Cocentered particles such as helical ribbons provide an essential step in the hierarchy of increasingly complex translation-rotation coupling. Experiments on sedimenting helical ribbons measure both relevant mobility tensors and show excellent agreement with simulations of ribbons made of interacting spheres. We observe quasiperiodic angular dynamics causing complex spatial trajectories. In tilt-spin phase space, orbits are closed due to time-reversal and reflection symmetry. As the helical ribbon length increases, a bifurcation occurs at which the stable sedimentation orientations switch. The particle at the bifurcation has axisymmetric translation-rotation coupling and particularly simple sedimentation dynamics. Some special trajectories are unconfined in space and may contribute disproportionately to particle transport rates.

We find the mixing induced by a small swimming organism in a density stratified fluid. We model the swimmer as a spherical squirmer and quantify mixing through a mixing efficiency that is the ratio of the rate of change of the potential energy of the fluid to the total work done by the swimmer. Assessing mixing in the near field and far field of the swimmer separately, we find that the near-field mixing aligns with past work, but the overall mixing is much larger than that caused by a point-sized swimmer (like force dipole), although still small in weak stratification. Equivalent results are also obtained for a homogeneous dilute suspension of noninteracting swimmers. Our study highlights the impact of swimmer size on mixing, revealing that small-sized swimmers cannot induce substantial mixing. However, we propose a few (unexplored) pathways through which small swimmers could induce significant mixing, ultimately contributing toward oceanic mixing.

Traditional categorization of gas flow regimes in porous media relies phenomenally on Darcy's law, yielding phenomenologically a “pre-Darcy” flow regime and a “post-Darcy” flow regime before and after the linear region, respectively. This study redefines the classification of gas flow regimes by integrating the underlying flow mechanisms, proposing four distinct regimes: the slip regime, the Darcy regime, the inertia regime, and the turbulence regime. Through a scaling analysis of the Forchheimer equation, a dimensionless number, Rd, is introduced as a criterion for the onset of the inertia regime. The classification is validated using an independently established gas seepage experimental platform, which confirms the presence of gas slip effects in the “pre-Darcy” regime. Experimental data from the inertia regime show a linear increase of critical Rd with a rising permeability (${\text{Rd}}_{\mathrm{critical}}\propto k$). The deduced critical Reynolds number, Re, further substantiates that at low permeability, gas slip effects delay the transition to the inertia regime, while at high permeability, increased pore size or decreased tortuosity may hinder the generation of inertial backflow. Furthermore, the Forchheimer equation provides a more accurate description of both the Darcy and inertia regimes compared to the cubic law, with its inertial coefficient determined through appropriate fitting correlations. This study offers valuable insights into gas flow regimes within porous media, and it provides experimental results for further reference.