This study proposes a physics-informed machine learning to enable using the erroneous flow data at near-wall grid points as the input to the wall model in a wall-modeled large-eddy simulation (LES). The proposed neural network predicts the amount of numerical error in the near-wall grid-point data and inputs the physically correct flow variables into the wall model by correcting the near-wall error. The input and output features of the neural networks are selected based on the physical relations of the turbulent boundary layer for robustness against various Reynolds and Mach number conditions. The proposed neural networks allow the wall model to accurately predict the wall shear stress from the erroneous near-wall information and yields accurate predictions of the turbulence statistics. Additionally, the proposed physics-informed machine-learning approach reproduces the asymmetry in the probability density functions of the predicted wall shear stress observed in direct numerical simulations, while the conventional wall model with input away from the wall does not. The results suggest that using the near-wall information for wall modeling may increase the fidelity of the wall-modeled LES.

Momentum-scalar coupling turbulence, a phenomenon observed in both natural and engineering contexts, involves the intricate interaction between multicomponent scalars and multiscale forces (i.e., multiple coupling mechanisms), resulting in a wide array of manifestations. Despite its importance, limited research has been conducted to comprehend the influence of these multicomponent and multiple coupling mechanisms on turbulence cascades. Hence, this study aims to provide a preliminary and theoretical exploration into how these multiple coupling mechanisms govern the cascades of turbulent kinetic energy and multicomponent scalars. To simplify the mathematical analysis, homogeneous and isotropic hypotheses of flow field have been applied. The key findings of this study can be summarized as follows. The first is validation of quad-cascade processes. The second is an examination of various cases involving single scalar components but multiple coupling mechanisms. Of particular interest is the coexistence of buoyancy-driven turbulence and electrokinetic turbulence, which introduces a new variable flux (VF) subrange resulting from their nonlinear interaction. Another extension considers an exponential modulation function, equivalent to the coexistence of multiple coupling mechanisms acting on a single scalar. The study identifies two new VF subranges. Third, binary scalar components and coupling mechanisms are investigated, indicating coupling mechanisms with significantly different strengths that can also induce complex interactions and new VF subranges. Fourth is the complexity when three or more different scalar components and coupling mechanisms coexist simultaneously: with the exception of certain special cases, closure of the problem becomes unattainable. This highlights the challenges inherent in addressing the simultaneous presence of multiple scalar components and coupling mechanisms. This research endeavor illuminates the theoretical understanding of the diverse scaling properties observed in momentum-scalar coupling turbulence across different scenarios.

Impulsively generated focused jets play a significant role in various applications, including inkjet printing, needle-free drug delivery, and microfluidic devices. As the demand for generating jets and droplets from medium to highly viscous liquids increases, understanding the role of viscosity in jetting dynamics becomes crucial. While previous studies have examined the viscous effects on walls, the impact on free surfaces has not been thoroughly understood. This study aims to bridge this gap by integrating experiments with numerical simulations to investigate the viscous effects on focused jet formation. We demonstrate that mass and momentum transfer along the tangential direction of the free surface contribute to focused jet formation, and viscosity plays a key role in this transfer process. The viscosity-induced diffusion of the shear flow and vorticity near the free surface reduces the jet speed. Based on experimental observations and simulation results, we propose an equation to predict the viscous jet velocity. These findings offer new perspectives on viscous interface dynamics in advanced manufacturing and biomedical applications.

We present a numerical study of the main substages preceding aerosol formation via bursting bubbles: capillary wave propagation along the bubble, convergence at the bubble's apex, and the ascent of a Worthington jet and its breakup to release liquid drops. We focus on two crucial yet overlooked aspects of the system: the presence of surface-active agents and dynamics driven by non-negligible gravitational effects, quantified by the Bond number. Our results propose a mechanism explaining capillary wave retardation in the presence of surfactants, involving the transition from bi- to unidirectional Marangoni stresses, which pull the interface upwards, countering the motion of the waves. We also quantitatively elucidate the variable nature of the waves' velocity with various surfactant parameters, including surfactant solubility and elasticity, a departure from the constant behavior well documented in clean interfaces.

This study presents a methodology focusing on the use of computational model and experimental data fusion to improve the Spalart-Allmaras (SA) closure model for Reynolds-averaged Navier-Stokes solutions. In particular, our goal is to develop a technique that not only assimilates sparse experimental data to improve turbulence model performance, but also preserves generalization for unseen cases by recovering classical SA behavior. We achieve our goals using data assimilation, namely the ensemble Kalman filtering approach, to calibrate the coefficients of the SA model for separated flows. A holistic calibration strategy is implemented via the parametrization of the production, diffusion, and destruction terms. This calibration relies on the assimilation of experimental data collected in the form of velocity profiles, skin friction, and pressure coefficients. Despite using observational data from a single flow condition around a backward-facing step (BFS), the recalibrated SA model demonstrates generalization to other separated flows, including cases such as the two-dimensional (2D) NASA wall mounted hump and the modified BFS. Significant improvement is observed in the quantities of interest, i.e., the skin friction coefficient $\left(C_f\right)$ and the pressure coefficient $\left(C_p\right)$, for each flow tested. Finally, it is also demonstrated that the newly proposed model recovers SA proficiency for flows, such as a NACA-0012 airfoil and axisymmetric jet, and that the individually calibrated terms in the SA model target specific flow-physics wherein the calibrated production term improves the recirculation zone while destruction improves the recovery zone.

Inspired by the thought-provoking paper of Meneveau and Marusic [J. Fluid Mech. 719, R1 (2013)], the universal expression of the self-scaling generalized Townsend-Perry constants for the high-order statistical moments is investigated. The measured results deviate from the previous attached-eddy-model–based Gaussian prediction because the wall-non-attached eddies with sub-Gaussian statistics mask the Gaussian behavior of the wall-attached eddies. Leveraging the generalized Gaussian distribution function and the logarithmic law for turbulence intensity, the universal expression of the self-scaling generalized Townsend-Perry constants, regardless of the eddy type, is derived. Moreover, asymptotic expression of the shape parameter in self-scaling generalized Townsend-Perry constants with Reynolds number is further characterized by data in boundary layers and atmospheric surface layers with Reynolds number $R{e}_{\tau }$ spanning over $O\left({10}^3\right)$ to $O\left({10}^6\right)$.

We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.

We study the generation of tones by ideally expanded round jets impinging on a flat plate. Data from large-eddy simulations performed for different nozzle-to-plate distances are explored, and we consider closure of the aeroacoustic feedback loop responsible for the tones by guided jet modes. Allowable frequency ranges for resonance, underpinned by the existence of modes with upstream-directed group velocities, are computed using two different models: a cylindrical vortex-sheet model, and a locally parallel stability model which considers a finite-thickness velocity profile. It is shown that inclusion of a finite-thickness velocity profile consistent with the mean flow in the vicinity of the plate improves the agreement between observed tones and model predictions. The frequencies of the largest tones found in the data are found to fall within, or very close to, the frequency limits of the finite-thickness model, correcting discrepancies observed with the vortex-sheet model. The same trend is observed in comparisons with experimental and numerical data gathered from the literature. Pressure eigenfunctions of the stability model are in good agreement with upstream-traveling disturbances educed from the data at the tone frequencies. This provides further evidence for the involvement of guided jet modes in the resonance mechanism.

In this study, we introduce a comprehensive theoretical model for viscous liquid systems exhibiting Rayleigh-Plateau instability, accommodating cases both with and without a solid fiber. Employing the lubrication approach and implementing the hydrodynamic interaction at the solid-liquid interface, we formulate one-dimensional evolution equations for the breakup of viscous liquid threads and films on a fiber. Through several validations, we showed that our model exhibits a good agreement with experimental results in comparison to numerical simulations. Finally, our model, which incorporates the flow effect from the inner boundary condition by reconsidering the ansatz of a conventional long-wave approximation, provides a necessary condition for satellite droplet formation and determines the most unstable mode proportional to ${k^{*}}^2$, where $k^{*}$ is the most unstable wavenumber. In addition, we observed that the volume of the satellite droplets exponentially decays depending on the wavenumber. Moreover, our single model integrates the findings of Goren's liquid film on a fiber and Rayleigh's viscous liquid thread, demonstrating its versatility and relevance to a wide range of systems.

We investigate the collapse of submerged cohesive granular columns as a function of their packing density and the cohesive force strength, via grain-resolving direct numerical simulations. The cohesive force acts to reduce the final runout distance of the collapsing columns. In addition, it significantly accelerates the initial contraction for loosely packed columns and decelerates the dilation for densely packed columns, leading to a larger or smaller excess pore pressure, respectively. Early on, the collapsing column exhibits distinct planar failure surfaces, whose angle with the horizontal increases with the packing density. We employ a network science-based approach to analyze the cohesive and contact force chains. Pronounced force-chain network structures form preferentially in the failure region. They tend to be larger for higher packing density, which induces a larger macroscopic cohesive resistance. The cohesive force tends to reduce the normal contact force, which results in shorter contact force chains.

Droplet impact on rotating surfaces experiences the tangential shear force from the rotating surface, generating a centrifugal force that either enhances the spreading or destabilizes the expanding lamella. In this study, we experimentally characterize the impact of a water droplet on rotating surfaces with various wettabilities, and theoretically analyze the observed impacting dynamics, including the enhanced spreading and the transition to the destabilization of the expanding lamella. Liquids with a wide range of viscosity are tested to explore the effect of liquid viscosity on the impacting dynamics. We propose a simplified approach to predict the tangential velocity induced by the surface's tangential shear force, and validate the predicted velocity by flow field measurement. We further deduce a quantitative description for the maximum spreading factor in the spreading regime, and derive the critical condition for the destabilization of the lamella for a water droplet. Good agreements are found between the predicted values and the measured ones for the impact on the rotating surfaces with various wettabilities.

Permafrost thaw is a major concern raised by the ongoing climate change. An understudied phenomenon possibly affecting the pace of permafrost thaw is the onset of convective motions within the active layer caused by the density anomaly of water. Here we explore the effects of groundwater convection on permafrost thawing using a model that accounts for ice-water phase transitions, coupled with the dynamics of the temperature field transported by the Darcy's flow across a porous matrix. Numerical simulations of this model show that ice thawing in the presence of convection is much faster than in the diffusive case and deepens at a constant velocity proportional to the soil permeability. A scaling argument is able to predict correctly the asymptotic velocity. Since in the convective regime the heat transport is mediated by the coherent motion of thermal plumes across the thawed layer, we find that the depth of the thawing interface becomes highly heterogeneous.

The dynamics of flexible filaments entrained in flow, important for understanding many biological and industrial processes, are computationally expensive to model with full physics simulations. In this paper, we describe a data-driven technique to create high-fidelity low-dimensional models of flexible fiber dynamics using machine learning; the technique is applied to sedimentation in a quiescent, viscous Newtonian fluid, using results from detailed simulations as the dataset. The approach combines an autoencoder neural network architecture to learn a low-dimensional latent representation of the filament shape, with a neural ordinary differential equation that learns the evolution of the particle in the latent state. The model was designed to model filaments of varying flexibility, characterized by an elastogravitational number $\mathcal{B}$, and was trained on a dataset containing the evolution of fibers beginning at set angles of inclination. For the range of $\mathcal{B}$ considered here (100–10 000), the filament shape dynamics can be represented with high accuracy with only four degrees of freedom, in contrast with the 93 present in the original bead-spring model used to generate the dynamic trajectories. We predict the evolution of fibers set at arbitrary angles and demonstrate that our data-driven model can accurately forecast the evolution of a fiber at both trained and untrained elastogravitational numbers.

Calibrated gel microspheres are used in several life-science applications, from embolization to DNA barcoding and drug delivery. Along with selecting or designing specific materials that depend on the application, various processes have been developed to produce such hydrogel particles. Here, we report a high throughput strategy that is based on the controlled fragmentation of an aqueous jet in air that results in droplets of monomer solution, their entry and collection in an oil bath, followed by polymerization of the emulsion droplets which thus turn into gel beads. Each step of the process is detailed and the operating conditions are optimized to obtain homogeneous polyacrylamide gel microspheres. The impact area of the stream of droplets at the free surface, that can be tuned with the help of an electric field, plays a major role in minimizing coalescence of droplets as well as mass transport between the dispersed phase and the continuous phase which is correlated to the sedimentation flow features of the dilute emulsion.

The circular surface wave (CSW) of a low-temperature gallium alloy in the immovable cell with a central bottom electrode and an upper ring electrode exposed to axial magnetic fields is studied experimentally. It is shown that, depending on the force parameter and geometrical characteristics of the cell [cell radius, height of the liquid metal (LM) layer, and position of the circular electrode], three modes can occur in the cell: rest, CSW, or axial rotation with a deep funnel on the surface providing the circular contact of the LM with the electrode. A mode map showing the boundaries of the CSW existence domain is plotted on the parameter plane. The mechanism which provides the existence of a stable CSW is suggested. It is shown that the CSW is a superposition of two intense large-scale vortices. The main vortex, whose axis coincides with the axis of the cylindrical cell, is generated by the Lorentz force localized near the bottom electrode and arising from the interaction of the divergent electric current with the vertical magnetic field. The intensity of the second vortex is an order of magnitude less, and the axis of rotation is directed to the contact area of the liquid metal with the ring electrode, which appears near the crest of the wave. Similar to the main vortex, it exists due to the interaction of the current converging to the contact area with the superimposed magnetic field. The second vortex provides the lifting of the LM ahead of the incoming wave. The intensity of both vortices is proportional to the product of the external field by the total current, which explains the linear relationship between the relative frequency of surface oscillations and their amplitude.

In flood events caused by a gradual increase in the flow rate of a watercourse, the rise in water level is often abrupt, while the fall in level is delayed. We show that such behavior can be demonstrated by considering stationary flows at a high Reynolds number in a prismatic open channel: Several geometries of the channel cross section lead to a subcritical instability that results in a discontinuous rise in the level when the flow rate exceeds a critical value $F_i$, and in a fall, also discontinuous, when the flow rate returns below a value $F_{\mathcal{o}}$ lower than $F_i$. This hysteretic behavior originates from the interplay between gravity, which drives the flow downstream, and turbulent friction with the channel wall. The potential existence of several solutions arising from this bifurcation requires careful consideration in flood simulations.

We study the trajectories of a model microorganism inside three-dimensional channels with square and rectangular cross sections. Using (1) numerical simulations based on the lattice-Boltzmann method and (2) analytical expressions using far-field hydrodynamic approximations and the method of images we systematically investigate the role of the strength and finite-size of the squirmer, confinement dimensions, and initial conditions in determining the three-dimensional trajectories of microswimmers. Our results indicate that the hydrodynamic interactions with the confining walls of the channel significantly affect the swimming speed and trajectory of the model microswimmer. Specifically, pullers always display sliding motion inside the channel: weak pullers slide through the channel center line, while strong pullers slide through a path close to any of the walls. Pushers generally follow helical motion in a square channel. Unlike pullers and pushers, the trajectories of neutral swimmers are not easy to generalize and are sensitive to the initial conditions. Despite this diversity in the trajectories, the far-field expressions capture the essential features of channel-confined swimmers. Finally, we propose a method based on the principle of superposition to understand the origin of the three-dimensional trajectories of channel confined swimmers. Such construction allows us to predict and justify the origin of apparently complex three-dimensional trajectories generated by different types of swimmers in channels with square and rectangular cross sections.

Heat transfer in wind turbulence over breaking waves is studied through direct numerical simulations. The air-water system is simulated on an Eulerian grid with the interface between the two phases captured by a coupled level set and volume-of-fluid method. To examine the effect of wave age, different cases representing slow, intermediate, and fast waves are considered for the scenario of air temperature being higher than the water temperature. The results show that the evolution of mean temperature profile responds nonmonotonically to the increasing wave age. At a small wave age, the mean temperature near the water surface increases after wave breaking. At intermediate and large wave ages, however, the temperature decreases after wave breaking, while the decrement magnitude is larger at the intermediate wave age. An investigation of the temperature fluctuation flux indicates that a combined effect of wave-coherent flux and turbulence-induced flux leads to a large magnitude of temperature decrement at the intermediate wave age. A further analysis of the production term in the transport equation of the turbulence-induced temperature flux elucidates the mechanism underlying the generation of the turbulence-induced flux at the intermediate wave age. The findings of the present study suggest that temperature responds in a more complex manner to wave age than velocity does and this phenomenon should be considered in models for air-sea interaction and weather forecasting.

Homeostasis plays a critical role in maintaining the delicate balance between preventing excessive bleeding and enabling clot formation during injuries. One pivotal aspect of homeostasis involves the development of platelet clots. In this study, we analyze numerically the behavior of platelet margination as a function of the adhesion energy between red blood cells (RBCs), driven by the presence of plasma proteins. We examine scenarios encompassing both physiological conditions and pathological states, such as those seen in patients with diabetes. Employing a two-dimensional simulation, we utilize rigid particles and a vesicle model to simulate platelets and RBCs, respectively. We employ the lattice Boltzmann method to solve the underlying model equations. We first demonstrate that platelet margination is primarily determined by lift forces and is not notably affected by whether the cells undergo tank-treading (TT) or tumbling (TB) behavior, as often reported. Specifically, we unveil instances where cells exhibit TT or TB behavior, yet their platelet concentration profiles closely resemble each other. Furthermore, we present a striking result concerning the impact of RBC adhesion. In microcirculation the hematocrit is in the range $5–20\%$. A moderate adhesion energy (falling within the physiological range) boosts platelet margination in microcirculation. However, this effect becomes small for larger hematocrit encountered in macrocirculation (e.g., $40\%$). This boost is more significant for a viscosity contrast (viscosity of cytoplasm over that the suspending fluid) equal to a known value for RBCs, as compared to the case without viscosity contrast. As we increase the adhesion energy (the pathological range), a noteworthy decline in platelet margination is found, albeit that for some flow strength the platelet margination reaches a minimum and increases again at higher adhesion energy. These results can be attributed to a combination of lift generated by the bounding walls and the formation of RBC clusters. Notably, our study sheds light on a critical consequence of excessive adhesion, typically observed in pathological conditions like diabetes mellitus.

Rotor-stator cavity flows are known to exhibit unsteady flow structures in the form of circular and spiral rolls. While the origin of the spirals is well understood, that of the circular rolls is not. In the present study the axisymmetric flow in an aspect ratio $R/H=10$ cavity is revisited numerically using recent concepts and tools from bifurcation theory. It is confirmed that a linear instability takes place at a finite critical Reynolds number $\text{Re}={\text{Re}}_c$ and that there exists a subcritical branch of large amplitude chaotic solutions. This motivates the search for subcritical finite-amplitude solutions. The branch of periodic states born in a Hopf bifurcation at $\text{Re}={\text{Re}}_c$, identified using a self-consistent method (SCM) and arclength continuation, is found to be supercritical. The associated solutions only exist, however, in a very narrow range of $\text{Re}$ and do not explain the subcritical chaotic rolls. Another subcritical branch of periodic solutions is found using the harmonic balance method with an initial guess obtained by SCM. In addition, edge states separating the steady laminar and chaotic regimes are identified using a bisection algorithm. These edge states are biperiodic in time for most values of $\text{Re}$, where their dynamics is analyzed in detail. Both solution branches fold around at approximately the same value of $\text{Re}$, which is lower than ${\text{Re}}_c$ yet still larger than the values reported in experiments. This suggests that, at least in the absence of external forcing, sustained chaotic rolls have their origin in the bifurcations from these unstable solutions.