We present a mesoscopic hydrodynamic model for a spreading drop of volatile partially wetting liquid on a solid porous layer of small thickness. Thereby, evaporation takes place under strong confinement, i.e., we consider a drop that spreads on one of two parallel plates that form a narrow gap. Our gradient dynamics model describes the coupled dynamics of the vertically averaged vapor density profile, the drop height profile, and the vertically averaged saturation profile in the porous layer. The underlying free energy incorporates saturation-dependent wettability, capillarity of the drop and within the porous layer, air and vapor entropy, and an entropic contribution relevant close to the complete filling of the porous layer. After developing the model, we discuss the resulting sorption isotherm and illustrate typical drop spreading and imbibition behavior, including the formation of a saturation halo within the porous substrate.

We investigate the behavior of a flexible stem completely submerged under a surface gravity wave of finite amplitude using fully resolved direct numerical simulations. By varying the rigidity of the stem over ten orders of magnitude, we explore its motion in the drag-dominated regime with realistic air and water properties. Our findings reveal two distinct structural responses of the stem depending on the ratio between its natural frequency ($f_{\mathrm{nat}}$) and the wave frequency ($f_{\mathrm{wave}}$). For $f_{\mathrm{nat}}/f_{\mathrm{wave}}\gg 1$, the stem maintains on average a straight configuration and exhibits streamwise oscillations in phase opposition with the wave, moving symmetrically with respect to the vertical direction. Conversely, for $f_{\mathrm{nat}}/f_{\mathrm{wave}}\ll 1$, the stem reconfigures under the influence of the Stokes drift, bending forward and breaking the symmetry, and exhibits oscillations that are more coherent with the surrounding flow field. Resonance is observed when $f_{\mathrm{nat}}\approx f_{\mathrm{wave}}$. These results provide insights into the dynamics of slender vegetation and manmade structures in wave fields, offering valuable implications for marine biology and engineering.

The drying of droplets of colloidal suspensions in cavities is of importance for applications such as inkjet printing, pattern analysis of dried blood, and fabrication of printed electronics. Nonuniformity of particle deposition can lead to a pinch point, a sharp local minimum of particle number density that is detrimental for some applications. In contrast to prior work that assumes the droplet contact line is pinned, here we focus on how cavity shape, solvent evaporation rate, and thermal Marangoni flow affect particle deposition when the contact line is free to move. A lubrication-theory-based model is developed to derive nonlinear evolution equations for the droplet height and vertically averaged particle concentration. Contact-line motion is accounted for by using a precursor film and disjoining pressure and solvent evaporation is described using the one-sided model. Finite-difference solutions for trapezoidal-like cavities show that a pressure maximum appears at the droplet edge as the evaporation rate or thermal Marangoni flows increase, or as the cavity depth decreases. The resulting inward flow causes the contact line to depin, which leads to an increase in the uniformity of particle deposition but also to the occurrence of a pinch point near the droplet edge.

Active particles with a temperature distribution, “hot particles,” have a distinct effect on the fluid that surrounds them. The temperature gradients they create deem the fluid's viscosity spatially dependent, therefore violating the linearity of the problem, making a full description of velocity and pressure fields challenging. Using energy dissipation analysis and Lorentz reciprocal theorem, we show that it is still possible to study global properties of such hot suspensions. Namely, we calculate the effective stress tensor and viscosity of a dilute hot suspension, adding a correction that includes contributions from the bulk fluid and the particles themselves. As examples of this method, we derive the effective stress and viscosity of a suspension of spherical particles with different heat distributions. We show that, when the particles are non-Brownian and all oriented along the same direction, the viscosity is no longer isotropic and depends on the direction of shear relative to the orientation of the particles. In such cases, the fluid is also non-Newtonian. If the particles' orientation is fixed due to an external field, the stress tensor is no longer symmetric, and the viscosity has odd components.

A Hamiltonian system of equations to describe the evolution of a dipole-type point vortex in an infinite strip of an ideal incompressible fluid bounded by impermeable solid boundaries was obtained. The existence of two conservation laws in involution was demonstrated. Exact solutions of this system of equations in quadratures were found in the general case. It has been demonstrared that the vortex executes periodic motions in the transverse direction while moving in the longitudinal direction. The properties and characteristics of the vortex motion in the strip were studied. Two limiting cases were identified. The first case is the vortex motion only in transverse direction with vortex annihilation at reaching the boundary. The second case is only the longitudinal motion of the vortex at a constant velocity.

After more than a century since Worthington's 1876 pioneering work, the topic of drop impact and the beautiful postimpact images that emerge continue to inspire scientists and the public alike due to the critical role that impact dynamics plays in cutting-edge engineering applications, with notable examples in spray cooling, spray coating, inkjet printing, pesticide dispersal, and the unlikely field of forensic science. For example, the pitting of turbine blades in steam power plants and the quality of solder bumps on printed circuit boards are directly affected by drop impact dynamics. Driven by recent advances in micro- and nanofabrication, which enabled coating of engineered surfaces with liquid films of controlled thickness, here, we characterize water drop impact dynamics (spreading, retraction, and breakup mechanism) on hierarchically textured silicon micropillars and microholes coated with a few microns thick of lubricant film. We observe that the droplet impact dynamics on overlubricated surfaces is invariant with the surface texture; specifically, micropillars and microholes with the same solid fraction exhibit similar postimpact dynamics. Our experiments show that there is an optimum lubricant layer thickness ($\approx 3-5\mu \mathrm{m}$) that maximizes drop breakup and splashing mechanism. Additionally, we observe increased suppression of drop splashing and breakup with lubricant viscosity, which we attribute to viscous dissipation in the wetting ridge. Our experiments also show enhanced drop splashing intensity when the density difference between the drop and lubricant oil increases, suggesting the role of hydrodynamic instability in postimpact dynamics. The new insights gained from this work improve current understanding by informing the relevant material properties and dynamical behaviors of the impacting drop that can be tuned to either suppress or enhance impact-induced drop splashing.

Archetypal falling behaviors of impervious objects are classified into four modes: fluttering, tumbling, steady descent, and chaotic motion. The classical scenario predicts these behaviors to be affected by three dimensionless quantities: thickness-to-width ratio, dimensionless inertia, and Reynolds number. In this article we explore experimentally the effect of permeability and porosity on the falling regimes of porous plates. By drilling several hole distributions in rectangular plates, both permeability and porosity are varied systematically. We discover that the introduction of porosity affects the stability of the falling regimes eliminating tumbling. Using a phenomenological model we show that a decrease in circulation induced by the introduction of holes is the primary mechanism for stabilizing the plates' trajectories.

Large secondary motions are generated in boundary layers if a surface heterogeneity of wavelengths comparable to the boundary-layer thickness exists. Examples of surface heterogeneity include roughness heterogeneity [e.g., Willingham et al., Phys. Fluids 26, 025111 (2014)], temperature heterogeneity [e.g., Bon and Meyers, J. Fluid Mech. 933, A57 (2022)], or combinations thereof. Meyers et al. [J. Fluid Mech. 862, R5 (2019)] introduced a simple model for these motions in the case of neutral stratification. These dynamics can significantly change in thermally stratified flows. An extension to the model considering buoyancy effects is presented, and the impact of different simplifying assumptions is investigated (namely, background gradient versus no background gradient, and constant eddy viscosity versus height-dependent eddy viscosity). All variants of the model, including the original, are validated against the direct numerical simulations (DNSs) of Bon and Meyers [J. Fluid Mech. 933, A57 (2022)] and Bon et al. [J. Fluid Mech. 970, A20 (2023)]. The DNS data concern a stably stratified channel flow with smooth walls and heterogeneous temperature on the bottom and top boundaries. For strong secondary motions, the model predictions are improved when the effect of background velocity and temperature gradients is included along with the buoyancy term. However, adding gradients alone or buoyancy alone only drives the results far from the DNSs. On the other hand, in the case of weak secondary motions, buoyancy alone shows limited improvement when compared to the original (neutral without gradients) formulation. These background gradients add physically important coupling terms in the equations that relate to vortex stretching and transport of mean-flow temperature by the secondary motions. Finally, adding a height-dependent eddy viscosity to the model improves the representation of secondary motions close to the wall.

Contact time of bouncing drops is one of the most essential parameters to quantify the water repellency of surfaces. Generally, the contact time on superhydrophobic surfaces is known to be Weber number independent. Here, we probe an additional characteristic time, transition time, inherent in water drops impacting on superhydrophobic surfaces, marking a switch from a predominantly lateral motion to an axial motion. Systematic experiments and numerical simulations show that the transition time is also Weber number independent and accounts for half the contact time. Additionally, we identify a Weber-independent partition of volume at the maximum spreading state between the rim and the lamella and show that the latter contains 1/4 of the total volume of the drop.

This study investigates the anisotropic growth dynamics of liquid bridges during droplet coalescence under acoustic levitation. Numerical and experimental results revealed that the early-time evolution of aliquid bridge follows a scaling law $d\sim t^{0.5}$ in the inertial regime, with different prefactors for horizontal and vertical growth. Sound-field simulation results indicate that the high aspect ratio of the liquid bridge is influenced by the nonuniform distribution of acoustic radiation pressure, leading to significant differences in the curvature of the bridge neck between the horizontal and vertical directions, which in turn affects the Laplace pressure distribution. The interplay between acoustic radiation pressure and Laplace pressure is analyzed, with Laplace pressure identified as the dominant driving force for bridge growth. A dimensionless parameter is introduced to quantify the contributions of acoustic and capillary forces, shedding light on understanding the mechanisms of anisotropic growth of liquid bridges under acoustic levitation.

A closure model is presented for large-eddy simulation (LES) based on the three-dimensional variational data assimilation algorithm. The approach aims at reconstructing high-fidelity kinetic energy spectra in coarse numerical simulations by including feedback control to represent unresolved dynamics interactions in the flow as stochastic processes. The forcing uses statistics obtained from offline high-fidelity data and requires only a few parameters compared to the number of degrees of freedom of LES. This modeling strategy is applied to geostrophic turbulence on the sphere and enables simulating indefinitely at reduced cost. The method accurately recovers the energy spectra and the zonal velocity profiles in the coarse model for three generic situations.

The current study uses direct numerical simulation to investigate the influence of parameterized distributed roughness on the separation-induced transition over a flat plate, under the influence of freestream turbulence and an adverse pressure gradient. Five cases, ranging from a smooth wall to a set of increasing roughness heights, were simulated to understand the interaction of the freestream “top-to-bottom” perturbation and the “bottom-to-top” perturbations by the roughness elements. The baseline is a benchmark case originating from Wissink and Rodi [Flow, Turbul. Combust. 71, 311 (2003)] to understand the effect of freestream turbulence on separation-induced transition. Rough elements were distributed within the streamwise location of $x/L=0.3\sim 0.9$ to cover the original separation bubble in the smooth-wall case. The roughness elements in the current study can suppress the global separation bubble size despite the slight local separations created by the arrays of rough elements. At low roughness height, the transition process is still dominated by fluctuations initiated by the freestream turbulence, and the vortex caused by the roughness merely accelerates the development of instability. With increasing roughness height, the instability induced by the generated vortex, originating from the staggered arrangement of the roughness elements, eventually becomes strong enough to cause turbulence directly and the turbulence becomes strong enough to suppress separation.

Using high-fidelity simulations, we study the self-induced flapping dynamics of an inverted elastic foil when placed in tandem with a stationary circular cylinder. The effect of wake interference on the inverted foil's coupled dynamics is examined at a fixed Reynolds number ($\mathrm{Re}$) as a function of nondimensional bending rigidity ($K_{\mathrm{B}}$) and the structure-to-fluid mass ratio ($m^{*}$). Our results show that there exists a critical $K_{\mathrm{B},\mathrm{Cr}}=0.25$, above which the downstream foil is synchronized with the unsteady wake, and the cylinder controls the flapping response and the wake vortex dynamics. During synchronization, two additional flapping modes, namely, the small- and moderate-amplitude flapping mode, are observed as a function of decreasing $K_{\mathrm{B}}$. Below $K_{\mathrm{B},\mathrm{Cr}}$, the downstream foil undergoes self-induced large-amplitude flapping (LAF) similar to that of an isolated foil counterpart. When the dynamics of the downstream foil are analyzed for a range of $m^{*}$, we can characterize the response dynamics into two regions: low and high sensitivity. The high-sensitivity region is observed when the dynamics are controlled by the cylinder vortex shedding, i.e., for foils with high stiffness. In this regime, the foil dynamics is negatively correlated with $K_{\mathrm{B}}$ and $m^{*}$. The low-sensitivity region is observed when the downstream foil is no longer synchronized with the wake and undergoes an LAF response, with dynamics that are weakly correlated with $K_{\mathrm{B}}$. A nondimensional parameter is proposed that combines the effect of the foil's inertia and elastic forces and can capture the foil's response when it is subjected to wake interference effects. The findings of this study aim to generalize our understanding of the self-induced flapping dynamics of inverted foils in an array configuration and have relevance to the development of inverted-foil-based renewable energy harvesters.

We study the statistics of longitudinal and transverse structure functions, as well as velocity circulation, in the inverse energy cascade of two-dimensional turbulence. Using direct numerical simulations of the incompressible Navier–Stokes equations, we show that transverse structure functions exhibit an anomalous scaling, in contrast to the self-similar behavior of longitudinal ones. We derive an analytical relation that shows that the scaling exponents of transverse structure functions and velocity circulation are related in two-dimensional turbulence.

We observe the spontaneous onset of three-dimensional motion from a quiescent, purely conductive state of a stably stratified fluid in a V-shaped enclosure heated from below, which ultimately self-organizes into a two-dimensional steady state without any external forcing to the initial configuration. We identify a dominant three-dimensional instability through modal stability analysis. Direct numerical simulations confirm this instability but also reveal that, after an initial period of spontaneous three-dimensional growth, the flow gradually self-organizes into a steady two-dimensional state without external intervention. This self-organization manifests consistently for any arbitrary infinitesimal three-dimensional disturbance to the initial quiescent configuration. We demonstrate that the mechanism driving this self-organization is the increasing dominance of viscous dissipation over buoyant production of disturbance kinetic energy at later stages of flow evolution from the initial quiescent state. Our investigation reveals a flow scenario in which the most natural transition pathway to the final state involves passing through an intermediate state with a higher dimension than the final state itself. Specifically, our final flow state is less complex than the three-dimensional most unstable eigenvector predicted by linear-stability analysis. We demonstrate that the entire flow evolution remains nonturbulent throughout and closely aligns with results from linear-stability analysis, distinguishing the present flow dynamics from transient chaos, which also features complex transient states that eventually converge to a less complex final state.

Multiphase flow in cohesive granular materials underlies various natural and industrial processes, yet the role of intergranular bonds is commonly overlooked. Herein, we probe the morphodynamics of two-phase fluid-induced deformation in a cohesion-tunable bonded granular medium. We illuminate a first-ever pattern diagram in the phase space of varying flow conditions and cohesion levels, with five distinct patterns spanning from fracturing with bond breakage to fingering without grain motion. The competition between skeleton cracking and fluid percolation results in a striking nonmonotonic trend between injection pressure and cohesiveness. We characterize these pattern transitions via dimensional analysis, effectively quantifying the balance between capillary, viscous, and cohesive forces at play.

The vertical transport of sediment in marine settings can be influenced by a settling-driven convective instability and velocity shear. We conduct three-dimensional numerical simulations to investigate vertical sediment transport out of a surface mixed layer under different shear strengths. We show how this transport is determined by a competition between the growth of the settling-driven convective instability (Rayleigh-Taylor) and the stratified shear instabilities, and provide implications for marine carbon dioxide removal. In weak shear scenarios (characteristic velocity difference $\mathrm{\Delta }U<0.05\mathrm{m}$ ${\mathrm{s}}^{-1}$), the Rayleigh-Taylor instability drives enhanced vertical sediment transport compared to Stokes particle settling; the sediment transport is weakly sensitive to the strength of shear, with the slowest effective settling velocity in the absence of shear. In the presence of strong shear scenarios $(\mathrm{\Delta }U>0.05\mathrm{m}$ ${\mathrm{s}}^{-1})$, stratified shear instabilities grow rapidly and suppress the Rayleigh-Taylor instability, and the effective settling of particles is significantly reduced. Furthermore, with an increase in the strength of shear instabilities, the effective particle settling velocity and the rate of mass transport decrease. We show how these estimates for particle transport out of the surface mixed layer relate to the limited potential for atmospheric carbon dioxide draw down via approaches that rely on particle dissolution in the surface ocean.

In this paper, we propose artificial-neural-network-based (ANN-based) subgrid-scale (SGS) models in the strain-rate eigenframe for large-eddy simulation (LES) of compressible turbulent channel flow. In the ANN modeling, both input and output variables are transformed to the local eigenframe of the strain-rate tensor to ensure that the model is coordinate-invariant. In addition, the grid information is integrated into input variables of the nerual network to address the grid anisotropy of the turbulent channel flow. The proposed coordinate-invariant ANN model achieves a higher correlation coefficient and lower relative error than traditional SGS models, including the dynamic Smagorinsky model (DSM), the Vreman model, and the wall-adapting local eddy-viscosity (WALE) model, in an a priori test. In an a posteriori test, the proposed model performs better in predicting structures and statistics of velocity and temperature, and it also gives a more accurate prediction of SGS fluxes. Furthermore, the proposed model exhibits high accuracy in situations with an untrained Reynolds number and a Mach number, demonstrating its generalization ability.