We explore how fluid elasticity affects the stabilization of an inherently unstable Marangoni-driven thin-film system through the application of parametric forcing. In the absence of elasticity, parametric forcing increases the threshold for the long-wave Marangoni instability mode in a thin liquid film, thereby stabilizing the system. A quiescent stable state is achievable within a finite forcing amplitude range, provided the forcing frequency is below a critical value. Outside this parameter range, the system is unstable on account of either Marangoni or Faraday instability. We find that the behavior for a film of viscoelastic liquid is different in two significant ways, as a result of fluid elasticity. Firstly, the neutral stability diagram in the amplitude versus frequency plane displays an island of stability, bounded by an upper and a lower frequency, as opposed to the Newtonian case, which displays only an upper frequency bound. Below the lower frequency bound and above the upper frequency bound, the film can be simultaneously subject to both Maranogni and Faraday instability. Secondly, fluid elasticity lowers the forcing amplitude at the neutral stability bound for both the Marangoni and Faraday instabilities, with a more significant reduction in the latter. As a result, both the threshold amplitude and the amplitude range for full stabilization of the thin-film system are reduced, which is attributed to the memory effect imparted by fluid elasticity.

The Lamb vector is pivotal in elucidating the physical origin of aerodynamic forces exerted on a body, and it is intricately linked to the advancement of vortex force theory. A thorough investigation of its full-life cycle evolution can greatly enhance our understanding of fluid dynamic behavior. The asymptotic expression of the Lamb vector near the no-slip boundary has been numerically validated, revealing its formation mechanisms in the viscous sublayer of supersonic flat plate flow. The wall-normal component is governed by boundary entropy and entropy flux, while the tangential component is dominated by the divergence of boundary vorticity, skin friction and dilatation-related terms. The spatiotemporal evolution equation, derived by Stokes-Helmholtz decomposition, highlights the competition between advection, stretching-tilting of transverse components of generalized Lamb vectors, and viscosity effects. The gaps in the full-life cycle of the Lamb vector are filled by defining the weakly nonlinear midfield wake region. The Lamb vector's behavior and underlying physics within this region are examined. Spatial variations in the wall-normal component of generalized Lamb vectors and viscosity cause anisotropic exponential decay, while advection and stretching-tilting of transverse components of generalized Lamb vectors lead to a distinct banded flow structure.

Molecular rotors form twisted conformations upon photoexcitation, with their fluorescence relaxation time serving as a measure of viscosity. They have been used to assess membrane viscosities but yield higher values compared to other methods. Here, we show that the rotor's relaxation time is influenced by a combination of membrane viscosity and interleaflet friction. We present a theory for the relaxation time and obtain a correction factor that accounts for the discrepancy. If the membrane's viscosity is known, molecular rotors may enable the extraction of the elusive interleaflet friction.

Polymer solutions can develop chaotic flows, even at low inertia. This purely elastic turbulence is well studied, but little is known about the transition to chaos. In two-dimensional (2D) channel flow and parallel shear flow, traveling wave solutions involving coherent structures are present for sufficiently large fluid elasticity. We numerically study 2D periodic parallel shear flow in viscoelastic fluids, and we show that these traveling waves become oscillatory and undergo a series of period-doubling bifurcations en-route to chaos.

We investigate the perturbations induced by a periodic bathymetry on traveling Boussinesq solitons in a two-dimensional configuration. We present two perturbation approaches to solve the nonlinear, dispersive, and nonautonomous differential equations of the model and compare the solutions with numerical simulations of the original system of equations. In the approximation for small periodic corrugations we built the solutions as modulated traveling waves using a Fourier series. The coefficients of the series are solved using the Green's function method and the path-ordered exponential method. At the second order in the relative height of bed corrugations, we obtain the perturbation as the fourth-order linear dispersive waves generated by the modulated traveling soliton in its wake. In the second approach, we rewrite the Boussinesq system into a perturbed Korteweg–de Vries nonlinear equation, and obtain the corresponding perturbed solitons. These analytic solutions are compared with the results of numerical simulations, for various parameters that characterize the effects of nonlinearity, dispersion, and bottom bathymetry. We also discuss the stability of the perturbed solitons in time. The perturbation approaches developed in this study are valid for any type of periodic bathymetries, and the method can readily be extended to nonperiodic ones.

Integrating floating photovoltaic (FPV) installations into offshore wind farms has been proposed as a major opportunity to scale up offshore renewable energy generation. The interaction between these hybrid wind–solar farms and the atmospheric boundary layer (ABL) is addressed in the present study. Idealized large-eddy simulations (LESs) are used to investigate the flow through both isolated wind and solar farms, as well as combined wind–solar farms, in varying configurations and under different atmospheric conditions. When the FPV modules are arranged in long strips parallel to the flow direction, secondary motions arise due to the temperature difference between the warm FPV modules and the colder sea surface, significantly affecting the horizontal distribution of mean wind speed in the ABL. Associated downdrafts between the strips increase entrainment of high-speed momentum from above, thereby increasing the wind speed at these locations. LESs of hybrid wind–solar farms reveal that this is beneficial for wind turbines when they are located between the FPV arrays, leading, for the cases that we considered, to a farm-averaged power increase of up to 30% compared to an isolated wind farm. It is shown that the ratio between inertial and buoyancy forces, quantified by a heterogeneity Richardson number ${\text{Ri}}_h$, plays a crucial role in the formation of secondary flows and the resulting wind farm power enhancement. We further show that no significant power gains, but also no losses emerge in situations when the solar panels are aligned perpendicular to the flow. Although the present results suggest a large potential for wind–solar hybridization, future research should focus on a wider range of scenarios, obtained from a realistic distribution of wind directions and speeds to quantify the potential beneficial impact on real annual wind power production.

We apply linear stability analysis to nearly incompressible flow over a two-dimensional zero-pressure-gradient boundary layer in the presence of a forward-facing step (FFS), with step height to local displacement thickness ratios between $0<h/{\delta }_s^{*}<3.2$. We employ a nominally sharp FFS with a 1 $\mu \mathrm{m}$ radius to closely resemble a prior wind tunnel experiment, but we also examine the impact of various step corner radii and slopes. The Navier-Stokes equations are solved on curvilinear grids to obtain the laminar basic states. After that, we use a combination of the harmonic linearized Navier-Stokes equations and the parabolized stability equations to compute the linear amplification of Tollmien-Schlichting instabilities. The $N$-factor envelopes for the FFS reveal crucial differences with respect to those obtained previously for backward-facing steps (BFS) with $0<h/{\delta }_s^{*}<1.3$, for which accurate predictions of transition onset could be obtained via $N$-factor correlations. As the boundary-layer flow recovers to its unperturbed state in the far wake of the BFS, the slope of the $N$-factor envelope is nearly the same as that of the unperturbed flat-plate boundary layer. In contrast, the $N$-factor envelope downstream of the FFS becomes flatter as the step height increases, i.e., $\mathrm{d}N$/$\mathrm{d}x$ becomes nearly 0, which causes the $N$-factor method to become sensitive to the prescribed value of the correlating $N$-factor value. In spite of this difficulty, the $N$-factor method still captures the overall trend associated with a progressively upstream shift in the transition location as the FFS height becomes larger. However, the critical step height corresponding to the onset of a significant upstream shift in transition location is not very well predicted when compared with the measured data. Within the framework of a variable $N$-factor method, the predicted reduction in the transition $N$-factor is given by $\mathrm{\Delta }N=1.89\arctan [(h/{\delta }_s^{*}-1.29)/0.179]-2.73$.

We model the turbulent kinetic energy of an arbitrary turbulent flow as an equilibrium plus a perturbation. Subsequently, perturbation theory is applied to understand the nature of both temporal and spatial fluctuations in either unsteady or inhomogeneous flows. The models are assessed using numerical simulations of the three-dimensional Kolmogorov flow. Implications for the formulation of turbulence models are discussed.

Fishes, cetaceans, and many other aquatic vertebrates undulate their bodies to propel themselves through water. Swimming requires an intricate interplay between sensing the environment, making decisions, controlling internal dynamics, and moving the body in interaction with the external medium. Within this sequence of actions initiating locomotion, biological and physical laws manifest complex and nonlinear effects, which do not prevent natural swimmers from demonstrating efficient movement. This raises two complementary questions: how to model this intricacy and how to abstract it for practical swimming. In the context of robotics, the second question is of paramount importance to building efficient artificial swimmers driven by digital signals and mechanics. In this study, we tackle these two questions by leveraging a biomimetic robotic swimmer as a platform for investigating optimal control strategies for thrust generation. Through a combination of machine learning techniques and intuitive models, we identify a control signal that maximizes thrust production. Optimum tail-beat frequency and amplitude result from the subtle interplay between the swimmer's internal dynamics and its interaction with the surrounding fluid. We then propose a practical implementation for autonomous robotic swimmers that requires no prior knowledge of systems or equations. Direct fluid-structure simulations confirm the effectiveness and reliability of the proposed approach. Hence, our findings bridge fluid dynamics, robotics, and biology, providing valuable insights into the physics of aquatic locomotion.

Fluids subject to both thermal and compositional variations can undergo doubly diffusive convection when these properties both affect the fluid density and diffuse at different rates. In natural doubly diffusive convection, the gradients of temperature and salinity are aligned with each other and orthogonal to gravity. The resulting buoyancy-driven flows are known to lead to the formation of a variety of patterns, including spatially localized states of convection surrounded by quiescent fluid. These states are known as convectons. Localized pattern formation in natural doubly diffusive convection has been studied under a specific balance where the effects of temperature and salinity changes are opposite but of equal intensity on the fluid density. In this case, a steady conduction state exists and convectons bifurcate from it. The aforementioned buoyancy balance underpins our knowledge of this pattern formation but it is an ideal case that can hardly be met experimentally or in nature. This article addresses how localized pattern formation in natural doubly diffusive convection is affected by departures from the balanced case. In particular, the absence of a conduction state leads to the unfolding of the bifurcations to convectons. In thermally dominated regimes, the background flow promotes localized states with convection rolls attached to the end walls, known as anticonvectons, and the existence of these states is found to be related to the emergence of convectons. Convectons are found to exist over a range of buoyancy ratio values, disappearing at saddle nodes of anticonvecton branches in the thermally dominated regime and smoothly transitioning into domain-filling states in the solutally dominated regime. These observations extend the scope of our understanding of localized pattern formation in fluid systems.

This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for subgrid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations.

Despite the large body of research on coalescence, firm agreement between experiment, theory, and computation has not been established for the very first moments following the initial contact of two liquid volumes. By combining a range of experimental and computational modeling approaches in two different geometries—namely, drop-drop and drop-bath configurations—we elucidated the influence of the intervening gas and van der Waals forces on coalescence. For the simple liquids considered here, the gas influences both pre- and postcontact regimes, with jump-to-contact being the primary mode of merging. Subsequently, wave-like air pockets are observed and ultimately influence the initial opening dynamics of the neck.

Using particle-based numerical simulations performed under pressure-imposed conditions, we investigate the transient dilation dynamics of a shear thickening suspension brought to shear jamming. We show that the stress levels, instead of diverging as predicted by steady-state flow rules, remain finite and are entirely determined by the coupling between the particle network dilation and the resulting Darcy backflow. System-spanning stress gradients along the dilation direction lead to cross-system stress differences scaling quadratically with the system size. Measured stress levels are quantitatively captured by a continuum model based on a Reynolds-like dilatancy law and the Wyart-Cates constitutive model. Beyond globally jammed suspensions, our results enable the modeling of inhomogeneous flows where shear jamming is local, e.g., under impact, which eludes usual shear thickening rheological laws.

In turbulent flows, tracking the source of a passive scalar cue requires exploiting the limited information that can be gleaned from rare, stochastic encounters with the cue. When crafting a search policy, the most challenging and important decision is what to do in the absence of an encounter. In this work, we perform high-fidelity direct numerical simulations of a turbulent flow with a stationary source of tracer particles, and obtain quasioptimal policies (in the sense of minimal average search time) with respect to the empirical encounter statistics. We study the trajectories under such policies and compare the results to those of the infotaxis heuristic. In the presence of a strong mean wind, the optimal motion in the absence of an encounter is zigzagging (akin to the well-known insect behavior “casting”) followed by a return to the starting location. The zigzag motion generates characteristic $t^{1/2}$ scaling of the rms displacement envelope. By passing to the limit where the probability of detection vanishes, we connect these results to the classical linear search problem and derive an estimate of the tail of the arrival time pdf as a stretched exponential, which agrees with Monte Carlo results. We also discuss what happens as the wind speed decreases.

We investigate the convective instability resulting from the dissolution of carbon dioxide (${\mathrm{CO}}_2$) into water in a heterogeneous Hele-Shaw cell utilizing both experimental and numerical approaches. Experiments are conducted in a Hele-Shaw cell with a variable gap width corresponding to a log-normally distributed permeability of variance ${\sigma }_{logK}^2=0.135$. Two mean gaps ($370\mu \mathrm{m}$ and $500\mu \mathrm{m}$) with the same correlation lengths (${\lambda }_x=0.032\mathrm{m}$ and ${\lambda }_z=0.016\mathrm{m}$) are considered. Experiments in homogeneous cells with a constant gap are also performed. The ${\mathrm{CO}}_2$ partial pressure ($P_{{\text{CO}}_2}$) is varied between $12\%\pm 1\%$ (0.12 bar) and $85\%\pm 1\%$ (0.85 bar). The convective patterns are visualized using Bromocresol green. The effect of the heterogeneity on the instability is analyzed through its wavenumber, amplitude, and growth rate. There is a good agreement between the experimental and numerical results. Fingers appear more dispersive and distorted in the heterogeneous media. Heterogeneous cases display a larger instability amplitude, faster growth rate, and smaller dimensionless wavenumber. This reflects that heterogeneity accelerates the instability and the merging of the fingers. A comparison of the autocorrelation function of the fingering patterns and the permeability field shows that heterogeneity increases the dimensionless correlation length of the fingering pattern, which slows down its growth when its size becomes comparable to the heterogeneity.

A Leidenfrost drop made of inflammable liquid exhibits increased evaporation when inflamed. Contrary to the classical Leidenfrost framework, the evaporation from the top part cannot be neglected anymore. Herein, we report the evaporation dynamics of an inflamed drop for various wall temperatures. The combustion duration is found to be significantly longer in the Leidenfrost state than below the Leidenfrost transition. For large drops, we show that we can split the evaporation of inflamed Leidenfrost drops into two independent systems: the bottom and top parts. Assuming that the bottom contribution does not depend on the combustion, the top contribution can be extracted and analyzed, which is observed (i) to remain smaller than the bottom contribution and (ii) to be constant in the temperature range considered. This implies that the top evaporation rate is solely due to the intrinsic burning rate of the flammable liquid at saturation temperature.

Biological microswimmers, like euglena, deform their body shape to swim through tight confinements having length scales comparable to the microswimmer length scale. Recently, it was shown that self-propelling active droplets can also squeeze through tight microconfinements by elongating their shape. However, the evolution of the velocity field generated by the active droplet as it deforms its shape to swim through increasingly tight microconfinements has remained scarcely studied. Using high-resolution fluorescence microscopy and $\mu$-particle image velocimetry analysis, we show here that as the swimming active droplet deforms from a spherical shape to a “stadiumlike” shape, and eventually to an elongated “capsulelike” shape in increasingly tighter microchannels, its hydrodynamic signature gradually changes from a symmetric, quadrupolar velocity field to an asymmetric velocity field. We characterize such alterations in the active droplet dynamics using the distributions of the local velocity magnitude, axial and transverse components of the local flow velocity, vorticity, and the ejected filled micelle concentration. Finally, we use finite-element-method-based numerical simulations to provide a qualitative understanding of the evolution of the velocity field stemming from the underlying physicochemical hydrodynamics in presence of a thin lubrication film. The present work delineates the chemohydrodynamic characteristics of active droplets navigating extreme confined spaces, which can be beneficial for many autonomous cargo-delivery applications in complex environment.

Using molecular dynamics simulations, we assess the ability of transition state theory (TST) to describe the slip length of a simple liquid in contact with a simple solid under a wide range of pressures and temperatures, as well as other system parameters. In the linear regime of low shear rates that is of practical interest, TST leads to an Arrhenius-type expression with temperature and density-dependent pre-exponential factors. Extensive comparison with molecular dynamics simulation results shows that the resulting model can fit simulation data very well. Of particular note is the model's ability to capture the strong dependence of slip on pressure; according to the model, this dependence originates in the work of expansion associated with hole formation in the activated state and appears in the Arrhenius exponent as part of the Gibbs free energy of activation. We also show that under certain conditions, the model reduces to particularly simple expressions for describing the slip as a function of the system thermodynamic state.

The variation laws of pressure peak during the impact phase of flat plate ditching available from previous experiments, numerical simulations, and theoretical investigations are inconsistent. Hence, the impact pressure and force on a two-dimensional flat plate are numerically studied by solving the compressible unsteady Reynolds-averaged Navier-Stokes equations and volume of fluid model. Under the premise of ensuring efficiency, the boundary effect, starting effect, and the influence of grid resolution and time step on the simulation results are eliminated. The results demonstrate that the pressure peak exhibits a rapid increase–gradual decrease variation law. The rapid increase is attributed to the formation and development of the spray sheet, during which the curvature of the waterline near the spray root quickly decreases, and the stagnation streamline rapidly changes from parallel to perpendicular to the plate. The subsequent gradual decrease of pressure peak is caused by the gradual variation of the spray sheet, during which the curvature of the waterline gradually descends, and the stagnation streamline gradually deviates from the direction perpendicular to the plate. Wagner and self-similar theories only hold approximately in the gradual decrease region, while they fail in the rapid increase region because they do not consider the formation and development of the spray sheet. The prediction formulas of the maximum pressure peak and unsteady normal force are proposed, which perform effectively under various ditching parameters.