We present a laboratory experiment to model convection in the atmosphere driven by latent heat of condensation (“moist convection”). The system consists of a tank filled with an aqueous solution containing a color indicator that renders the fluid yellow and transparent when acidic and blue and opaque when basic. A sodium lamp positioned above the tank serves as a heat source. Initially, the solution is entirely acidic and stably stratified in temperature. A basic layer is progressively generated at the tank's bottom through water electrolysis, forming an initially stable, blue region. This layer is internally heated by absorbing the heat from the sodium lamp, modeling the latent heat of condensation in the atmosphere. Over time, instabilities develop at the interface between the yellow and blue layers. We investigate the variation of the instability wavelength and complement our observations with a linear stability analysis to elucidate the underlying mechanisms and the process of wavelength selection. Direct numerical simulations are then employed to explore the first steps of the nonlinear regime in connection with experimental observations.

We study numerically the dynamical evolution of two different vorticity arrays with an initially uniform magnetic field in two-dimensional incompressible magnetohydrodynamics. We concentrate particularly on the role of the strength of the background magnetic field, which is always assumed weak in the sense that its energy is much less than the kinetic energy of the vortical flows. Within the context of a weak background field, we are able to identify four distinct regimes. When the field is so weak that the back-reaction of the Lorentz force can be ignored (the kinematic regime), classical flux expulsion occurs. As the field strength is increased, the first signs of the dynamical influence of the small-scale field generated is in the disruption of vortex filaments, with flux expulsion still occurring in the vortex cores. A further increase in field strength leads to the regime of vortex disruption, in which the magnetic field is expelled, but is then of sufficient strength to disrupt or destroy the vortices. For yet stronger fields, even the large-scale field can be sufficiently strong to be dynamically active; flux expulsion is then prevented, and the field is dynamically active throughout the evolution. Furthermore, in the case of a row of vortices, we show that the orientation of the background field significantly influences the evolution, especially at higher field strengths.

Breath figures are the complex patterns that form when water vapor condenses into liquid droplets on a surface. The primary question concerning breath figures is how the condensing vapor is allocated between the growth of existing droplets and the nucleation of new ones. Although numerous theoretical studies have concentrated on scenarios resulting in highly polydisperse droplet ensembles, a companion paper [Bouillant et al., Phys. Rev. Lett. 134, 188204 (2025)] demonstrates that nearly monodisperse patterns can be achieved on defect-free substrates in a diffusion-controlled regime. The objective of this work is to present a theoretical framework that elucidates the formation and evolution of nearly monodisperse patterns in breath figures. We discover that, following a short nucleation phase, the number of droplets remains constant over an extensive range of timescales due to collective effects mediated by the diffusion of vapor. The spatial extent of these diffusive interactions is identified through asymptotic matching, based on which we provide an accurate description of breath figures through a mean-field model. The model accounts for the subdiffusive growth of droplets as well as for the arrest of nucleating new droplets, and reveals the scaling laws for the droplet density observed in experiments. Finally, droplets expand and ultimately coalesce, which is shown to trigger a scale-free coarsening of the breath figures.

Understanding the dynamics of fluid transport and trapping within microscale cavities is important for a range of environmental, industrial, and research applications. Using PDMS microfluidic channels, we explore the displacement and retention of (wetting) oil by an invading flow of (nonwetting) water at low Reynolds number $(\mathrm{Re}\ll 1)$ in noncontiguous pores, and examine the influence of trapping velocity, viscosity ratio, and pore aspect ratio. We find that increasing capillary numbers lead to a greater amount of oil trapped per cavity. This is contrary to findings for interconnected porous media in which the availability of multiple pathways for fluid flow leads to more displacement with increased flow rates. This result can be attributed to a dynamic transition from a meniscus displacement to a viscous fingering displacement, by which the advancing water front shifts from a discrete triple contact line at channel walls to a continuous layer of oil enveloping the water. Data from all pore geometries can be collapsed onto a single trend by subtracting the amount of oil captured in the zero capillary number limit, indicating that increased oil retention at higher values of capillary number is not dependent on pore geometry. A model for steady-state, three-dimensional flow based on the long-wave approximation was developed to analyze the amount of fluid retained as a function of capillary number and viscosity ratio. Model predictions are qualitatively consistent with several experimental observations, including the shape of the interface of the trapped oil and the trend that increasing capillary number leads to greater oil trapping per pore. Our results highlight the need to quantitatively investigate the transient dynamics of fluid invasion in multiphase systems that exhibit localized entrapment.

An immersed-boundary method-based incompressible flow solver was used to study the vertical diamond formation that occurs within fish schools and the resulting hydrodynamic performance enhancements and wake dynamics. The vertical spacing $H$ between the top and bottom fish within the diamond was varied to understand the impact of this spatial parameter on performance enhancements. At lower $H$ spacings, thrust enhancement and drag reduction were experienced by all four fish; these effects were maximized at $H$ = 0.27 body length. At this spacing, the follower obtains the largest benefits with a 15.5% drag reduction and 6.0% thrust increase compared to solitary swimming. The top and bottom fish extract a more than 6.0% thrust increase, while a less significant drag decrease is experienced. In contrast, the leader faces an increase in thrust and decrease in drag. Power consumption of the leader and follower are reduced as well; however, the top and bottom fish power consumption is increased by more than 6.0% in this formation. By examining the vortex dynamics, pressure distribution, and wake velocity patterns, mechanisms responsible for the performance enhancements in low $H$ vertical diamonds were identified. The leader benefits were obtained through body-body interactions with positive signed pressure ahead of the top and bottom fish. The top and bottom fish extracted anterior suction, and therefore drag reduction, from the leader's vortex rings. The caudal fins of the top and bottom fish generated strong leading-edge vortices (LEVs) in the interior of the diamond, therefore, enhancing thrust. These strengthened LEVs convected downstream forming coherent vortex legs within a complex pattern of vortex rings. The wake-body interaction between the top and bottom fish vortex rings and the follower fish (i) generated strong anterior suction pressure and (ii) produced a like-signed vortex ring and boundary layer vorticity interaction resulting in a reduction of drag. Finally, the follower's caudal fin extracted a wake-fin interaction and thrust increase from spanwise-compressed vortices generated by the top and bottom fish. A Reynolds number study confirmed enhancements in the lower $H$ diamond over a sparser diamond are obtained across a range of Re from 1000 to 8000. This study revealed the complex wake dynamics and body-body, wake-body, fin-fin, and wake-fin interactions that can be leveraged for performance benefits in vertical diamond fish schools. The findings provide insights into optimizing the configurations of fish-inspired robotic swarms for greater efficiency.

Human respiratory activities induce the exhalation of a cloud of air laden with droplets. These droplets can harbor pathogens and play a role in the transmission of infectious diseases. Experimentally determining the size and velocity of these droplets, along with the properties of the exhaled air cloud, is crucial for predicting their behavior postemission and developing effective strategies to mitigate infection transmission. Despite the efforts of the scientific community, there is still a lack of comprehensive characterization of exhaled droplet size distribution, with different studies yielding significantly varied results. Additionally, while several studies have measured airflow rate and velocity, droplet velocity is rarely measured and typically only within a limited size range. In this study, we use an enhanced version of the interferometric laser imaging for droplet sizing (ILIDS) technique to simultaneously measure the size and velocity of droplets exhaled by 23 volunteers during speaking, coughing, and breathing. This method allows us to detect droplet diameters as small as $2\mu \mathrm{m}$, extending the size range reported in the literature for the coupled measure of droplet size and velocity. The ILIDS technique addresses several issues encountered in previous studies by (i) directly measuring droplets larger than $20\mu \mathrm{m}$, (ii) conducting measurements close to the mouth to reduce droplet evaporation and dilution effects, and (iii) distinguishing between ambient air dust and exhaled droplets, eliminating the need for air filtration. Additionally, this study assesses the impact of protective masks on droplet size and velocity distributions, as well as the variability of the results among different volunteers and the same volunteers repeating the tests multiple times.

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.

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 $\mathrm{\Delta }N=1.89\arctan [(h/{\delta }_s^{*}-1.29)/0.179]-2.73$.

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.

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.

Traumatic brain injury (TBI) is a serious health issue. Studies have highlighted the severity of rotation-induced TBI. However, the role of cerebrospinal fluid (CSF) in transmitting the impact from the skull to the soft brain matter remains unclear. Herein, we use experiments and computations to define and probe this role in a simplified setup. A spherical hydrogel ball, serving as a soft brain model, was subjected to controlled rotation within a water bath, emulating the CSF, and filling a transparent cylinder. The cylinder and ball velocities, as well as the ball's deformation over time, were measured. We found that the soft hydrogel ball is very sensitive to decelerating rotational impacts, experiencing significant deformation during the process. A finite-element code is written to simulate the process. The hydrogel ball is modeled as a poroelastic material infused with fluid and its coupling with the suspending fluid is handled by an arbitrary Lagrangian-Eulerian method. The results indicate that the density contrast, as well as the rotational velocity difference, between the hydrogel ball and the suspending fluid, play a central role in the ball's deformation due to centrifugal forces. This approach contributes to a deeper understanding of brain injuries and may portend the development of preventive measures and improved treatment strategies.

Oscillating foil turbines (OFTs) can be used to produce power from rivers and tides by synchronizing their heaving motion with the strong lift force of vortices shed at their leading edge. Prior work has shown that compliant membrane OFTs, which passively camber, exhibit enhanced leading edge vortex (LEV) stability and improved lift and power compared with rigid foil OFTs for specific kinematics. This work seeks to understand (a) the performance of compliant membrane OFTs over their full kinematic parameter space and (b) separate the roles of membrane camber and extensibility in LEV stabilization. We characterize the performance of a compliant membrane OFT over a wide range of kinematic parameters through prescribed motion experiments in a free-surface water flume. The optimal frequency of the compliant membrane OFT is found to be lower than that of a rigid foil OFT due to the enhanced LEV stability of the membrane. The lift and power of compliant and inextensible membrane foils are then compared to determine whether camber alone is effective for LEV stabilization or if extensibility plays an important stabilizing role. The deformation of the compliant membrane OFT is measured using laser imaging. We observe that the role of extensibility changes for different angles of attack. At low angles of attack, membrane deformation is consistent through the half cycle coinciding with similar performance to the inextensible foil. At higher angles of attack, the compliant foil has a larger deformation and dynamically decambers corresponding with delayed stall and enhanced lift and power.

We present numerical simulations investigating the evolution of liquid droplets into baglike structures in turbulent airflows. The droplet bag breakup problem is of significance for many multiphase processes in scientific and engineering applications. Turbulent fluctuations are introduced synthetically into a mean flow, and the droplet is inserted when the air-phase turbulence reaches a statistically stationary state. The morphological evolution of the droplet under different turbulence configurations is retrieved and analyzed in comparison with laminar aerobreakup results. While the detailed evolution history of individual droplets varies widely between different realizations of the turbulent flow, common dynamic and morphological evolution patterns are observed. The presence of turbulence is found to enhance the drag coefficient of the droplet as it flattens. At late times, the droplet becomes tilted and increasingly corrugated under strong turbulence intensity. We quantify these phenomena and discuss their possible governing mechanisms associated with turbulence intermittency. Lastly, the influences of liquid-gas viscosity ratio are examined and the implications of air-phase turbulence on the later bag film breakup process are discussed.

The transport of matter by turbulent flows plays an important role, in particular in a geophysical context. Here, we study the relative movement of groups of two (pairs) and four (tetrahedra) Lagrangian particles using direct numerical simulations of the stably stratified Boussinsesq equations, with Brunt-Väisälä frequency $N$ and Coriolis parameter $f$. We cover regimes close to homogeneous isotropic turbulence, to flows dominated by stratification and rotation, keeping fixed the ratio $N/f=5$. The flows studied are anisotropic, so the relative motion between two particles depends not only on the initial separation between the particles, but also on their orientation with respect to the vertical axis. In all cases considered, we demonstrate that the relative particle motion differs depending on whether dispersion is considered forward or backward in time, although the asymmetry becomes less pronounced when stratification and rotation increase. On the other hand, the strong fluctuations in the dispersion between two particles become more extreme when $N$ and $f$ increase. We also find evidence for the formation of shear layers, which become more pronounced as $N$ and $f$ become larger. Finally, we show that the irreversibility on the dispersion of a set of particles initially forming a regular tetrahedron becomes weaker when the influence of stratification and rotation increases, a property that we relate to that of the perceived rate-of-strain tensor.

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.

The transition route from laminar to turbulent flow in a magnetohydrodynamic (MHD) duct with a square cross section is investigated in the limit of low magnetic Reynolds number. In the presence of a transverse magnetic field, Hartmann and Shercliff layers are present on the walls orthogonal and parallel to the field direction, respectively. We assume reflection symmetries in both transverse directions, and investigate the competition between transition mechanisms specific to each boundary layer using direct numerical simulations. Independently of the initial location of a finite perturbation, transition relies exclusively on a tripping of the Shercliff layer by perturbations, while the Hartmann layer plays a passive role. This is explained, using a dynamical systems interpretation, by the spatial localization of the edge states in the Shercliff layer at the expense of the Hartmann layer. The link between these nonlinear coherent structures and the linear optimal modes known from nonmodal stability and energy stability theory is pointed out.

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

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

We 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.