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.

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.

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.

An experimental investigation of the Richtmyer-Meshkov instability is conducted in spherical geometry, where convergence effects are more pronounced and the vorticity distribution is specific to the geometry. The gas lens technique is employed within a conical chamber to generate a spherical converging shock wave. This shock wave triggers the instability at a single-mode $\mathrm{air}/{\mathrm{SF}}_6$ interface for two different initial amplitudes. The displacement and the growth of the perturbations at the interface are monitored using a high-speed Mie-scattering laser tomoscopy method, and the results are compared to numerical simulations and new theoretical predictions. The instability amplitude initially grows, stabilizes, and then reduces before the arrival of the reflected shock wave. Numerical simulations demonstrate good agreement with the experiments, and they indicate a weak effect of the installed grid materializing the perturbation. In addition to the experimental and numerical results, the theoretical model developed here agrees well with the experiments, although a time shift is observed between theory and experiments in the stabilization regime. A comparison to other models available in the literature shows that, in the studied configurations, compressibility has a negligible effect on the development of the instability. Our model demonstrates that convergent Rayleigh-Taylor effects are the main stabilizing mechanisms in these configurations.

In this study, we investigated the dynamics of a droplet impacting and oscillating a polycarbonate cantilever beam of nine varying lengths. We analyzed the cantilever's damping and vibration frequency in relation to a resonance length, where the frequencies of the droplet and the cantilever are equal. In shorter beam lengths, the beam vibrates at a frequency higher than that of the droplet. Upon reaching the resonance length, the frequencies of both the droplet and the cantilever align, and the cantilever is out of phase with the oscillation of the droplet's apex. This leads to increased damping rates. At this resonance length, the droplet's force and the direction of the cantilever oppose each other. When the cantilever length exceeds the resonance length, it synchronizes more with the droplet apex. This alignment allows the droplet force and the cantilever to work in phase. Our findings provide fundamental insights into the damping effect of droplet impacts on elastic surfaces around resonance.

The Faraday instability has been extensively studied in bounded containers but only recently has research on this phenomenon in flexible domains been conducted. Here, we study floating liquid droplets with Faraday waves excited on their surface, which undergo a slow time evolution toward a stable noncircular shape. We develop a theoretical model for the evolution of the boundary of the droplet, thus allowing us to simulate its full transient motion toward steady state. By changing the forcing frequency and amplitude of our system, we observe a variety of stable droplet shapes. We experimentally measure the geometrical properties of these droplets and conditions under which different shapes are stable, which match our theoretical predictions well. Interesting transient behavior such as hysteresis is also discussed, where the final droplet shape depends on its previous shape. Finally, we touch upon droplets that do not reach a steady state shape, instead oscillating periodically in time or rotating at a constant angular velocity.

This study aims to evaluate the effect of freestream turbulence (FST) on wakes produced by disks with different porosity. The wakes are exposed to various freestream turbulence “flavors,” where turbulence intensity and integral length scale are independently varied. The turbulent wakes are interrogated through hot-wire anemometry from 3 to 15 diameters downstream of the disks. It is found that disks with low porosity behave similarly to a solid body, in terms of both entrainment behavior and scaling laws for the centerline mean velocity evolution. Far from the disks, the presence of FST reduces both the wake growth rate and entrainment rate, with a clear effect of both turbulence intensity and integral length scale. As porosity increases, these “solid body” FST effects gradually diminish and are reversed above a critical porosity. The entrainment behavior in disk-generated wakes is significantly influenced by the presence of large-scale coherent structures, which act as a shield between the wake and the surrounding flow, thus impeding mixing in the near wake. We found that higher porosity, turbulence intensity, or integral length scale weakens the energy content of these structures, thereby limiting their influence on wake development to a shorter distance downstream of the disk. This, in turn, potentially reduces the influence of large-scale engulfment on the overall entrainment mechanism to a shorter distance downstream of the disks as well. For low-porosity disks, freestream turbulence intensity initially promotes near-wake growth through the suppression of large-scale structures; however, farther downstream, the wakes grow faster when the background is nonturbulent.

To achieve decarbonization targets, wind turbines are growing in hub height and rotor diameter, and they are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is accomplished primarily through a simplified model form that neglects certain flow processes, such as atmospheric stability, and through the parametrization of ABL and wake turbulence through a wake spreading rate. In this study, we systematically analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large-eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the turbulence in the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We then analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the relative balance of turbulence and advection for both the streamwise momentum deficit and wake-added TKE primarily through the nonlinear interactions of the base flow with the deficit flow. The stable cases are most affected by increased shear and veer in the base flow and the neutral case is most affected by the increased ambient turbulence intensity. These differences in the base flow that arise from stratification are relatively more important than the buoyancy forcing terms in the wake-added TKE budget. The wake-added TKE depends on the ABL stability. An existing wake-added TKE model that neglects the effects of ABL stability yields $15–25\%$ error compared to large-eddy simulation, with errors that are higher in stable conditions than neutral. These results motivate future research to develop fast-running models of wake-added TKE that account for stability effects.

We investigate the dynamics of pendulum chains immersed in turbulent boundary layers. We combine qualitative video analysis of the artist Ned Kahn's kinetic façades of buildings, and laboratory experiments on a unidimensional weakly coupled chain of pendulums. We performed analysis of both the façades and the laboratory scale model. We show that pendulum waves traveled in the direction of the wind. These waves originate from the excitation by the spatiotemporal pressure fluctuations. We identified two dispersion relation branches. The first branch corresponds to a resonant response of each pendulum at its natural frequency of oscillations. The second branch corresponds to an excitation by the advected pressure fluctuations along the chain. Using local pressure sensors, we show a quantitative agreement between the convection velocity of the pendulum chain waves and the pressure fluctuations. Eventually, we propose a model in Fourier space to describe the magnitude of each branch. We show that at a small wind speed, the pendulum response is dominated by the resonance at their natural frequency. At larger wind speed, the response becomes dominated by the advected pressure fluctuations.

In this study, we conduct numerical investigations into the impact of droplet collisions on solid surfaces, with a specific focus on the influence of wettability and initial diameter. Previous studies have proposed two distinct scaling laws, namely $W{e}^{1/2}$ and $W{e}^{1/4}$, where $We$ denotes the Weber number, to describe the maximum spreading diameter ratio in the capillary regime. Our energy analysis reveals that only the $W{e}^{1/2}$ scaling accurately characterizes the capillary regime. Additionally, we elucidate that the observed data slope of $1/4$ arises from the $W{e}^{1/2}$ scaling while the initial diameter also plays a role within the low-$We$ range. To address this, we introduce a modified Weber number ($W{e}^{*}$), dependent on wettability, defined through energy conservation and accounting for the initial diameter $apriori$. Utilizing the $W{e}^{*}$, we establish a generalized scaling for the maximum spreading diameter ratio, enabling the consolidation of numerical and experimental findings onto a single curve, regardless of wettability. Furthermore, this scaling demonstrates excellent agreement with numerical results for both low and relatively high-$We$ regimes but without splashing.