We show that floating ice blocks with asymmetric shapes can self-propel with significant speeds due to buoyancy-driven currents caused by melting. In water baths with temperatures between $10{}^{\circ }\mathrm{C}$ and $30{}^{\circ }\mathrm{C}$, model right-angle ice wedges are found to move in the direction opposite to the gravity current which descends along the longest inclined side. We describe the measured speed as a function of the length and angle of the inclined side, and the temperature of the bath in terms of a propulsion model which incorporates the cooling of the surrounding fluid by the melting of ice. The heat pulled from the surrounding liquid by the melting ice block generates a thermal convection flow, leading to momentum exchange and a net propulsion force. The translation velocity is explained by balancing the propulsion force by drag. We further show that the ice block moves robustly in a saltwater bath with ocean-like salinity and maintains the same direction of motion as in freshwater. A simplified model is further developed to describe the propulsion of asymmetric ice blocks in saltwater, incorporating the effects of rising meltwater and the sinking of the surrounding bath water due to cooling. For sufficiently large temperature, we find that the cooling-induced sinking flow generates a stronger force than the upward flow from the meltwater. Consequently, the net propulsion force is in the same direction and nearly the same magnitude as that observed in freshwater. These findings suggest that melting-driven propulsion may be relevant to the motion of icebergs in sufficiently warm oceanic environments.

Liquid films coating vertical cylinders can form annular liquid collars which translate downwards under gravity. We investigate the dynamics of a thin viscoplastic liquid film coating the interior or exterior of a vertical cylindrical tube, quantifying how the yield stress modifies both the Rayleigh-Plateau instability leading to collar formation and the translation of collars down the tube. We use thin-film theory to derive an evolution equation for the layer thickness, which we solve numerically to examine the nonlinear dynamics. Instability and collar formation occur when gravity is sufficiently strong to make the fluid yield initially. We use matched asymptotics to derive a model describing the quasisteady translation of a slender liquid collar when the Bond number is small. The structure of the asymptotic solution for a viscoplastic collar shares some features with the Newtonian version, but there are several novel asymptotic regions that emerge at the two ends of the collar. The global force balance, which determines the collar's speed, is modified by a leading-order contribution from viscous drag in the collar when the liquid is viscoplastic. We use the asymptotic model to describe slow changes in collar volume when the film thicknesses ahead of, and behind, the collar are unequal. When the film thickness ahead of the collar is less than a critical value that we determine, viscoplastic collars adjust their volume and reach a steadily translating state. This contrasts with the Newtonian problem, where the only state in which steady translation occurs is unstable to small changes in the film thickness.

A dynamic averaging algorithm combined with a high-order spectral (HOS) model is introduced for wave reconstruction and prediction using radar data from stationary or moving ships. The algorithm enables gradual reconstruction of waves entering the radar's blind zone and improves accuracy by reducing the effects of shadowing modulation, particularly under steep wave conditions. The effects of nonlinearity on wave prediction accuracy are examined across a range of sea states with varying wave steepness and directional spreading angles. Results show that the HOS model, which includes third-order nonlinear effects, outperforms both linear and second-order models. Its advantage is especially clear in steep or narrowly spread wave fields, where simpler models fail to accurately predict the timing and height of large waves, leading to wave prediction errors at the ship's position up to three times higher than those from the HOS model. Additionally, when the ship slows down in head waves or speeds up in following waves, the relative velocity between the waves and the ship decreases. This reduction in relative speed extends both the time required for accurately reconstructing waves in the blind zone and the length of the predictable wave field ahead of the ship.

Ice melting is a complex, dynamic, and multiscale process involving many feedback effects. An essential but poorly understood factor for floating ice is the potential to overturn, as dramatically demonstrated by capsizing icebergs. Here we study the melting-induced reshaping of ice coupled to its free rotation dynamics and find that periods of stable equilibrium are punctuated by spontaneous capsize events. Laboratory experiments on floating ice show that melting produces faceted and angular shapes whose tendency to orient to the waterline is repeatedly upset by rolling over. Similar geometries and motions are reproduced in simulations that drive the shape development via differential melt rate over the surface and which solve for the rotational dynamics subject to shape-dependent forcing from gravity, buoyancy, and hydrodynamics. Melting gradually drives the structure toward postural instability while also priming other orientations that prove stable when reached by abrupt flipping. These findings show how the shape and motions of ice are inextricably linked at fundamental scales, and they reveal mechanisms that may be operative for natural conditions.

We study the dynamics of sail membranes during a model of a tacking maneuver, when the sail angle of attack is reversed in order to sail upwind. In successful tacking the sail flips to the mirror-image shape, while in unsuccessful tacking the sail remains stuck in a metastable state close to the initial shape. We investigate whether the sail flips, and if so, how long it takes and the subsequent dynamics, over a parameter space that describes the sail membrane properties and the kinematics of tacking. We find that the “steady” parameters—stretching rigidity, pretension, and angle of attack—mostly determine whether a membrane flips or not. Flipping is more likely with larger values of the stretching rigidity, pretension, and angle of attack. The dynamical parameters—membrane mass density, concavity of angle-of-attack transition kinematics, and time length of the tacking maneuver—mainly affect how long flipping takes. With large membrane mass the membrane can maintain the momentum from the tacking motion long enough to reach the flipped state, but it may also take longer to converge to a steady shape. Concave-down angle-of-attack profiles and small tack times are generally associated with shorter flip times but a few exceptions exist, because these kinematics can also give a larger acceleration to the fluid-sail system that persists for longer times. We also investigate slack sails and find that they are more difficult to flip.

This study examines the dynamics of roll waves that spontaneously arise in muddy debris flows, where phase separation is not observed. To this end, a set of bulk mass and momentum balance equations is derived from the depth-averaged model proposed by Meng et al. [J. Fluid Mech. 943, A19 (2022)]. The derived equations are shown to be well-posed, with the threshold Froude number for flow instability slightly exceeding the classical $2/3(1-\mathrm{\Gamma })$, which corresponds to dry granular flows on rough planes. A high-resolution shock-capturing scheme is employed to resolve the evolution of debris roll waves, which emerge from initially steady, uniform flows subjected to sinusoidal perturbations. These waves grow under the influence of inertial forces and eventually saturate into steady, traveling waveforms. A traveling-wave solution is subsequently constructed, accurately capturing the steady traveling waves observed in the simulations. This theoretical framework is further applied to natural debris roll waves observed in the Illgraben torrent, Switzerland. Simulated time series of the flow depth and wave speeds, based on the $\mu \left(I\right)$-dependent basal granular friction law, exhibit excellent agreement with field measurements. Numerical results also reveal that large-amplitude waves, which carry significant mass flux, are dynamically unstable and tend to fragment into multiple smaller-amplitude waves. These smaller waves are overtaken and merged by trailing waves with larger amplitudes and faster propagation speeds, a phenomenon consistent with field observations.

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.

When particles of a few tens of microns are spread on the surface of water, they aggregate under the action of capillary forces and form a thin floating membrane, a particle raft. In a tank with a raft made of graphite powder, we generate in the laboratory gravity surface waves, whose wavelength about 17 cm is very large compared to the thickness of the raft of order $10\mathrm{\mu }\mathrm{m}$. For a sufficiently strong wave amplitude, the raft breaks up progressively by developing cracks and producing fragments whose sizes decrease on a timescale long compared to the period of the wave. We characterize the breaking mechanisms. Then we investigate the area distribution of the fragments produced during the fragmentation process. The visual appearance of the fragments distributed in size and surrounded by open water bears a notable resemblance to the floes produced by the fracturing of sea ice by waves in the polar oceans. Fragmentation concepts and morphological tools built for sea ice floes can be applied to our macroscopic analog, on which the entire dynamic evolution is accessible. However, the mechanics of the two systems differ, as our particle raft breaks due to the viscous stresses, whereas the sea ice fractures due to its bending by the waves.

The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full three-dimensional information of the flow field in both high spatial and temporal resolution, a condition rarely satisfied in turbulence experiments, especially during field scale measurement of atmospheric turbulence. To circumvent this issue, an intermittency-anisotropy framework is proposed through which we successfully extract the features of small-scale anisotropy from single-point measurements of turbulent time series by exploiting the properties of small-scale intermittency. Specifically, this framework quantifies anisotropy by studying the contrasting effects of burstlike activities on the scalewise production of turbulence kinetic energy between the horizontal and vertical directions. The veracity of this approach is tested by applying it over a range of datasets covering an unprecedented range in the Reynolds numbers $(\mathrm{Re}\approx {10}^3–{10}^6)$, sampling frequencies (10 kHz to 10 Hz), surface conditions (aerodynamically smooth surfaces to typical grasslands to forest canopies), and flow types (channel flows, boundary-layer flows, atmospheric flows, and flows over forest canopies). For these diverse datasets, the findings indicate that the effects of small-scale anisotropy persists up to the integral scales of the streamwise velocity fluctuations and there exists a universal relationship to predict this anisotropy from the two-component state of the Reynolds stress tensor. This relationship is important towards the development of next-generation closure models of wall turbulence by incorporating the effects of anisotropy at smaller scales of the flow.

In this experimental study on a methane-hydrogen fired laboratory-scale pressurized annular combustor, various steady and transient operating conditions were explored. Under steady operation, the thermoacoustic stability depended strongly on the equivalence ratio, but only weakly on the mass flow rate and hydrogen power fraction. During transient equivalence-ratio ramps, the predominant instability of the system switched between standing and spinning azimuthal modes. The ramping rate influenced the thermoacoustic amplitude during the switching, as well as the onset and decay of the different modes. The strong acoustic reflection at the choked outlet produced significant harmonic content during both steady and transient operation. Nonlinear time-series analysis and clustering algorithms showed that the Jensen-Shannon complexity and the permutation entropy could accurately classify the modal dynamics in an unsupervised manner. The classification revealed that standing azimuthal modes, with several preferred orientations, dominated under steady operation. The amplitude of the heat-release-rate (HRR) oscillations around the annulus depended on the mode orientation. The energy contribution from the harmonic components was isolated via bandpass filtering, revealing that the orientation of the first harmonic ($n=2)$ followed the fundamental mode, eliminating negligible HRR oscillation regions at the pressure node of the fundamental mode. By filtering out the higher-order harmonic content, intermittent switching between high-amplitude periodicity and low-amplitude chaos in the fundamental azimuthal mode was uncovered. Tools from dynamical systems theory confirmed the existence of chaos and demonstrated that the intermittency belongs to the type-II Pomeau-Manneville class. This study provides evidence of the type-II intermittency route to chaos in an annular combustor with longitudinal and azimuthal modes.

The exploration of a two-dimensional wind-driven ocean model with no-slip boundaries reveals the existence of a turbulent asymptotic regime where energy dissipation becomes independent of fluid viscosity. This asymptotic flow represents an out-of-equilibrium state, characterized by a vigorous two-dimensional vortex gas superimposed onto a western-intensified gyre. The properties of the vortex gas are elucidated through scaling analysis for detached Prandtl boundary layers, providing a rationalization for the observed anomalous dissipation. The asymptotic regime demonstrates that boundary instabilities alone can be strong enough to evacuate wind-injected energy from the large-scale oceanic circulation.

When a drop of a volatile liquid is deposited on a uniformly heated wettable, thermally conducting substrate, one expects to see it spread into a thin film and evaporate. Contrary to this intuition, due to thermal Marangoni contraction, the deposited drop contracts into a spherical-cap-shaped puddle, with a finite apparent contact angle. Strikingly, this contracted droplet, above a threshold temperature, well below the boiling point of the liquid, starts to spontaneously move on the substrate in an apparently erratic way. We describe and quantify this self-propulsion of the volatile drop. It arises due to spontaneous symmetry breaking of thermal Marangoni convection, which is induced by the nonuniform evaporation of the droplet. Using infrared imaging, we reveal the characteristic interfacial flow patterns associated with Marangoni convection in the evaporating drop. A scaling relation describes the correlation between the moving velocity of the drop and the apparent contact angle, both of which increase with the substrate temperature.

We experimentally investigate the amplitude of the common sound heard when we pour water, tea, or coffee on a filled receptacle. Using water jets from circular nozzles, we find that pouring is audible when the nozzle distance from the free surface is above one-third of the jet breakup length. The sound amplitude increases with the steepness of the jet corrugation, informing that thin jets are louder than thick ones for a given pouring height. Since the jet corrugation is related to the air entrainment rate, the sound of pouring can serve as a practical noninvasive probe in aeration processes. After the jet breaks up into drops impacting on the free surface, the pouring sound amplitude increases with the nozzle diameter, unlike before breakup.

The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a classical problem. The gas–liquid interface is hydrodynamically unstable, forming striking fingerlike patterns that have attracted research interest for decades. Generally, both the gas and liquid phases are taken to be incompressible, with the capillary number being the key parameter that determines the severity of the instability. Here, we consider a radially outward displacement driven by the steady compression of a gas reservoir. The associated gas-injection rate is then unsteady due to the compressibility of the gas. We identify a second nondimensional parameter, the compressibility number, that plays a strong role in the development of the fingering pattern. We use an axisymmetric model to study the impact of compressibility number on the unsteady evolution of injection rate and gas pressure. We use linear stability analysis to show that increasing the compressibility number delays the onset of finger development relative to the corresponding incompressible case. Finally, we present and compare a series of experiments and fully nonlinear simulations over a broad range of capillary and compressibility numbers. These results show that increasing the compressibility number systematically decreases the severity of the fingering pattern at high capillary number. Our results provide an unprecedented comparison of experiments with simulations for viscous fingering, a comprehensive understanding of the role of compressibility in unstable gas–liquid displacement flows, and insight into a new mechanism for controlling the development of fingering patterns.

We present and analyze a theoretical model for the dynamics and interactions of “capillary surfers,” which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [I. Ho et al., Phys. Rev. Fluids 8, L112001 (2023)], we reported the results of an experimental investigation of the surfer system, which showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers' positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good agreement with experimental data. Moreover, we conduct a linear stability analysis of bound state solutions and compute numerically the associated eigenvalues. We find that the spacings of the bound states are quantized on the capillary wavelength, with stable branches of equilibria separated by unstable ones. Generally, our work shows that self-propelling objects coupled by capillary waves constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.

We present an experimental study of capillary surfers, a new fluid-mediated active system that bridges the gap between dissipation- and inertia-dominated regimes. Surfers are wave-driven particles that self-propel and interact on a fluid interface via an extended field of surface waves. A surfer's speed and interaction with its environment can be tuned broadly through the particle, fluid, and vibration parameters. The wave nature of interactions among surfers allows for multistability of interaction modes and promises a number of novel collective behaviors.

This paper is devoted to a specific motion observed for glycerin droplets sliding on a horizontal hydrophobic substrate under the influence of a shear flow. In this regime, the droplet elongates in the flow direction, adopting a rivulet shape. Waves develop on the droplet sheared surface, resulting in a wavy contracting and stretching motion mechanism, similar to the movement of a caterpillar. If long enough, the droplet can break up into several droplets that can be submitted to a pearling instability. Furthermore, these droplets can also coalesce.

The leading-edge vortex (LEV) formation on the caudal fin (CF) has been identified as playing a key role in efficient lift-based thrust production of fish-like propulsion. The enhancement of the CF LEV through its interaction with vortices formed upstream due to a median fin with a distinct shape is the focus of this paper. High-speed, high-fidelity videos and particle imaging velocimetry (PIV) were obtained from rainbow trout during steady forward swimming to visualize the undulatory kinematics and two-dimensional flow behavior. Body kinematics are quantified using a traveling-wave formulation that is used to prescribe the motion of a high-fidelity three-dimensional surface model of the fish body for a computational fluid dynamics (CFD) study. The pressure field of the CFD result is compared and validated with the PIV result from the experiment. Using CFD, the vortex forming and shedding behaviors of the anal fin (AF) and their capturing and interaction with the trunk (TK) and the CF are visualized and examined. Coherent AF-bound LEVs are found to form periodically, leading to thrust production of the AF. The vortices subsequently shed from the AF are found to help stabilize and reinforce the LEV formation on the CF by aiding LEV initiation at stroke reversal and enhancing LEV during a tail stroke, which leads to enhancement of lift-based thrust production. The CF is found to shed vortex tubes (VTs) that create backward-facing jets, and the ventral-side VT and the associated backward jets are both strengthened by vortices shed by the AF. An additional benefit of the AF is found to be reduction of body drag by reducing the lateral crossflow that leads to loss of beneficial pressure gradient across the body. Through varying AF-CF spacing and AF height, we find that CF thrust enhancement and TK drag reduction due to the AF are both affected by the position and size of the AF. The position and area of the AF that led to the most hydrodynamic benefit are found to be the original, anatomically accurate position and size. In this paper, we demonstrate the important effect of vortex interaction among propulsive surfaces in fish-like propulsion.

This study aims to understand the impact of instabilities and turbulence arising from canopy mixing layers on wind-driven wildfire spread. Using an experimental flume (water) setup with model vegetation canopy and thermally buoyant plumes, we study the influence of canopy-induced shear and turbulence on the behavior of buoyant plume trajectories. Using the length of the canopy upstream of the plume source to vary the strength of the canopy turbulence, we observed behaviors of the plume trajectory under varying turbulence yet constant cross-flow conditions. Results indicate that increasing canopy turbulence corresponds to increased strength of vertical oscillatory motion and variability in the plume trajectory/position. Furthermore, we find that the canopy coherent structures characterized at the plume source set the intensity and frequency at which the plume oscillates. These perturbations then move longitudinally along the length of the plume at the speed of the free stream velocity. However, the buoyancy developed by the plume can resist this impact of the canopy structures. Due to these competing effects, the oscillatory behavior of plumes in canopy systems is observed more significantly in systems where the canopy turbulence is dominant. These effects also have an influence on the mixing and entrainment of the plumes. We offer scaling analyses to find flow regimes in which canopy induced turbulence would be relevant in plume dynamics.

Air vehicles of all scales are susceptible to large-amplitude gusts that may lead to vehicle damage and instability. Therefore, effective physics-based control strategies and an understanding of the dominant unsteady flow physics underpinning gust encounters are desired to improve safety and reliability of flight in these conditions. To this end, this paper develops and experimentally demonstrates a proportional output-feedback lift regulation strategy based on the classical unsteady aerodynamic theories of Wagner and Küssner for wings encountering large-amplitude transverse gusts without a priori knowledge of gust strength or onset time. The tested vertical gust velocities ranged between 25% and 71% of the freestream speed. This strategy is found to successfully generalize to gusts of different strengths and directions, as well as wings at pre- and post-stall angles of attack. In addition, this paper applies dynamical systems analysis to Wagner's aerodynamic model to reveal the effect of the pitch-axis location, pitch input, and closed-loop feedback gains on the stability and robustness of the system along with the flow physics responsible. The real-time output feedback control strategy is experimentally tested in a water tow tank facility equipped with a transverse gust generator. Time-resolved force and flow-field measurements are used to discover the salient flow physics during these encounters and illustrate how closed-loop actuation mitigates their lift transients.