We study the freezing of water drops on a copper substrate for temperatures ranging from $-9$ to $-79{}^{\circ }\mathrm{C}$. We propose a thermal and geometrical analytical model for the freezing front dynamics. It assumes a propagation of the front at the center described by the three-phase (liquid, ice, substrate) Stefan model in one dimension. The growth is characterized by an effective diffusion coefficient that increases as the substrate temperature decreases. We also consider a spherical front that meets the edges of the drop perpendicularly. Our model captures well our experimental data between $-9$ and $-40{}^{\circ }\mathrm{C}$ and highlights the importance of the heat diffusion in the liquid for the freezing process. Beyond these temperatures, the adhesion of the drops to the copper decreases and the substrate temperature must be considered equal to $-41{}^{\circ }\mathrm{C}$ to rationalize the experimental findings.

Steady polygonal hydraulic jumps have a complex flow structure and are formed when a circular jump loses stability through an increase in the downstream liquid height beyond a critical value. We report the experimental observation of a universal corner shape in polygonal hydraulic jumps over a wide range of experimental conditions that include the flow rate, weir geometry, and flow history, as defined by the tip radius of curvature and the corner angle. The tip radius of curvature is nearly constant over all experimental conditions, whereas the corner angle weakly depends on gravitational effects. Knowledge of the corner angle allows one to determine the global jump shape, as defined by a dimensionless geometry number related to the isoperimetric inequality, thus giving a complete description of the jump shape.

High-resolution wind detection plays a crucial role in aviation safety and aerodynamic research. A pulsed coherent Doppler wind lidar (CDWL) with sub-meter/sub-second resolution is demonstrated. The pseudorandom modulation (PRM) method is used to break the link between laser pulse duration and spatial resolution. Benefiting from the flexible pulse duration, the detection accuracy degradation related to the short pulse is largely mitigated. The backscattered spectra and wind profiles measured by the proposed lidar are compared with those obtained by a conventional pulsed CDWL, validating its capacity of radial wind detection within 700 m at 0.9 m/0.5 s resolution. With the help of the proposed high-resolution lidar, the meter-scale perturbation on the wind field from an electric fan is detected in a field experiment.

Dense suspensions of swimming bacteria exhibit chaotic flow patterns that promote the mixing and transport of resources and signaling chemicals within cell colonies. While the importance of active turbulence is widely recognized, the structure and dynamics of the resulting collective flows are the subject of intense investigation. Here, we combine microfluidic experiments with proper orthogonal decomposition (POD) analysis to quantify the dynamical flow structure of this model active matter system under a variety of conditions. In isotropic quasi-two-dimensional turbulence, the modal analysis encompasses the most energetic spatiotemporal flow structures across a range of suspension activity levels and benchmarks the potential for low-dimensional order representations of active turbulence. In confined geometries, POD analysis illustrates the role of boundary interactions for the transition to bacterial turbulence, and it quantifies the evolution of coherent active structures in externally applied flows. Beyond establishing the physical flow structures underpinning the complex dynamics of bacterial turbulence, the low-dimensional representation afforded by this modal analysis will facilitate data-driven modeling of active turbulence.

We present an experimental study of a new kind of dual drop-wave entity existing on a localized structure in a water Faraday-wave system. A nonpropagating hydrodynamic soliton can juggle a single drop of $\sim$2–3.5 mm diameter for about ${10}^2$–${10}^4$ rebounds. By analyzing the drop trajectories, several regimes are observed: periodic bouncing, period doubling, period tripling, a sawtooth state, and chaotic/erratic trajectories. We present evidence that the most stable cases result from detuning of the drop self-oscillations and synchronization with the soliton's sloshing motion. This synchronization ensures stability and thus longer lifetimes. We analyzed the lifetime of the drop, concluding that the periodic behavior, which appears for the lowest-amplitude solitons, is the most stable state. Further analysis shows that lifetimes follow a Weibull distribution.

In a viscoelastic flow over a microfluidic canopy of polymeric pillars, we report the spontaneous emergence of waves in the form of propagating regions of low flow velocity compared to the surrounding flow. The occurrence of the wave is chaotic and shows characteristics of elastic turbulence. We systematically study the coupling between the low-velocity wave and the microfluidic canopy by combining flow velocimetry experiments and high-speed tracking of the pillars. The waves form an angle $\pm \beta$ with the primary flow direction that depends on the geometry of the pillar array. If the canopy is composed of flexible structures, the passage of a wave deflects the structures locally in a manner reminiscent of the emergence of the Monami waves observed in inertial turbulence over canopies of vegetation. Due to the analogies with classical (inertial) canopy turbulence, we name our observed phenomenon canopy elastic turbulence.

Homogeneous and isotropic turbulence can be generated by many different mechanisms, from classical passive grids to jet arrays. By using high-speed jets, a jet array becomes a promising way to produce intense turbulence with large energy dissipation rates in water and wind tunnels. In this paper, a systematic experimental investigation was conducted to understand how the turbulence decay scales with the jet velocity, nozzle size, and nozzle spacings. Three-dimensional particle tracking was performed to quantify the spatial distribution of different turbulent characteristics. Combined with several previous experiments focusing on near-field measurements, our results provide a clear picture of the decay of the kinetic energy and the energy dissipation rate as well as the development of the inhomogeneity and anisotropy of turbulence generated by a jet array. Suggestions and design considerations for future wind and water tunnels are also provided.

Isolated supercooled water drops have been observed to move spontaneously while freezing in vacuum. This motion is caused by an increase of the evaporation rate during the early stages of freezing, which transfers momentum to the drops, similar to rocket propulsion. As in other cases of self-propulsion, symmetry breaking is necessary, and occurs when ice nucleation occurs away from the center of the drop. The self-propulsion velocity was modeled analytically for a simplified case, and numerically for two experiments. The model predicts peak velocities on the order of 1 m/s in vacuum, and a drop kinematics similar to that observed experimentally. In air, the self-propulsion velocity is expected to be much smaller but may be detectable for micron-sized drops.

Intermittent swimming, also termed “burst-and-coast swimming,” has been reported as a strategy for fish to enhance their energetical efficiency. Intermittent swimming involves additional control parameters, which complexifies its understanding by means of quantitative and parametrical analysis, in comparison with continuous swimming. In this study, we used a hybrid computational fluid dynamic (CFD) model to assess the swimming performance in intermittent swimming parametrically and quantitatively. A Navier-Stokes solver is applied to construct a database in the multidimensional space of the control parameters to connect the undulation kinematics to swimming performance. Based on the database, an indirect numerical approach named “gait assembly” is used to generate arbitrary burst-and-coast gaits to explore the parameter space. Our simulations directly measured the hydrodynamics and energetics under the unsteady added-mass effect during burst-and-coast swimming. The results suggest that the instantaneous power of burst is basically determined by undulatory kinematics. The results show that the energetical performance of burst-and-coast swimming can be better than that of continuous swimming, but also that an unoptimized burst-and-coast gait may become very energetically expensive. These results shed light on the mechanisms at play in intermittent swimming, enabling us to better understand fish behavior and to propose design guidelines for fishlike robots.

We present here the effect of mechanical vibrations on a breath figure. By impacting a falling steel ball on a plastic plate covered on its bottom side by a breath figure, we show that in a few milliseconds, the figure can evolve even more dramatically than it would in minutes in the natural aging process. We quantify the variations of droplet number and sizes with time for various substrate accelerations and mean initial droplets radii. We show that, above an acceleration threshold, the final number of droplets decreases more and more with acceleration. We interpret this result by the contact line unpinning provoking oscillations of the droplets radii, which makes the drops contact and coalesce with neighbors. Finally, we introduce a new parameter to characterize the droplet number decrease. We have plotted it as a function of an effective Bond number built with the substrate acceleration and mean droplet radius. Interestingly, all the data fall on a single master curve.

In this study, we present a series of simulations of gravity currents where ambient and intruding temperatures are on opposite sides of the temperature of maximum density. We use these simulations to describe how cabbeling (mixing of parcels of fluid that leads to a parcel of fluid that is denser) affects the evolution of gravity currents. We show that initially buoyant currents (called hypopycnal currents) undergo mixing in the body and tail region of the gravity current, which generates dense water from cabbeling. We investigate the maximum distance that the initial current progresses as a function of a parameter controlling the nonlinearity of the equation of state (referred to as $\mathrm{\Theta }$). We find that the maximum distance that the current progresses is a nonlinear function of $\mathrm{\Theta }$. For low $\mathrm{\Theta }$ hypopycnal currents reverse direction after they begin flowing, and cabbeling occurs over a limited spatial extent. As $\mathrm{\Theta }$ is increased, currents achieve a larger maximum distance of propagation, allowing the dense water formed by cabbeling to sink and form a secondary current along the bottom of the domain (called a hyperpycnal current). As we increase the parameter controlling the nonlinearity of the equation of state, the hyperpycnal current becomes much larger in scale. We discuss some general characteristics of the hyperpycnal current and highlight that once it forms, larger values of $\mathrm{\Theta }$ lead to a larger spatial extent of the current but narrower distributions of density and temperature.

Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number Le), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of ${\mathrm{Pr}}_t\approx 1$ and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as ${\mathrm{Le}}^{1/3}$, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a ${\mathrm{Le}}^{1/2}$ scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number $\mathrm{Pr}\approx 10$, slightly below that for cold seawater where $\mathrm{Pr}=14$. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate.

In one-dimensional (1D) evolution models of gas giant planets, an outer convection zone advances into the interior as the surface cools, and multiple convective layers form beneath that convective front. To study layer formation below an outer convection zone in a similar scenario, we investigate the evolution of a stably stratified fluid with a linear composition gradient that is constantly being cooled from above. We use the Boussinesq approximation in a series of two-dimensional simulations at low and high Prandtl numbers ($\mathrm{Pr}=0.5$ and 7), initialized with constant temperature everywhere, and cooled at different rates. We find that multiple convective layers form at $\mathrm{Pr}=7$, as the result of an instability in the diffusive thermal boundary layer below the outer convection zone. At low Pr, layers do not form because the temperature gradient within the boundary layer is much smaller than at large Pr and, consequently, is not large enough to overcome the stabilizing effect of the composition gradient. For the stratification used in this study, on the long-term the composition gradient is an ineffective barrier against the propagation of the outer convection zone and the entire fluid becomes fully mixed, whether layers form or not. Our results challenge 1D evolutionary models of gas giant planets, which predict that layers are long-lived and that the outer convective envelope stops advancing inwards. We discuss what is needed for future work to build more realistic models.

The transitional flow which initiates within the junction (anastomosis) of an arteriovenous fistula (AVF) is known to be a contributing factor in the onset of vascular disease. A novel treatment method involving the implantation of a flexible stent across the anastomosis has enabled the retention of a large proportion of functioning AVFs, despite the propensity for stent malapposition to occur at the sharp inner curve of the anastomosis. Large eddy simulations of a single patient-specific AVF with and without the presence of a stent captured oscillatory flow behavior emanating from the interface of the two inlet flows in the stent-absent case, however, these oscillatory features were subdued in the stented case. The stent-absent case generally had higher turbulent kinetic energy (TKE) in the anastomosis which led to larger cycle-to-cycle variations in wall shear stress (WSS). The significantly lower TKE generated at the heel of the stented AVF was contained within the malapposed stent, thereby resulting in lower WSS fluctuations. However, a slight increase in turbulence downstream of the malapposed stent edge was noted. This detailed study reveals a significant decrease in turbulence within the AVF in the presence of the stent, thereby providing a level of understanding underpinning the success of the treatment strategy (in this patient case) from a fluid dynamic perspective.

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by a small gap. The governing equation of flow within a Hele-Shaw cell is Darcy's law, which also describes flow through a porous medium. In this work, we derive a generalization to Darcy's law starting from a three-dimensional fluid with a parity-broken viscosity tensor with no isotropy. We discuss the observable effects of parity-odd fluids in various physical setups relevant to Hele-Shaw experiments, such as channel flow, flow past an obstacle, bubble dynamics, and the Saffman-Taylor instability. In particular, we show that when such a fluid is pushed through a channel, a transverse force is exerted on the walls, and when a bubble of air expands into a region of such fluid, a circulation develops in the far field, with both effects proportional to the parity-odd viscosity coefficients. The Saffman-Taylor stability condition is also modified, with these terms tending to stabilize the two-fluid interface. Such experiments can in principle facilitate the measurement of parity-odd coefficients in both synthetic and natural active matter systems.

In wall turbulence, meandering behaviors of large-scale structures observed in the logarithmic layer are a crucial spatial feature to understand the spatial organization of these structures and to improve the structure-based turbulence model. These structures extend from the near-wall region to the edge of boundary layers $\left(\delta \right)$. Thus, their meandering motions leave an imprint on the two-point turbulence statistics across the flow, especially in the logarithmic region. Herein, we demonstrate the influence of the meandering motions of wall-attached structures on the two-point correlation and the premultiplied two-dimensional spectra by analyzing the direct numerical simulation data of the turbulent boundary layer at ${\text{Re}}_{\tau }\approx 1000$. The meandering magnitudes of wall-attached structures increase with their height $\left(l_y\right)$ but significantly differ among the identified structures even at a given $l_y$. In addition, the wall-attached structures of streamwise velocity fluctuations $\left(u\right)$ are found to be aligned along with a preferred spanwise offset regardless of the meandering motion. This feature is confirmed through the conditional two-point correlations of $u$ within the meandering structures, which leads to a distinct X pattern in the logarithmic region. We further examine the spectral behavior of the meandering structures across the streamwise and spanwise wavelengths (${\lambda }_x$ and ${\lambda }_z$, respectively) through the premultiplied two-dimensional spectra. With increasing meandering magnitudes, the energy spectra are more inclined to the ${\lambda }_z$ direction. Furthermore, the energy spectra of the strong meandering structures are bounded by a linear relationship ${\lambda }_x\sim {\lambda }_z$ over the large-scale range, reminiscent of self-similar scaling predicted by the attached-eddy hypothesis. In particular, the upper bound is aligned along ${\lambda }_x\approx 2{\lambda }_z$ over ${\lambda }_z>\delta$, which is absent in the energy spectral of the total $u$. This result reveals that the meandering motions allow the large-scale structures to contain wide spanwise scale energy that is self-similar in the logarithmic region. Finally, a discussion on the near-wall parts of the meandering structures is given with an emphasis on Townsend's inactive eddies.

A circular jet breaks up into droplets via the Rayleigh-Plateau instability, retaining a circular cross section throughout. If, however, the nozzle from which the jet issues is elongated, the circular symmetry is broken, and the jet forms a chainlike structure with neighboring links separated by ${90}^{\circ }$. The cause of this structure is two-dimensional capillary-inertial oscillation of jet cross sections in their own plane. We perform an experimental study of chain oscillations as a function of flow rate using careful prelaminarization and 12 elliptical nozzles with different areas and eccentricities. The oscillation frequencies inferred from the observed chain-link structure do not agree with those predicted by Rayleigh's infinitesimal theory [L. Rayleigh, Proc. R. Soc. London 29A, 71 (1879)]. However, they do agree with an extended nonlinear theory of Bohr [N. Bohr, Philos. Trans. R. Soc. A 209, 281 (1909)] that accounts for finite-amplitude effects. This agreement shows that our fluid chains are nonlinear oscillations whose frequency decreases with increasing amplitude. We perform direct numerical simulations of chain oscillations using a volume-of-fluid method and find good agreement with the predictions of Bohr's theory. Finally, we generalize Bohr's theory to the case of two interacting modes with quadrupolar and octapolar azimuthal dependencies. The resulting solution explains qualitatively the “dimpled” shape of the jet's surface observed in the experiments.

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated, and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence it is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase sensitivity and vortex formation dynamics.

Mechanisms of droplet production from bursting bubbles have been extensively studied for single bubbles, but remain sparsely investigated in more complex collective settings. We discuss jet and film drop velocity-size relationships from physics-based mechanisms as a potential means to further differentiate between various mechanisms and correctly determine the drops origin. We report dynamical experiments of drop production by bursting bubbles in single and collective setups. In the collective bubbling experiment, subsurface quasimonodisperse bubbles are rising up to the surface where, depending on the surfactant concentration, they can either merge or assemble in rafts of monodisperse bubbles. Drop trajectories are recorded, analyzed, and shown to exhibit uniquely distinctive features for the different production mechanisms: centrifuge film drops are ejected sideways, and jet drops are ejected vertically. Different single-burst scalings are finally compared to the experimental size-velocity relationships, and reveal that drops coming from collective bubble bursting appear slower and more scattered than when coming from single bursting bubbles.

The hawkmoth is able to sustain a steady hover or level flight at lower speeds. However, previous wind tunnel experiments have suggested that long sequences of steady forward flight are less common at higher flying speeds ($>4.0\mathrm{m}/\mathrm{s}$) despite changes to the flight posture. This flying speed is about one-half of the theoretical prediction based on its body mass. It is unclear why hawkmoths have not been observed achieving steady flight at higher speeds. This paper aims to compare the aerodynamics involved in hawkmoth hovering to those in forward flight. High-speed video recordings and three-dimensional surface reconstruction were used to capture a hawkmoth's wing kinematics when hovering and at forward flight speeds of 2 and 4 m/s. Following reconstruction, the insect model was simulated using an in-house immersed-boundary-method based computational fluid dynamics (CFD) solver. The CFD solver provided a quantitative measure of the force generation, power consumption, and vortex structures generated during sustained flight. These results enabled the analysis of certain trends in how a hawkmoth adjusts flapping kinematics and its associated unsteady aerodynamics changes across different flight speeds. The results show that the moth minimizes drag as flying speed increases, but it immediately loses its lift producing upstroke even at the slow forward flight speed (2 m/s). A significant amount of negative lift is generated during upstrokes at the high forward flying speed (4 m/s). This negative lift in the upstroke potentially reduces maximum sustained flight speeds. This paper provides physical insight into the low-speed flights in flying insects.