Intermittency is one of the central obstacles for understanding small-scale dynamics in the fully developed hydrodynamic turbulence. The modern approach is largely based on the multifractal theory of Parisi and Frisch which is, however, phenomenological. It was shown recently that the intermittency can be related to the hidden scale invariance. The latter is a statistical scaling symmetry unbroken in a rescaled (projected) formulation of equations of motion. In the present paper, we consider a shell model of turbulence and describe how the hidden symmetry manifests itself through all scales, both in the inertial interval and in the transition to forcing and dissipation ranges. In the inertial interval, we derive anomalous scaling laws from the hidden symmetry. Then we show how a complicated form of the dissipation range is controlled by intermittent rescaled Reynolds numbers within a large range of dissipation scales. This dissipative intermittency can be removed by using a special class of dissipation models. For such models, the hidden scale invariance is restored both in the inertial interval and the dissipation range. Overall, the presented approach deduces the multifractal theory and some of its basic conclusions from the hidden scaling symmetry of equations of motion.

The enhancement of skin-friction drag and surface heat flux by the transition to turbulence is a crucial physical phenomenon for the design of high-speed vehicles. An interpretable mapping of how various flow phenomena such as turbulence and the streamwise growth of the boundary layer (BL) thickness influence these key surface quantities is desirable for advancing our understanding of fundamental flow physics, as well as informing engineering design analysis. To accomplish such a mapping, an angular momentum integral (AMI) equation, originally derived for incompressible flows by Elnahhas and Johnson [J. Fluid Mech. 940, A36 (2022)], is here introduced for compressible turbulent BL flows of a calorically perfect gas. By isolating the laminar BL friction at the same Reynolds number, the AMI equation obtains a straightforward interpretation for skin-friction alteration by other flow phenomena relative to an equivalent laminar BL. Similarly, a moment of total enthalpy integral (MTEI) equation is proposed to quantitatively map the effects of turbulence and other physical flow phenomena to the Stanton number relative to an equivalent laminar BL. Direct numerical simulations (DNSs) of zero pressure gradient isothermal flat plate BLs up to edge Mach number of 7 are used to demonstrate the utility of the AMI and MTEI equations. The DNS cases span a variety of wall-temperature boundary conditions ranging from nominally adiabatic to strongly cooled walls. The derivation of the AMI equation itself suggests the use of shear stress-weighted average viscosity, which collapses the relative influence of turbulence on compressible BL skin friction over the wide range of edge Mach numbers and temperature boundary conditions considered. The AMI results quantify how the variation of mean density inside a turbulent BL impacts the ability of correlated velocity fluctuations to transport momentum and enhance the skin friction coefficient relative to the equivalent laminar BL. From an alternative viewpoint, the results demonstrate how the effect of compressibility on laminar BLs can be used to gain insight into turbulent BLs. The MTEI results similarly demonstrate how the mean density alters the impact of turbulence on the transport of total enthalpy and Stanton number. In doing so, the MTEI results highlight the relative role of turbulent fluxes of enthalpy and mean kinetic energy on the Stanton number. In light of these results, the AMI and MTEI equations provide a quantitative perspective on the fundamental physics of skin friction and surface heat flux in high-speed BLs, which may prove useful for evaluating flow control schemes and complementing existing analysis tools.

While understanding breaking waves is crucial for the development of parametrizations used in ocean wave modeling for both deep and shallow water, the complete process of wave breaking is not well understood. Here we present direct numerical simulations of two-dimensional solitary waves that shoal and break on a uniform beach in shallow water, with the presence of storm surge represented by an inshore region. The storm surge depth, beach slope, and wave amplitude are varied to study the dependence of energy dissipation in the breaker on wave and bathymetric parameters. We classify wave breaker types and find a separation between plunging and spilling breakers when scaled by breaking amplitude and depth. We compare energy dissipation during the breaking process with results from the literature without storm surge. A representation of energy dissipation in this solitary wave breaker data is also compared with prior experiments and simulations of breakers in deep water, and possibilities of a unifying model are explored. We conclude that a previously developed shallow-water inertial dissipation model for wave breaking on a uniform slope can be extended to this storm surge environment with good data collapse, and we further discuss possibilities for a general parametrization of wave breaking valid across different depth regimes.

Bubbles appear when a carbonated drink is poured in a glass. Very stable bubble chains are clearly observed in champagne, showing an almost straight line from microscopic nucleation sites from which they are continuously formed. In some other drinks such as soda, such chains are not straight (not stable). Considering pair interactions for spherical clean bubbles, bubble chains should not be stable, which contradicts these observations. The aim of this work is to explain the conditions for bubble chain stability. For this purpose, experiments and direct numerical simulation are conducted. The bubble size as well as the level of interface contamination are varied to match the range of parameters in typical drinks. Both factors are shown to affect the bubble chain stability. The transition from stable to unstable behavior results from the reversal of the lift force, which is induced by the bubble wake. A criteria based on the production of vorticity at the bubble surface is proposed to identify the conditions of transition from stable to unstable bubble chains. Beyond carbonated drinks, understanding bubble clustering has impact in many two-phase problems of current importance.

Cleaning surfaces with air bubbles in an aqueous medium has been a topic of discussion in recent years due to the growing interest in sustainable methods for cleaning biological surfaces such as agricultural produce. Specifically, in a bubble-injection method, inclined surfaces are targeted by many millimetric air bubbles that collide with and slide along the surface. The collision and subsequent sliding of these air bubbles exert shear stress on the surface, causing contaminants to be removed. The shear stress is proportional to the tangential speed of the bubble with respect to the surface divided by the thickness of the thin film of liquid between the bubble and the solid surface. In this study, we conduct experiments to test the cleaning efficacy at different angles of inclination of a contaminated surface. We use two different types of surface coated with either a protein solution or a bacterial biofilm. Our experimental results indicate that bubbles exhibit the highest cleaning efficacy at the surface angle of $\theta \approx {20}^{\mathrm{o}}$ with respect to the horizontal plane for polydisperse bubbles in the range of 0.3–2 mm and with an average radius of 0.6 mm. To gain a better understanding of the underlying mechanism, we perform a numerical analysis of a single air bubble colliding with a clean surface at various angles. Our numerical and theoretical results show that the average shear force that the bubble exerts on the surface reaches a maximum at $\theta \approx 22.5^{\mathrm{o}}$ which agrees well with the experiments. We also compare the maximum shear stress in sliding phase with the shear stress required for removing different types of bacteria as a fluid-mechanics-based guideline for geometrical design of bubble cleaning devices.

We investigate the cleaning mechanism of an oil-impregnated porous surface by utilizing a method of vortex ring interaction. The kinetic energy of a vortex ring is exploited to expunge the trapped oil from the spherical-bead-based porous surface. Qualitative and quantitative measurements were made using high-speed shadowgraphy imaging, planar laser-induced fluorescence (PLIF) imaging, and particle image velocimetry (PIV) techniques. The interaction phenomenon is explored from the perspective of vortex ring dynamics followed by oil sheet dynamics. Five different strengths of a vortex ring [characterized by the circulation ($\mathrm{\Gamma }$) -based Reynolds number (${\mathrm{Re}}_{\mathrm{\Gamma }}=2550$–14 260: ${\mathrm{Re}}_{\mathrm{\Gamma }}=\mathrm{\Gamma }/\nu$, where $\nu$ is the kinematic viscosity)] and two types of surface porosity ($\varphi$) (open area ratio, 0.21 and 0.41) are considered for parametric analysis. The interaction process with oil is divided into three regimes: (i) penetration, (ii) bag formation, and (iii) bag breakup. Depending on the strength of the vortex ring, it is observed that surface cleaning takes place from both upstream and downstream regions of the porous surface. The vortex rings with higher ${\mathrm{Re}}_{\mathrm{\Gamma }}$ can expunge more oil through a complicated interaction process involving Rayleigh-Taylor- and Rayleigh-Plateau-type instabilities. However, along with ${\mathrm{Re}}_{\mathrm{\Gamma }}$, the interaction dynamics depend strongly on the shape and $\varphi$ value. The interaction process is characterized by vorticity cancellation, Kelvin-Helmholtz (KH) instabilities, and three-dimensional interactions.

We investigate the effect of a forest of pillars on a granular layer steadily flowing over a rough inclined plane. We quantify experimentally how the steady flow rate of grains is affected by the interpillars distance for different layer thicknesses and slope angles. We then propose a model based on a depth-average approximation associated with $\mu \left(I\right)$ rheology that considers the additional force exerted by the pillars on the granular layer. This model succeeds in accounting for most of the observed results when taking into account some inertia due to the nonvanishing Froude number of the flow.

Production, drainage, and stability of foam films, i.e., films in contact with their menisci, are fascinating problems that remain still unsolved. In this article, we propose to explore the regime of large velocities and large film sizes. This is not accessible in experiments classically conducted in the literature and allows us to study the regime of large extension and large extension rates. With our setup, we make soap films up to 2 m high by pulling a horizontal fishing line driven by belts out of a soapy solution at velocities ranging from 20 cm/s to 250 cm/s. We characterize the thickness profile of the central part of the film that behaves like a rubber band under tension. We show that its thickness profile is well described by a static model in which a homogeneous elastic film is stretched by its own weight. This leads to an exponential thickness profile with a characteristic length given by a competition between gravity and surface elasticity. The prefactor is fixed by the shape and area of the film, governed by the fishing line motion but also by a continuous extraction of foam film from the lateral menisci, thicker than the central part, and that progressively invades the film from its lateral boundaries. The model we propose captures the subtle interplay between gravity, film elasticity, and film extraction and leads to predictions in good agreement with our experimental data.

The flow-induced vibration of a whisker in the wake of a movable circular cylinder with time-varying streamwise gaps was experimentally investigated to understand how whiskers detect the variation of upstream target's swimming status. A time-resolved particle image velocimetry was used to characterize the vortex flow dynamics and vibrations of whisker across various initial gaps and gap growth rates. Results showed that despite the time-varying gaps, the evolution of vortex flow and whisker dynamics remained overall synchronized. Due to the nonlinear decaying rate of vortex strength along streamwise direction, the vibrations of whisker sensor were more sensitive to gap growth rates with smaller initial gaps. However, the sensitivity of whisker (i.e., the decaying rate of whisker vibration intensity over unit time) to gap growth rates gradually decreased when such growth rate became sufficiently high, regardless of initial gaps. Using a physical model based on the balance between whisker inertial force, system damping, restoring force, and flow loading with time-varying magnitudes, we well described the response of whisker sensor in the cylinder wake flow; the model revealed that the reduction of whisker's sensitivity under high gap growth rate was attributed to the sufficiently strong vortices initiated by the fast movement of upstream cylinder, which compensated the influence of vortex strength decay due to the growth of gap. In addition to cases with whisker vibrating in the wake centerline, our complementary measurements with the whisker in the cylinder edge highlighted the time-varying equilibrium vibration positions of whisker sensor due to the “wake-stiffness” effect.

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.