The propagation of horizontal dam-break flows induced by the release of a rectangular column of a liquid phase into a negligible ambient fluid is investigated by combining numerical simulations and laboratory experiments. Varying both the geometry of the initial column and liquid properties, the parameter space covered allows the investigation of the transition from inertial to viscous slumping barely considered so far. In light of the Reynolds number $\mathrm{Re}$ based on the initial parameters of the fluid column, we report a newly investigated transient regime following the inertial slumping regime and prior to the viscous-dominated one. The transient intermediate regime is shown (i) to only exist for $\mathrm{Re}\gtrsim 10$ and (ii) to be characterized by an inertial overshoot followed by a strong deceleration of the front position accompanied by an excess and a deficit of fluid at the front and at the origin, respectively, with respect to the expected theoretical prediction of the viscous-dominated regime. Beyond the intuitive idea of an adaptive transition from the inertial to fully viscous slumping, these results highlight and quantify the influence of initial inertia on the spreading of a liquid, which may be particularly useful for modeling industrial and geophysical applications.

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence of gas kinetic effects, since the height of the gas lubrication film which is displaced during dynamic wetting is often comparable to the mean free path of the gas. At higher Weber and Reynolds numbers, on the other hand, inertial effects dominate and the density of the gas becomes important in determining whether a splash occurs. In this article, sphere impacts on a liquid body are investigated in a rarefied atmosphere using high-speed photography. It is found that the threshold entry speed for cavity formation is influenced by the density of the surrounding gas, whereas changing the mean free path of the gas has no effect. We attribute this phenomenon to the gas slowing the sealing of the thin crown sheet behind the sphere. This assertion is supported with experimental measurements of the liquid sheet thickness. In the range of parameters considered, the splash crown influences the movement of the contact line.

We present a framework to quantitatively describe energy exchange in high-speed turbulent flows, also including the hypersonic regime. Governing equations are introduced which control the transport of the mean-field kinetic energy ($k_m$), the turbulence kinetic energy ($k_t$), the mean-field internal energy ($e_m$), and the turbulence internal energy ($e_t$). The common terms in the transport equations are found to represent energy exchanges and interactions among $k_m, k_t, e_m$, and $e_t$. The routes of energy exchange are then highlighted and quantified in hypersonic boundary-layer flow, with special attention paid to the effects of wall cooling.

In this article, we present a predictive model for the amplitude of impulse waves generated by the collapse of a granular column into a water layer. The model, which combines the spreading dynamics of the grains and the wave hydrodynamics in shallow water, is successfully compared to a large dataset of laboratory experiments, and captures the influence of the initial parameters while giving an accurate prediction. Furthermore, the role played on the wave generation by two key dimensionless numbers, i.e., the global Froude number and the relative volume of the immersed deposit, is rationalized. These results provide a simplified, yet comprehensive, physical description of the generation of tsunami waves engendered by large-scale subaerial landslides, rockfalls, or cliff collapses in a shallow water.

The motion of a free rising skirt bubble is studied using direct numerical simulation covering the range of Eötvös (Bond) and Morton numbers where they can be observed. We investigate the skirt bubble motion (terminal velocity and drag), the flow field structure (inside the skirt film, around the bubble, and inside the gas film that forms the skirt) as well as the geometrical characteristics of the skirt (both length and thickness). A unified relation for the terminal velocity (and drag force) is provided for all bubble shapes (dimple, skirt, and spherical cap bubbles) when considering Eötvös numbers (based on bubble diameter) larger than 100. The velocity field around and inside the bubble is investigated resulting in the clarification of the wake structure with a major difference with the flow deduced from experimental observations during the 1970s. The numerical simulations reveal that only one recirculation is observed inside the bubble while two vortices are highlighted in the wake. We confirm that a parallel Poiseuille flow develops inside the skirt film resulting in an intense vorticity field. Original modeling is improved with a Reynolds correction that makes possible the prediction of the film thickness in very good agreement with the only experimental value available in the literature. Our simulations combined with experimental observations suggest the existence of a maximum value for the skirt length.

An experimental investigation is conducted to evaluate the effect of polymer injection on the development of a zero-pressure-gradient bypass transitioning boundary layer on a flat plate. Planar particle image velocimetry and planar laser-induced fluorescence measurements conducted at multiple streamwise stations allow for a characterization of the development of the bypass transition process induced by a two-dimensional trip wire in both Newtonian and polymer-injected flow. Two different trip placements with respect to the injection slot are considered to study the effect of polymer injection within the wake of the trip wire and within the laminar boundary layer upstream of the trip. The transition process is initiated in a separated shear layer downstream of the trip wire, where a rapid amplification of the velocity perturbations via an inflectional Kelvin-Helmholtz instability leads to vortex shedding and subsequent breakdown to turbulence. A similar transition process is observed with polymer injection, but a more rapid initial growth of perturbations is observed, leading to earlier transition. Nonetheless, an onset of polymer effect is seen in the late transition stages and leads to significant levels of drag reduction in the developing turbulent boundary layer.

When the interface between a dielectric and a conducting liquid is excited by an oscillatory electric field, electrostatic Faraday waves can be induced. Here, we study the response of the interface to an ac electric field, which is superposed by either a second ac field of different frequency, or by a dc field. An algorithm based on light refraction at the fluidic interface is used to obtain the spatiotemporal response of the Faraday waves, and the critical voltage corresponding to onset of instability, the interfacial oscillation frequency, and the dominant wavelengths are determined. The influence of the mixing ratio, which denotes the relative amplitudes of the different components of the driving signal, is analyzed, and the experimental results are compared with theoretical predictions. For ac/ac driving, gradual variations of the mixing ratio can induce a jump of the pattern wavelength, which is a result of the transition from harmonic to a subharmonic oscillation. For ac/dc driving, the interface oscillates either harmonically or subharmonically, and the response wavelength can be tuned continuously by adjusting the admixture of the dc component. For both driving modes, the experiments show good agreement with theory.

The Arctic Ocean's main thermocline may be characterized by a series of fine-scale thermohaline staircase structures that are present in a wide range of regions, the formation mechanism of which remains unclear. Recent analysis has led to the proposal of a theoretical model which suggested that these staircase structures form spontaneously in the ocean when the turbulent intensity determined by the buoyancy Reynolds number ${\text{Re}}_b$ is sufficiently weak. In the current work, we have designed a series of ${\text{Re}}_b$ controlled direct numerical simulations of turbulence in the Arctic Ocean thermocline to test the effectiveness of this theory. In these simulations, the staircases form naturally when ${\text{Re}}_b$ falls in the range predicted by the instability criterion. The exponential growth rate of the layering mode matches well with the prediction of the theoretical model. The staircases formed in our simulations are further compared with the classical diffusive interface model, which argues that stable staircase structures can only form when the density ratio $R_{\rho }$ is smaller than the critical value of $R_{\rho }^{cr}={\tau }^{-1/2}$. Here $\tau$ is the ratio of haline diffusivity over thermal diffusivity. We show that the staircase structure can stably persist in our model regardless of whether or not $R_{\rho }<R_{\rho }^{cr}$ is satisfied.

We studied homogeneous stably stratified turbulence in a triply periodic domain over a wide range of stratification strengths. We evaluated the statistically stationary, volume-averaged budgets of Reynolds stresses, turbulent potential energy, and turbulent vertical density flux. By separately studying the three components of the turbulent kinetic energy (TKE), we examined the role of pressure-strain correlations and observed connections between changes in the energetics to regime shifts of the mixing coefficient $\left(\mathrm{\Gamma }\right)$ as a function of the turbulent Froude number $\left({\text{Fr}}_k\right)$. As we increase stratification, we find that pressure-strain correlations become more important in producing the vertical component of TKE $\left(k_w\right)$. At the stratification strength where direct production and pressure-strain correlations equally generate $k_w$, we observe the maximum value of $\mathrm{\Gamma }$, and it remains constant as stratification is increased further. However, when we greatly increase stratification from this point, the pressure-strain correlations become the dominant source of $k_w$ with direct production becoming negligible, and this change is accompanied by the mixing coefficient decreasing from its maximum value. Finally, we find that this final transition for the mixing coefficient coincides with a sign change of the pressure scrambling term in the vertical density flux budget.

Objects inserted in a fast-flowing soap film are observed to cause strong disturbances on the film, resembling shock waves. Currently a prevailing opinion is that these shock waves correspond to sudden increases in film thickness caused by elastic symmetric waves, or the propagation of film thickness changes driven by surface tension variations with the film surface area. Here, we show by laser interferometry that these “shock waves” in fact originate from the antisymmetric waves studied by Taylor, which correspond to the bending of the liquid film with no thickness change. This phenomenon thus forms an example of symmetry breaking. These shock waves maintain an antisymmetric structure, but the structure size varies with the size of the intruding object. Our results indicate that these structures could be objects for studying solitary waves, rather than the traditional shocks corresponding to density jumps in compressible flows.

Despite the well-known limitations of linear stability theory in describing nonlinear and turbulent flows, it has been found to accurately capture the transitions between certain nonlinear flow behavior. Specifically, the transition in heat flux scaling in rotating convective flows can be well predicted by applying a linear stability analysis to simple profiles of a convective boundary layer. This fact motivates the present study of the linear mechanisms involved in the stability properties of simple convective setups subject to rotation. We look at an idealized two-layer setup and gradually add complexity by including rotation, a bounded domain, and viscosity. The two-layer setup has the advantage of allowing for the use of wave interaction theory, traditionally applied to understand stratified and homogeneous shear flow instabilities, in order to quantify the various physical mechanisms leading to the growth of convective instabilities. We quantitatively show that the physical mechanisms involved in the stabilization of convection by rotation take two different forms acting within the stratified interfacial region, and in the homogeneous mixed layers. The latter of these we associate with the tendency of a rotating flow to develop Taylor columns (TCs). This TC mechanism can lead to both a stabilization or destabilization of the instability and varies depending on the parameters of the problem. A simple criterion is found for classifying the influence of these physical mechanisms.

The mixing of binary fluids by stirrers is a commonplace procedure in many industrial and natural settings, and mixing efficiency directly translates into more homogeneous final products, more enriched compounds, and often substantial economic savings in energy and input ingredients. Enhancements in mixing efficiency can be accomplished by unorthodox stirring protocols as well as modified stirrer shapes that utilize unsteady hydrodynamics and vortex-shedding features to instigate the formation of fluid filaments which ultimately succumb to diffusion and produce a homogeneous mixture. We propose a PDE-constrained optimization approach to address the problem of mixing enhancement for binary fluids. Within a gradient-based framework, we target the stirring strategy as well as the cross-sectional shape of the stirrers to achieve improved mixedness over a given time horizon and within a prescribed energy budget. The optimization produces a significant enhancement in homogeneity in the initially separated fluids, suggesting promising modifications to traditional stirring protocols.

Studies of particle motion in vortical flows have mainly focused on pointlike particles. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an inertialess rigid dumbbell in a two-dimensional steady vortex. While the system remains analytically tractable, the particle experiences the nonlinearity of the surrounding velocity field. By exploiting the rotational symmetry of the flow, we reduce the problem to that of a two-dimensional dynamical system, whose fixed points and periodic orbits can be used to explain the motion of the dumbbell. For all vortices in which the fluid angular velocity decreases with radial distance, the center of mass of the dumbbell follows a spirographic-like trajectory around the vortex center. This results from a periodic oscillation in the radial direction combined with revolution around the center. The shape of the trajectory depends strongly on the initial position and orientation of the dumbbell, but the dynamics is qualitatively the same irrespective of the form of the vortex. If the fluid angular velocity is not monotonic, the spirographic-like motion is altered by the existence of transport barriers, whose shape is now sensitive to the details of the vortex. This analysis may be extended to study the dynamics of inertial and/or self-propelled dumbbells in a two-dimensional vortex.

We investigate gunwale bobbing, a phenomenon in which a person jumping on the gunwales of a canoe achieves horizontal propulsion by forcing it with vertical oscillations. The canoe moves forward by surfing the resulting wave field. After an initial transient, the canoe achieves a cruising velocity which satisfies a balance between the thrust generated from pushing downwards into the surface gradients of the wave field and the resistance due to a combination of profile drag and wave drag. By superposing the linear wave theories of Havelock [Proc. R. Soc. A 95, 354 (1919)] for steady cruising and Helmholtz for an oscillating source, we demonstrate that such a balance can be sustained. We calculate the optimal parameter values to achieve maximum canoe velocity. We compare our theoretical result to accelerometer data taken from an enthusiastic gunwale bobber and to estimates from videos of other canoeing aficionados. Finally, we discuss the similarities and differences with other examples of macroscopic wave-driven bodies and comment on possible applications to competitive sports.

Unforced shoaling waves experience growth and changes to wave shape. Similarly, wind-forced waves on a flat-bottom likewise experience growth/decay and changes to wave shape. However, the combined effect of shoaling and wind-forcing on wave shape, particularly relevant in the near-shore environment, has not yet been investigated theoretically. Here, we consider small-amplitude, shallow-water solitary waves propagating up a gentle, planar bathymetry forced by a weak, Jeffreys-type wind-induced surface pressure. We derive a variable-coefficient Korteweg–de Vries–Burgers (vKdV–B) equation governing the wave profile's evolution and solve it numerically using a Runge-Kutta third-order finite difference solver. The simulations run until convective prebreaking—a Froude number limit appropriate to the order of the vKdV–B equation. Offshore winds weakly enhance the ratio of prebreaking height to depth as well as prebreaking wave slope. Onshore winds have a strong impact on narrowing the wave peak, and wind also modulates the rear shelf formed behind the wave. Furthermore, wind strongly affects the width of the prebreaking zone, with larger effects for smaller beach slopes. After converting our pressure magnitudes to physically realistic wind speeds, we observe qualitative agreement with prior laboratory and numerical experiments on breakpoint location. Additionally, our numerical results have qualitatively similar temporal wave shape to shoaling and wind-forced laboratory observations, suggesting that the vKdV–B equation captures the essential aspects of wind-induced effects on shoaling wave shape. Finally, we isolate the wind's effect by comparing the wave profiles to the unforced case. This reveals that the numerical results are approximately a superposition of a solitary wave, a shoaling-induced shelf, and a wind-induced, bound, dispersive, and decaying tail.

In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid motion. In this paper, we develop a numerical method for the simulation of cylindrical fibers by extending our previous work on inextensible bending fibers [O. Maxian et al., Phys. Rev. Fluids 6, 014102 (2021)] to fibers with twist elasticity. In our “Euler” model, twist is a scalar function that measures the deviation of the fiber cross section relative to a twist-free frame, the fiber exerts only torque parallel to the centerline on the fluid, and the perpendicular components of the rotational fluid velocity are discarded in favor of the translational velocity. In the first part of this paper, we justify this model by comparing it to another commonly used “Kirchhoff” formulation where the fiber exerts both perpendicular and parallel torque on the fluid, and the perpendicular angular fluid velocity is required to be consistent with the translational fluid velocity. Through asymptotics and numerics, we show that the perpendicular torques in the Kirchhoff model are small, thereby establishing the asymptotic equivalence of the two models for slender fibers. We then develop a spectral numerical method for the hydrodynamics of the Euler model. We define hydrodynamic mobility operators using integrals of the Rotne-Prager-Yamakawa tensor, and evaluate these integrals through a slender-body quadrature, which requires on the order of 10 points along a smooth fiber to obtain several digits of accuracy. We demonstrate that this choice of mobility removes the unphysical negative eigenvalues in the translation-translation mobility associated with asymptotic slender-body theories, and ensures strong convergence of the fiber velocity and weak convergence of the fiber constraint forces. We pair the spatial discretization with a semi-implicit temporal integrator to confirm the negligible contribution of twist elasticity to the relaxation dynamics of a bent fiber. We also study the instability of a twirling fiber, and demonstrate that rotation-translation and translation-rotation coupling change the critical twirling frequency at which a whirling instability onsets by $\sim$20%, which explains some (but not all) of the deviation from theory observed experimentally. When twirling is unstable, we show that the dynamics transition to a steady overwhirling state, and quantify the amplitude and frequency of the resulting steady crank-shafting motion.

Two-dimensional channel flow simulations of FENE-P (finitely extensible nonlinear elastic-Peterlin) fluid in the elasto-inertial turbulence (EIT) regime reveal distinct regimes ranging from chaos to a steady traveling wave which takes the form of an arrowhead structure. This coherent structure provides insights into the polymer/flow interactions driving EIT. A set of controlled numerical experiments and the study of transfer between elastic and turbulent kinetic energies highlight the role of small- and large-scale dynamics in the self-sustaining cycle of chaos in EIT flows.

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated.

Saffman and Turner [P. G. Saffman and J. S. Turner, J. Fluid Mech. 1, 16 (1956)] argued that the collision rate for droplets in turbulence increases as the turbulent strain rate increases. However, the numerical simulations of Dhanasekaran et al. [J. Dhanasekaran et al., J. Fluid Mech. 910, A10 (2021)] in a steady straining flow showed that the Saffman-Turner model is oversimplified because it neglects droplet-droplet interactions. These result in a complex dependence of the collision rate on the strain rate and on the differential settling speed. Here we show that this dependence is explained by a sequence of bifurcations in the collision dynamics. We compute the bifurcation diagram when strain is aligned with gravity and show that it yields important insights into the collision dynamics. First, the steady-state collision rate remains nonzero in the limit $\mathrm{Kn}\to 0$, contrary to the common assumption that the collision rate tends to zero in this limit (Kn is a nondimensional measure of the mean free path of air). Second, the nonmonotonic dependence of the collision rate on the differential settling speed is explained by a grazing bifurcation. Third, the bifurcation analysis explains why so-called closed trajectories appear and disappear. Fourth, our analysis predicts strong spatial clustering near certain saddle points, where the effects of strain and differential settling cancel.

Barnacle-type roughness can be considered as a hybrid form of roughness that combines some of the topographical features of traditional regular rough surfaces composed of discrete roughness elements of uniform size and shape, and of irregular rough surfaces that exhibit features with a wide distribution of sizes and shapes, covering the surface with a random areal distribution. In this study, the influence of barnacle-type rough surfaces with increasing coverage on wall-bounded turbulence is investigated using direct numerical simulations of turbulent channel flow. The barnacle-type rough surfaces were generated with an algorithm that mimics the settlement behavior of barnacles, and the set of seven different surfaces describe the evolution of barnacle fouling with increasing coverage ranging from a lightly fouled surface with small isolated barnacle clusters (10% coverage) to a surface that is fully covered by barnacles (85% coverage). The roughness function recovers the expected trend with frontal solidity, attaining its maximum at a frontal solidity of approximately 0.2. Mean flow, Reynolds stress, and dispersive stresses show signatures of the clustering of roughness features, i.e., the barnacle colonies, at low coverage. This is most distinct for the streamwise Reynolds stresses where a double peak is observed at the lowest coverage; the inner peak can be interpreted as a partial recovery of smooth-wall behavior over the large connected unfouled sections of this surface. The flow over the rough surfaces is further investigated by a topographical characterization of the blanketing layer, i.e., the effective shape of the rough surface “perceived” by the outer flow. A linear relationship between the roughness function and the effective slope of the blanketing layer is observed.