Vortex models have been used for decades as computationally efficient tools to investigate unsteady aerodynamics. However, their utility for separated flows—particularly when such flows are subjected to incident disturbances—has been hindered by the tradeoff between the model's physical fidelity and its expectation for fast prediction (e.g., relative to computational fluid dynamics). In this work, it is shown that physical fidelity and speed can be simultaneously achieved by assimilating measurement data into the model to compensate for unrepresented physics. The underlying inviscid vortex model captures the transport of vortex structures with a standard collection of regularized vortex elements that interact mutually and with an infinitely thin flat plate. In order to maintain a low-dimensional representation, with fewer than $O\left(100\right)$ degrees of freedom, an aggregation procedure is developed and utilized in which vortex elements are coalesced at each time step. A flow state vector, composed of vortex element properties as well as the critical leading-edge suction parameter, is advanced within an ensemble Kalman filter (EnKF) framework. In this framework, surface pressure is used to correct the states of an ensemble of randomly initiated vortex models. The overall algorithm is applied to several scenarios of an impulsively started flat plate, in which data from a high-fidelity Navier-Stokes simulation at Reynolds number 500 are used as a surrogate for the measurements. The assimilated vortex model efficiently and accurately predicts the evolving flow as well as the normal force in both the undisturbed case (a separated flow) as well as in the presence of one or more incident gusts, despite lack of a priori knowledge of the gust's characteristics.

We investigate velocity variations inside and surrounding a gravity-driven drop impacting on and moving through a confining orifice, wherein the effects of edge geometry (round vs sharp edged) and surface wettability (hydrophobic vs hydrophilic) of the orifice are considered. Using refractive-index matching and time-resolved particle image velocimetry, we quantify the redistribution of energy in the drop and the surrounding fluid during the drop's impact and motion through a round-edged orifice. The measurements show the importance of (a) the drop kinetic energy transferred to and dissipated within the surrounding liquid and (b) the drop kinetic energy due to internal deformation and rotation during impact and passage through the orifice. While a rounded orifice edge prevents contact between the drop and orifice surface, a sharp edge promotes contact immediately upon impact, changing the near-surface flow field as well as the drop passage dynamics. For a sharp-edged hydrophobic orifice, the contact lines remain localized near the orifice edge, but slipping and pinning strongly affect the drop propagation and outcome. For a sharp-edged hydrophilic orifice, on the other hand, the contact lines propagate away from the orifice edge and their motion is coupled with the global velocity fields in the drop and the surrounding fluid. By examining the contact line propagation over a hydrophilic orifice surface with minimal drop penetration, we characterize two stages of drop spreading that exhibit a power-law dependence with variable exponent. In the first stage, the contact line propagates under the influence of impact inertia and gravity. In the second stage, inertial influence subsides and the contact line propagates mainly due to wettability.

The lateral migration of a suspended vesicle (a model of red blood cells) in a bounded shear flow is investigated numerically at vanishing Reynolds number (the Stokes limit) using a boundary integral method. We explore, among other parameters, the effect of the viscosity contrast $\lambda ={\eta }_{\mathrm{in}}/{\eta }_{\mathrm{out}}$, where ${\eta }_{\mathrm{in}},{\eta }_{\mathrm{out}}$ denote the inner and the outer fluids' viscosities. It is found that a vesicle can either migrate to the center line or towards the wall depending on $\lambda$. More precisely, below a critical viscosity contrast ${\lambda }_c$, the terminal position is at the center line, whereas above ${\lambda }_c$, the vesicle can be either centered or off-centered depending on initial conditions. It is found that the equilibrium lateral position of the vesicle exhibits a saddle-node bifurcation as a function of the bifurcation parameter $\lambda$. When the shear stress increases the saddle-node bifurcation evolves towards a pitchfork bifurcation. A systematic analysis is first performed in two dimensions (due to numerical efficiency), and the overall picture is confirmed in three dimensions. This study can be exploited in the problem of cell sorting and can help understand the intricate nature of the dynamics and rheology of confined suspensions.

The power output of wind farms depends strongly on spatial turbine arrangement, and the resulting turbulent interactions with the atmospheric boundary layer. Wind farm layout optimization to maximize power output has matured for small clusters of turbines, with the help of analytical wake models. On the other hand, for large farms approaching a fully developed regime in which the integral power extraction by turbines is balanced through downward transport of the mean kinetic energy, the influence of turbine layout is much less understood. The main goal of this work is to study the effect of turbine layout on the power output for large wind farms approaching a fully developed regime. For this purpose we employ an experimental setup of a scaled wind farm with 100 porous disk models, of which 60 are instrumented with strain gauges. Our experiments cover a parametric space of 56 different layouts for which the turbine-area density is constant, focusing on different turbine arrangements including nonuniform spacings. The strain-gauge measurements are used to deduce surrogate power and unsteady loading on turbines for each layout. Our results indicate that the power asymptote at the end of the wind farm depends on the layout in different ways. Firstly, for layouts with a relatively uniform spacing we find that the power asymptote in the fully developed regime reaches approximately the same value, similarly to the prediction of available analytical models. Secondly, we show that the power asymptote in the fully developed regime can be lowered by inefficient turbine placement, for instance when a large number of the turbines are located in the near wake of upwind turbines. Thirdly, our experiments indicate that an uneven spacing between turbines can improve the overall power output for both the developing and fully developed part of large wind farms. Specifically, we find a higher power asymptote for a turbine layout with a significant streamwise uneven spacing (i.e., a large streamwise spacing between pairs of closely spaced rows that are slightly staggered). Our results thereby indicate that such a layout may promote beneficial flow interactions in the fully developed regime for conditions with a strongly prevailing wind direction.

A resonance between a long wave and a short wave occurs if the phase velocity of the long wave matches the group velocity of the short wave. Rogue waves modeled as special breathers (pulsating modes) can arise from these resonant interactions. This scenario is investigated for internal waves in a density stratified fluid. We examine the properties of these rogue waves, such as the polarity, amplitude and robustness, and show that these depend critically on the specific density stratification and the choice of the participating modes. Three examples, namely, a two-layered fluid, a stratified fluid with constant buoyancy frequency, and a case of variable buoyancy frequency are examined. We show that both elevation and depression rogue waves are possible, and the maximum displacements need not be confined to a fixed ratio of the background plane wave. Furthermore, there is no constraint on the signs of nonlinearity and dispersion, nor any depth requirement on the fluid. All these features contrast sharply with those of a wave packet evolving on water of finite depth governed by the nonlinear Schrödinger equation. The amplitude of these internal rogue waves generally increases when the density variation in the layered or stratified fluid is smaller. For the case of constant buoyancy frequency, critical wave numbers give rise to nonlinear evolution dynamics for “long wave-short wave resonance,” and also separate the focusing and defocusing regimes for narrow-band wave packets of the nonlinear Schrödinger equation. Numerical simulations are performed by using baseband modes as initial conditions to assess the robustness of these rogue waves in relation to the modulation instability of a background plane wave.

The paper presents phenomenology of interaction and penetration of liquid-liquid material interfaces initiated by shock-driven collapse of single and multiple microbubbles situated near the material interface. Previous experimental studies have established such a generic setting as relevant for the investigation of sonoporation, i.e., the perforation of live cells by microbubble collapses. We consider a planar or spherical, single- or dual-layer, material interface between a gelatin material and water. A single or several ideal-gas microbubbles are positioned near the interface. Bubble collapse is initiated by a shock wave with a pressure profile specific to laser generation and is flat when hitting the gas-water interface. The interfacial acoustic impedance match singles out the collapse-induced re-entrant jet as main event. High-resolution sharp-interface numerical methods are employed to ensure that wave dynamics, hydrodynamics, and interface transporting are accurately resolved. Bubble configurations are varied between single and double and between attached and with standoff distance. Parameters varied are shock-wave peak pressure and viscosity ratio between single and double layers of gelatin and the surrounding water. For inertia-dominated cases, two regimes are observed, the first characterized by linear growth of the penetration depth and the second by a $t^{2/3}$ scaling. The latter range is affected by viscosity which reduces penetration speed. The results show that process parameters, in particular shock overpressure, control not only penetration depth but also the size of the interface perforation, indicating means to steer processes in biomedical applications.

We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles ($\beta =-{15}^{\circ }$, $-{30}^{\circ }$, and $-{45}^{\circ }$, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of $\text{Ka}=13.1$ and 330), and flow Reynolds numbers covering the range $\text{Re}=0.6–193$. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about $40\mathrm{mm}$ symmetrically on either side the centerline of the film span ($80\mathrm{mm}$ in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number $\text{Ka}(=13.1)$ flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid $\text{Ka}(=330)$ flows, rivulets were observed typically above $\text{Re}\approx 30,$ depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with increasing Re, reaching a maximum that shifted to higher Re at larger inclinations. Furthermore, in flows that displayed pronounced rivulet formation [i.e., large (negative) $\beta$ and higher Re], the local film-height standard deviation in regions corresponding to the rivulet crests and troughs was reduced compared to the film-height standard deviation calculated over the entire examined film region. The mean rivulet wavelength also increased at larger inclinations, peaking at 26 mm when $\text{Ka}=330$. Based on our experimental results and theoretical arguments, we hypothesize that the formation of rivulets can be attributed, at small $\beta$, to a secondary Rayleigh-Taylor instability mechanism that destabilizes the suspended two-dimensional wavefronts, and at larger $\beta$, to the primary Rayleigh-Taylor instability mechanism of a flat film coating the underside of the inclined plate.

We suggest longitudinal strips attached to an airfoil surface as a new stall control device. Their effects on the stall characteristics and flow modifications are experimentally investigated. The airfoil considered is SD7003 and the Reynolds numbers are $\mathrm{Re}=60000$ and 180 000 based on the chord length and freestream velocity. The drag and lift forces on the airfoil are measured by varying the angle of attack from $\alpha =0^{\circ }$ to 16° with and without strips. The optimal strip configuration is determined using a response surface method. Without strip, abrupt stalls occur at $\alpha ={11}^{\circ }$ and 12.5° for $\mathrm{Re}=60000$ and 180 000, respectively, whereas broad stalls occur without much changing the stall angles by optimal strips. The lift coefficient and lift-to-drag ratio are significantly increased by the strips at post-stall angles of attack. A corner vortex is generated at each corner of strip near the leading edge. Clockwise and counterclockwise streamwise vortices are generated at the left- and right-facing corners, respectively, and they slowly move away from the corners while travelling downstream. These vortices provide additional momentum to the airfoil suction surface, resulting in fully attached flow above the strips and reattachment of flow above grooved surface. The longitudinal strips presented here are different from other devices such as the vortex generator, trip wire, burst control plate, and zigzag tapes used for the separation control of low Reynolds number airfoil, in that the strips are installed nearly on the whole airfoil surface but with their heights lower than the boundary layer thickness, and produce positive control effects at post-stall angles of attack but little affect the aerodynamic performance at prestall angles of attack.

The equilibrium state of a flexible fiber settling in a viscous fluid is examined using a combination of macroscopic experiments, numerical simulations, and scaling arguments. We identify three regimes having different signatures on this equilibrium configuration of the elastic filament: weak and large deformation regimes wherein the drag is proportional to the settling velocity as expected in Stokes flow and an intermediate elastic reconfiguration regime where the filament deforms to adopt a shape with a smaller drag which is no longer linearly proportional to the velocity.

Due to the inherent nonlinearity of fluid dynamics, a large class of oscillating flows gives rise to rectified effects of steady motion. It has recently been shown that particle transport in such flows leads to differential displacement and efficient sorting of microparticles. Here we present a model that generalizes a Maxey-Riley-like equation for particle motion, incorporating important viscous and inviscid effects near oscillating interfaces and efficiently bridging the acoustofluidic and microfluidic approaches. Resulting in direct predictions for particle motion on slower timescales, the model predicts a richer and qualitatively different behavior from that expected from simplified radiation-force formalisms: depending on experimental control parameters, the net effect of interfacial oscillation can be either an attraction to or a repulsion from the interface, and particles can be captured at a fixed distance or released. These results are verified in comparison with experiments.

We consider freely decaying homogeneous anisotropic turbulence whose energy spectrum $E\left(k\right)$ at $k\to 0$ is given by $E\left(k\right)=C{k}^2+o\left(k^2\right)$ at an initial instant, where $k$ is the wave number and $C$ is a $k$-independent positive number. An argument is given to show that there are an infinite number of invariants characterizing the large-scale structure of the turbulence. This is a generalization of Saffman's argument, which shows the existence of a finite number of invariants [P. G. Saffman, J. Fluid Mech. 27, 581 (1967)]. By applying a similar argument to homogeneous anisotropic passive scalar turbulence without any scalar source, we show that there are an infinite number of invariants characterizing the large-scale structure of passive scalar fields. Theoretical analysis based on the invariance and a self-similarity assumption for the large-scale evolution shows that the anisotropy of the velocity and passive scalar fields is persistent at large scales. The decay laws of the velocity and passive scalar fields are derived by a simple dimensional analysis.

High-resolution three-dimensional large-eddy simulations are used to investigate the effects of internal solitary waves (ISWs) breaking over a sloping boundary. The lock release method is applied in a two-layer stratified fluid system to generate three different breaking mechanisms (i.e., plunging, collapsing, and surging breakers). The different breaking types are investigated in terms of their effects on the dynamics of the ISW and the interaction of the ISW with the sloping boundary. During each breaking event, the pycnocline region entrains fresher water from the upper layer and saltier water from the lower one. The associated increase of the intermediate density layer also induces changes of the pycnocline water density. This process occurs with a velocity that can be evaluated using the bulk entrainment parameter. We show how the intermediate layer features depend on the ISW shoaling and breaking dynamics and we discuss entrainment in breaking ISWs. The instabilities induced by boundary layer separation allow entrainment of saltier water, while the run-up of the gravity current causes the decrease of the intermediate layer mean density. Simultaneously, the entrained water mixes into the pycnocline region. For all cases, the temporal evolution of the instantaneous mixing efficiency is discussed. The plunging breaker case shows the largest amount of mixing, which is mostly induced by rear-edge overturning in the onshore direction. The largest entrainment is observed in the surging breaker case in response to the large gravity current flowing upslope. The paper discusses how the different turbulent instabilities induced by the ISWs breaking affect the time delay between the times when entrainment of patches of salty and fresh water from the neighboring layers occurs and the time the density of the intermediate layers becomes fairly uniform via mixing. We finally point out that the entrainment parameter and the mixing efficiency describe two different effects of the turbulent instabilities occurring in a stratified fluid in terms of changes of the bulk density profile.

We characterize the local concentration dependence of segregation velocity and segregation flux in both size and density bidisperse gravity-driven free-surface granular flows as a function of the particle size ratio and density ratio, respectively, using discrete element method simulations. For a range of particle size ratios and inlet volume flow rates in size-bidisperse flows, the maximum segregation flux occurs at a small particle concentration less than 0.5, which decreases with increasing particle size ratio. The segregation flux increases up to a size ratio of 2.4 but plateaus from there to a size ratio of 3. In density bidisperse flows, the segregation flux is greatest at a heavy particle concentration less than 0.5, which decreases with increasing particle density ratio. The segregation flux increases with increasing density ratio for the extent of density ratios studied, up to 10. We further demonstrate that the simulation results for size-driven segregation are in accord with the predictions of the kinetic sieving segregation model of Savage and Lun [J. Fluid Mech. 189, 311 (1988)].

In this paper we investigate experimentally the waves produced by a parabolically shaped wave maker partially immersed into a water-filled basin and oscillating in the vertical direction. The main motivation of our study is to follow the analogy between light waves that focus on caustics, creating zones of intense light concentration, and surface waves in liquids. Similarly to light focusing, the surface waves undergo spatial focusing leading to the growth of their amplitudes till they reach a cusp singularity. We detect three regimes. In the first one, which corresponds to small forcing amplitudes, the wave field agrees well with geometrical optics and with Pearcey diffraction theory near the caustics. In the second regime, weak nonlinearities are detected. However, waves still focus as predicted. In the third regime, at large forcing amplitude, a large-scale mean flow is generated. This flow is concentrated in two symmetric jets emerging from the wave maker front wall and producing two counter-rotating eddies because of the finite size of the basin. This large-scale flow modifies the shape of the wave fronts and leads to a displacement of the cusp towards the wave maker, modifying the analogy between light and surface waves.

Direct numerical simulations of incompressible homogeneous-isotropic turbulence laden with a dilute suspension of inertial point particles are performed in conjunction with a wavelet multiresolution analysis of the results. The use of spatially localized wavelet basis functions enables the simultaneous consideration of physical and scale spaces in the spectral characterization of the flow field of the carrier phase and the concentration field of the dispersed phase. The multiresolution analysis of the dispersed phase provides statistical information about the spatial variabilities of a scale-dependent coarse-grained number density field and the local energy spectra of its fluctuations, characterizing the sensitivities of those quantities to variations in scale and Stokes number. In particular, the spatial variabilities of the wavelet energy spectrum of the particle concentration fluctuations are observed to be maximum in regimes where the particles preferentially concentrate. The results highlight the scale-dependent inhomogeneities of the structures in the concentration field generated by preferential concentration, and the existence of characteristic scales of interaction between the dispersed and carrier phases. Additionally, an interphase multiresolution analysis is performed that indicates the occurrence of a spatial anticorrelation between the enstrophy and kinetic-energy spectra of the carrier phase and the particle concentration at small scales in regimes where preferential concentration is important. This anticorrelation vanishes as the scale is increased and is largely suppressed when the preferential-concentration effect is negligible.

The physalis method for resolved numerical simulation of particulate flows, recently extended to include particles-fluid heat transfer, is applied to the turbulent flow past a planar particle array perpendicular to the incoming mean flow. The array consists of nine equal spheres. Periodicity boundary conditions are imposed on the boundaries of the computational domain parallel to the mean flow. The Reynolds number based on the particle diameter and mean incident flow is 120, the Taylor-scale Reynolds number is close to 30, and the ratio of particle radius to the Kolmogorov length is about 10. A detailed characterization of the flow and heat transfer is given including probability distribution functions of temperature and streamwise velocity, contour maps of the temperature fluctuations, diagonal Reynolds stresses, turbulent heat flux, and the various contributions to the energy budget. Turbulence moderately increases the heat transfer and considerably shortens the thermal wake of the particles. Temperature and streamwise velocity develop very differently downstream of the spheres in spite of the fact that the Prandtl number equals 1, because of the blockage by the spheres, which has no counterpart for the temperature.

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry produced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady-state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach applies the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cutoff length beyond which the bending forces become subdominant to an external body force.

The effect of different definitions of the momentum flux on the properties of the coherent structures of the logarithmic region of wall-bounded turbulence is investigated by comparing the structures of intense tangential Reynolds stress with those of the alternative flux proposed in [Jiménez, J. Fluid Mech. 809, 585 (2016)]. Despite the fairly different statistical properties of the two flux definitions, it is found that their intense structures show many similarities, such as the dominance of “wall-attached” objects, and geometric self-similarity. The new structures are wider, but not taller, than the classical ones, and include both high- and low-momentum regions within the same object. It is concluded that they represent the same phenomenon as the classical groups of a sweep, an ejection, and a roller, suggesting that these groups should be considered the fundamental coherent structures of the momentum flux. The present results show that the properties of these composite momentum structures are robust with respect to the definition of the fluxes.

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the nonbreaking base state is linearly stable, implying that only a finite-amplitude perturbation can trigger breakup. Consequently, the stable base solution is surrounded by its finite basin of attraction. The basin boundary, which separates initial droplet shapes returning to the nonbreaking base state from those becoming unstable and breaking up, is characterized using edge tracking techniques. We numerically construct the edge state, a dynamically unstable equilibrium whose stable manifold forms the basin boundary. The edge state equilibrium controls if the droplet breaks and selects a unique path towards breakup. This path physically corresponds to the well-known end-pinching mechanism. Our results thereby rationalize the dynamics observed experimentally [H. A. Stone and L. G. Leal, J. Fluid Mech. 206, 223 (1989)].

We study the fronts that appear when a shear-thickening suspension is submitted to a sudden driving force at a boundary. Using a quasi-one-dimensional experimental geometry, we extract the front shape and the propagation speed from the suspension flow field and map out their dependence on applied shear. We find that the relation between stress and velocity is quadratic, as is generally true for inertial effects in liquids, but with a prefactor that can be much larger than the material density. We show that these experimental findings can be explained by an extension of a phenomenological model originally developed to describe steady-state shear thickening. This is achieved by introducing a sole additional parameter: the characteristic strain scale that controls the crossover from startup response to steady-state behavior. The theoretical framework we obtain points out a linkage between transient and steady-state properties of shear-thickening materials.