Numerical simulations were carried out to examine a ${24}^{\circ }$ compression ramp interaction in which the confinement effect of sidewalls was very strong. The ratio of turbulent boundary-layer thickness to domain width at the start of the interaction was $\delta /w=0.12$. Inflow conditions of $M_{\infty }=2.25$ and ${\mathrm{Re}}_{\theta i}=1800$ were chosen to match previous simulations. Comparing to the limited data available from similar computations, the centerline separation length scale $L_s/\delta$ was seen to vary with the flow confinement parameter $\delta /w$, as previously recognized in reflected shock interactions. Significant differences in flow structure were observed between these computations with confining sidewalls and previous computations with periodic boundary conditions at the lateral boundaries of the domain. The most intense turbulent fluctuations occurred in the corners of the domain. Symmetric and antisymmetric motions of the separation region were identified in the instantaneous flow using conditional averages and spatial correlations. The presence of the sidewalls was found to influence both the mean and unsteady flow. Accurately capturing the sidewall flows is judged to be essential in realistic modeling of confined flows.

Historically, there has been little faith in particle tracking velocimetry (PTV) as a tool to make quantitative measurements of thermal counterflow in He II, since tracer particle motion is complicated by influences from the normal fluid, superfluid, and quantized vortex lines, or a combination thereof. Recently, we introduced a scheme for differentiating particles trapped on vortices (G1) from particles entrained by the normal fluid (G2). In this paper, we apply this scheme to demonstrate the utility of PTV for quantitative measurements of vortex dynamics in He II counterflow. We estimate $\ell$, the mean vortex line spacing, using G2 velocity data, and $c_2$, a parameter related to the mean curvature radius of vortices and energy dissipation in quantum turbulence, using G1 velocity data. We find that both estimations show good agreement with existing measurements that were obtained using traditional experimental methods. This is of particular consequence since these parameters likely vary in space, and PTV offers the advantage of spatial resolution. We also show a direct link between power-law tails in transverse particle velocity probability density functions (PDFs) and reconnection of vortex lines on which G1 particles are trapped.

Existing methods to identify the interfaces separating different regions in turbulent flows, such as turbulent/nonturbulent interfaces, typically rely on subjectively chosen thresholds, often including visual verification that the resulting surface meaningfully separates the different regions. Since machine learning tools are known to help automate such classification tasks, we here propose to use an unsupervised self-organizing map (SOM) machine learning algorithm as an automatic classifier. We use it to separate a boundary layer undergoing bypass transition into two distinct spatial regions, the turbulent boundary layer (TBL) and non-TBL regions, the latter including the laminar portion prior to transition and the outer flow which possibly contains weak free-stream turbulence. Both regions are separated by the turbulent boundary layer interface (TBLI). The data used in this study are from a direct numerical simulation and are available on an open database system. In our analysis of one snapshot in time, every spatial point is characterized by a 16-dimensional vector containing the magnitudes of the components of total and fluctuating velocity, magnitudes of the velocity gradient tensor elements, and the streamwise and wall-normal coordinates, all normalized by their global standard deviation. In an unsupervised fashion, the SOM classifier separates the points into TBL and non-TBL regions, thus identifying the TBLI without the need for user-specified thresholds. Remarkably, it avoids including vortical streaky structures that exist in the laminar portion prior to transition as well as the weak free-stream turbulence in the turbulent boundary layer region. The approach is compared quantitatively with existing methods to determine the TBLI (vorticity magnitude, cross-stream velocity fluctuation). Also, the SOM classifier is cast as a linear hyperplane that separates the two clusters of data points, and the method is tested by finding the TBLI of other snapshots in the transitional boundary layer data set, as well as in a fully turbulent boundary layer with similar levels of free-stream turbulence. Variants in which the approach failed are also summarized.

The motion of wall-bounded drops moving on solid substrates driven by a fully turbulent channel flow is experimentally investigated for four substrates of different wetting properties. An appropriate scaling has been found to describe the dimensionless drop velocity (capillary number) in terms of a dimensionless flow attack velocity, taking into account the surface wetting properties. The derived model agrees very well with the experimental observations.

Flapping insects are remarkably agile fliers, adapted to a highly turbulent environment. We present a series of high-resolution numerical simulations of a bumblebee interacting with turbulent inflow. We consider both tethered and free flight, the latter with all six degrees of freedom coupled to the Navier-Stokes equations. To this end, we vary the characteristics of the turbulent inflow, either changing the turbulence intensity or the spectral distribution of turbulent kinetic energy. Active control is excluded in order to quantify the passive response real animals exhibit during their reaction time delay, before the wing beat can be adapted. Modifying the turbulence intensity shows no significant impact on the cycle-averaged aerodynamical forces, moments, and power, compared to laminar inflow conditions. The fluctuations of aerodynamic observables, however, significantly grow with increasing turbulence intensity. Changing the integral scale of turbulent perturbations, while keeping the turbulence intensity fixed, shows that the fluctuation level of forces and moments is significantly reduced if the integral scale is smaller than the wing length. Our study shows that the scale-dependent energy distribution in the surrounding turbulent flow is a relevant factor conditioning how flying insects control their body orientation.

We present high-resolution simulations of the instability and subsequent breakdown of standing waves, or seiches, in a fluid continuously stratified in the vertical direction. It is well known that such waves can evolve to form nonlinear, dispersive wave trains. When the initial dimensionless amplitude is large, it is possible that a stratified shear instability develops, possibly at the same time as dispersive wave trains. While both dispersion and shear instability serve to move energy from large to small scales, they are fundamentally different. The development into wave trains is nondissipative in nature, and in the asymptotic limit of small but finite amplitude seiches may be described by variants of the Korteweg–de Vries (KdV) equation. Shear instability, on the other hand, yields Kelvin-Helmholtz billows, which in turn provide one of the basic archetypes of transition to turbulence, with greatly increased rates of mixing and viscous dissipation. We discuss how the two phenomena vary as the aspect ratio of the tank and the height of the interface between lighter and denser fluids are changed, highlighting cases where the two phenomena coexist. A quantitative accounting for the evolution of the horizontal modewise decomposition of the kinetic energy of the system in addition to the creation of a semianalytical model of the evolution of the fundamental mode is presented. Finally, the mixing is characterized during the evolution of the seiche, illustrating a fundamental transition that occurs as the aspect ratio is decreased.

A one-dimensional (1D) reduced-order model (ROM) is developed for a 3D Rayleigh-Bénard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}={10}^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's function (GRF) method, which involves applying many localized weak forcings to the system one at a time and calculating the responses using long-time averaged direct numerical simulations (DNSs), the system's linear response function (LRF) is computed. Another matrix, called the eddy flux matrix (EFM), which relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, is also calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings and that the LRF can predict well the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigenvectors or singular vectors are compared with the leading proper orthogonal decomposition modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square root of the Rayleigh number, they perform equally well for flows at other $\mathrm{Ra}$, at least in the investigated range of $5\times {10}^5\le \mathrm{Ra}\le 1.25\times {10}^6$. The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system.

We show that Leidenfrost droplets made of an aqueous solution of surfactant undergo a violent explosion for a wide range of initial volumes and concentrations. This unexpected behavior turns out to be triggered by the formation of a gel-like shell during the evaporation when the surface concentration of surfactant reaches some critical value. Shortly thereafter, the temperature sharply increases above the normal boiling point, leading to fast bubble growth, shell stretching, and explosion. However, most of the droplet life is characterized by a self-similar evolution of the radial surfactant distribution during which surface and mean concentrations grow in proportion, independently of the initial conditions. The temperature rise (attributed to boiling point elevation with surface concentration) and nucleation followed by growth of vapor bubbles inside the shell are key features leading to the explosion, differing from the implosion (buckling) scenario reported by other authors.

Ferromagnetic microparticles energized by an alternating magnetic field exhibit fascinating collective behavior ranging from the emergent self-assembled spinners to a variety of self-organized rolling states. Despite their simplicity, quantifying their essentially multibody collective behavior remains elusive due to a multitude of relevant interactions, from short-range collisions to long-range magnetic and hydrodynamic forces. Here we develop a high-performance computational algorithm based on smoothed particle hydrodynamics to quantify the role of individual interactions in the emergent collective state. The computational model provides insight into the role of hydrodynamic interaction on the onset of collective behavior and allows characterization of dynamic regimes that are hard to access experimentally. Comparison with high-resolution experimental data allows validation of the algorithm. Our work expands the scope of modern computational tools for predictive modeling of microscopic active systems and provides insight into the intricate role of hydrodynamic interactions on the onset of collective behavior in living and synthetic active matter.

The dynamic frictional force between solid surfaces in relative motion differs from the static force needed to initiate motion, but this distinction is not usually thought to occur for liquid drops moving on a solid. Recent experiments [Gao et al., Nat. Phys. 14, 191 (2018)] have challenged this view and claim to observe an analog of solid-on-solid friction for sliding drops. We use molecular dynamics simulations to investigate the forces that moving liquids exert on solids in several situations. In contrast to the indirect techniques required in laboratory experiments, the forces involved in friction are directly accessible in these calculations. We find that, aside from possible inertial effects due to the abrupt initiation of motion and aging effects for unconfined drops, the frictional forces are constant in time.

A parametric study of the magnetic dipole behavior in resistive incompressible magnetohydrodynamics inside a rotating sphere is performed, using direct numerical simulations and considering Reynolds and Ekman numbers as controlling parameters. The tendency is to obtain geodynamolike magnetic dipole reversal regimes for sufficiently small Ekman and large Reynolds numbers. The typical dipole latitude obtained in the reversal regime is around ${40}^{\circ }$ (with respect to the rotation axis of the sphere). A statistical analysis of waiting times between dipole reversals is also performed, obtaining a non-Poissonian distribution of waiting times, indicating long-term memory effects. We also report the presence of a $1/f$ frequency power spectrum in the magnetic dipole time series, which also shows a tendency to grow toward lower frequencies as the Ekman number is decreased.

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.