A numerical model within the framework of the linear potential flow theory is developed to study interactions between water waves and perforated elastic disks. The boundary element method for hydrodynamic loads and modal function expansion for structural deformation are closely coupled, and disks are either simply supported or clamped at their edges. To model the flow past a perforated surface, a quadratic pressure drop model of practical validity is adopted. The established numerical model is applied to perform a multiparameter study to investigate the effects of wave amplitude, flexural rigidity, edge conditions, and open-area ratio on the hydrodynamic responses. It is found that the nondimensional hydrodynamic responses, including: wave exciting force, hydroelastic deflection, and wave energy absorption, are increased with the increasing the incident wave amplitude due to the nonlinear nature of the quadratic pressure discharge model. With increasing the flexural rigidity or rendering stronger constraints at the edge, the perforated elastic disk experiences an increase in the wave exciting force but a reduction in hydroelastic deflection, whereas they have negligible effects on the wave power absorption.

In this work we present experimental results of the flow and clogging of monodisperse spheres in a silo geometry, with an obstacle placed near the exit aperture. In previous work, it has been shown that the placement of an obstacle in a two-dimensional silo can suppress clogging. We extend prior work to investigate the effects of obstacle size, and find that larger obstacles are better at suppressing clogs; however, most obstacles will suppress clogging. We investigate the local velocity, granular temperature, and local packing for several specific cases, and find that the mechanisms of clog suppression may be different depending on the exact size of the obstacle, with one case not suppressing clogs at all. We find bulk granular temperatures are increased with the presence of an obstacle, but local temperatures near the exit may not be. We also find the average packing is not substantially affected by an obstacle, but the local packing can be quite different. Specifically, large obstacles introduce spatial disorder that percolates, resulting in a more fluid system overall. We also observe spatiotemporal inhomogeneity in the flows.

Oscillating grid turbulence (OGT) is a specific situation that enables us to investigate the equilibrium between the turbulent kinetic energy, $k$, and the dissipation rate, $\epsilon$, without any mean flow. One of its main features is that, in homogeneous fluids, the turbulence intensity decreases with the distance to the vibrating grid used to generate the forcing. OGT is thus usually described in terms of depth profiles of turbulent quantities. In this paper, we discuss experiments realized in two different setups, and we compare our results for all turbulent quantities with past studies. The results on the turbulent kinetic energy and the integral length scale lead us to propose a parametric model for the eddy viscosity, ${\nu }_t$, taking into account the spatial decay of the turbulence being slightly different from previous descriptions. Indeed, we find that ${\nu }_t$ is best described as a constant value over a certain depth, $H_s$, before decreasing quickly as a power law in $z^{-3/2}$. The specific depth $H_s$ is defined at the depth where a discontinuity of the integral length scale is observed. Physically, it corresponds to the depth at which the presence of the grid no longer influences the flow. We also describe OGT in the case of a two-layer fluid. The description of the turbulence at depths $z$ far from the position of the interface $h$ $(0<z/h<0.6)$ is very similar to the case of a homogeneous fluid, whereas the region near the interface $(0.6<z/h<1)$ is strongly altered by the presence of the fluid boundary. Surprisingly, ${\nu }_t$ (unlike the other turbulent quantities) no longer depends on $z$ in such a configuration. Finally, we investigate mixing processes at the interface in this context. Thanks to large field measurement (about the width of the tank), we were able to identify large-scale coherent structures as well as the turbulent flow. We discuss the entrainment law of the interface and its relationship with the Richardson number based on different definitions used in previous studies, as well as by using our observations of the turbulent flow properties at the interface. Our observations suggest that mixing at the interface in OGT is controlled by the turbulent flow properties at the interface but could also be influenced by weak mean flow features. This could explain why it is difficult to discriminate a simple dependence of the training rate with the Richardson number.

This work presents a numerical investigation of the dynamics of freely falling annular disks released from still in infinite water. Based on the large eddy simulation, a dynamic fluid body interaction model and moving computational method are utilized to obtain the full six degrees of freedom of the disks. In particular, we performed a comprehensive analysis of the influencing factors on the falling styles of the disks, i.e., the inner to outer diameter ratio $(0\le \eta \le 0.9)$, the dimensionless moment of inertia $(4\times {10}^{-4}\le I^{*}\le 4.2\times {10}^{-4})$ and the body to fluid density ratio $(1.2\le {\rho }^{*}\le 6)$. $\eta$ is found to be a key parameter for the falling trajectory and the corresponding flow structures, with $\eta =0.6$ as a turning point from regular to random motion. From low to high $I^{*}$, although the disks still exhibit hula-hoop (HH) motion, the dispersion degree of each period and the fluid forces against the disk's inertia increase gradually. We find that regardless of ${\rho }^{*}$, the disk trajectory exhibits HH motion, while more discrete vortices are generated for heavy disks. Ultimately, the mechanism of the planar precession of HH motion is explained by combining the time evolution of horizontal displacement, fluid forces, and vortical structures. Consequently, a hysteresis effect is observed during falling.

We design a controlling protocol for the traditional viscous fingering instability by taking advantage of an electro-osmotic flow generated by an external electric field. Under the coupled action of time-varying electric currents and injection rates, fully nonlinear simulations show that, besides setting the number of fingers on the interface, our strategy can either delay or promote the self-similar regime by several orders of magnitude, or even suppress it. In addition, we can produce self-similar shapes ranging from almost circular, mildly perturbed boundaries to fully developed fingered structures with large perturbation amplitudes. All these features are controlled without altering the material properties of the fluids and cell's geometry.

We develop a tractable interaction model for a polyatomic gas, whose kinetic equation combines a Vlasov-type mean field forcing due to an intermolecular potential, and a Boltzmann-type collision integral due to rotational interactions. We construct a velocity moment hierarchy for the kinetic equation, and find that, under the high Reynolds number condition, the pressure equation becomes decoupled from the angular momentum and stress. For the heat flux, we propose a closure by prescribing the specific-heat capacity of the gas flow. Setting the specific-heat capacity to that of a constant-pressure process leads to the system of equations for a balanced flow, where the momentum transport equation contains the mean field forcing, which is an averaged effect of the intermolecular potential. Remarkably, the balanced flow equations do not contain any information about internal thermodynamic properties of the gas, and are thereby applicable to a broad range of different gases. We conduct numerical simulations for an airlike gas at normal conditions in the inertial flow regime, where the pressure is constant throughout the domain. We find that the presence of the intermolecular potential produces a distinctly turbulent flow, whose time-averaged Fourier spectra of the kinetic energy and temperature exhibit Kolmogorov's power decay.

Wavelet-based adaptive large-eddy simulation (WA-LES) is an extension of the LES method where wavelet threshold filtering is used to separate resolved (more energetic) from residual (less energetic) turbulent flow motions. The effect of unresolved less energetic coherent structures is approximated through deterministic closure models. The method has been recently extended to compressible flows, where the governing equations are expressed in terms of wavelet-based density-weighted Favre-filtered variables. In this study, a novel localized dynamic model for compressible WA-LES of inhomogeneous flows is developed and tested for wall-bounded turbulence. The proposed model, which is based on the solution of the additional evolution equation for the subgrid-scale turbulent kinetic energy, extends the original incompressible formulation in De Stefano et al. [Phys. Fluids 20, 045102 (2008)] to compressible flows. The new modeling procedure is successfully validated for a classical benchmark case that is the supersonic turbulent flow in a plane channel.

The present paper investigates the planar flow past a circular cylinder for Reynolds numbers between 1000 and 10 000. The flow is studied as a dynamical system, so the present investigation is motivated by the presence of complex patterns, as the Reynolds number increases, in the force-time signals when the system goes from the periodic to the chaotic regime. The 2D numerical simulations were performed with a Lagrangian particle method called diffused vortex hydrodynamics (DVH). This computational approach allows high spatial resolutions with an accurate description of different vortical scales shed in the flow field. Flow analysis was executed with the typical tools used in the study of dynamical systems (i.e., Fourier spectra, Poincaré sections, and phase space maps) and is supported by discussion of the near and far wake topologies. During the transition of the system from a regular to a chaotic regime, the lift time signal shows intermittent irregular patterns.

Pressure oscillations applied to human airways can help patients to evacuate bronchial mucus, a highly non-Newtonian gel. To explore the fluid mechanics aspects of these therapies, we perform numerical simulations of pulsated non-Newtonian fluids in two-dimensional channels. The fluid rheology is modeled with the Herschel-Bulkley law, reproducing two essential nonlinear mechanical properties of the mucus, namely, the yield-stress and shear-thinning/thickening properties. The flow dynamics is simulated using the lattice-Boltzmann method over large ranges of the three main nondimensional parameters, i.e., the pulsation rate or Womersley number $\alpha$, the flow index $n$ quantifying the shear-thinning/thickening effect, and the Bingham number controlling the yield stress. The ratio between the fluctuating and average parts of the oscillatory forcing is examined through three typical cases: a purely oscillating flow, a weakly oscillating flow, and a strongly oscillating flow. For each configuration, specific sets of parameters are found to have a drastic effect on the dynamics of mucus plugs, which suggests new therapeutic strategies for patients suffering from bronchial obstructions.

We analyze the linear stability of monoclinal traveling waves on a constant incline, which connect uniform flowing regions of differing depths. The classical shallow-water equations are employed, subject to a general resistive drag term. This approach incorporates many flow rheologies into a single setting and enables us to investigate the features that set different systems apart. We derive simple formulas for the onset of linear instability, the corresponding linear growth rates and related properties including the existence of monoclinal waves, development of shocks, and whether instability is initially triggered upstream or downstream of the wave front. Also included within our framework is the presence of shear in the flow velocity profile, which is often neglected in depth-averaged studies. We find that it can significantly modify the threshold for instability. Constant corrections to the governing equations to account for sheared profiles via a “momentum shape factor” act to stabilize traveling waves. More general correction terms are found to have a nontrivial and potentially important quantitative effect on the properties explored. Finally, we have investigated the spatial properties of the dominant (fastest growing) linear modes. We derive equations for their amplitude and frequency and find that both features can become severely amplified near the front of the traveling wave. For flood waves that propagate into a dry downstream region, this amplification is unbounded in the limit of high disturbance frequency. We show that the rate of divergence is a function of the spatial dependence of the wave depth profile at the front, which may be determined straightforwardly from the drag law.

Experimental data obtained via particle image velocimetry are used to investigate the self-wrinkling of premixed flame fronts induced by Darrieus-Landau (DL) instability and its interaction with turbulence from low to moderately high Reynolds numbers in a Bunsen configuration. At low Reynolds, hence in quasilaminar conditions, the DL instability is experimentally triggered by varying the mixture ratio. Conversely, in turbulent cases, the DL instability is triggered by varying the Bunsen nozzle diameter so that flames can be compared at the same equivalence ratio and jet Reynolds numbers. The differences between stable and unstable Bunsen flames at low Reynolds number are discussed in terms of vorticity generation downstream in the flame as well as total flame strain and its normal and tangential components. The straining pattern of a single DL cusp is calculated along the flame front to create a reference case for higher turbulence intensity cases and assess the influence of self-wrinkling of the flame front on the reactant flow field, i.e., the channeling effect. The results obtained are consistent with recent direct numerical simulations of single DL-cusp propagating in a quiescent environment. In addition, inspection of strain-curvature joint probability density function, curvature correlation coefficient and crossing length statistics will show that, even from the intermediate Reynolds numbers explored, unstable flames under the influence of self-wrinkling effects possess the statistical characteristics that stable flames gain only at high turbulence levels, where a unified and turbulence dominated regime is likely to be reached, although with the persistence of some residual differences.

In this paper, a detailed two-dimensional numerical study on the nonlinear behaviors of electrohydrodynamic flows of Oldroyd-B viscoelastic dielectric liquid between two coaxial cylinders is conducted. The liquid is subjected to strong unipolar injection from inner annulus. The entire set of coupled equations, including the Navier-Stokes equations, simplified Maxwell's equations, and constitutive equations, is solved by the finite-volume method. Detailed analyses of elastic effects on the flows are presented with corresponding explanation. A bifurcation mode, namely supercritical bifurcation, has been found comparing to the subcritical bifurcation of Newtonian fluids. The linear stability criteria and nonlinear ones corresponding to the onset and stop of the flow motion, respectively, are presented under different elastic conditions. Comparing to Newtonian fluids, the linear stability criteria do not change at low Weissenberg number and decline when Weissenberg number is more than 1, and the nonlinear criteria are larger than that of Newtonian fluids. In addition, viscoelastic fluids show more dynamic behaviors. For example, two charge-void regions rotate in the domain because of azimuthal stress. Due to the first principal normal stress, two parts of charge-void regions first rotate to each other and then are pushed apart. These behaviors are explained in detail and are closely related to the elastic effects.

We study entrainment in dry thermals in neutrally and unstably stratified ambients, and moist thermals in dry-neutrally stratified ambients using direct numerical simulations. We find, in agreement with results of Lecoanet and Jeevanjee [J. Atmos. Sci. 76, 3785 (2019)], that turbulence plays a minor role in entrainment in dry thermals in a neutral ambient for Reynolds numbers $\text{Re}\lesssim {10}^4$. We then show that the net entrainment rate increases when the buoyancy of the thermals increases, either by condensation heating or because of an unstably stratified ambient. This is in contrast with the findings of Morrison et al. [J. Atmos. Sci. 78, 797 (2021)]. We also show that the role of turbulence is greater in these cases than in dry thermals and, significantly, that the combined action of condensation heating and turbulence creates intense small-scale vorticity, destroying the coherent vortex ring that is seen in dry and moist laminar thermals. These findings suggest that fully resolved simulations at Reynolds numbers significantly larger than the mixing transition Reynolds number $\text{Re}={10}^4$ are necessary to understand the role of turbulence in the entrainment in growing cumulus clouds, which consist of a series of thermals rising and decaying in succession.

We investigate the effect of density and viscosity differences on a swarm of large and deformable bubbles dispersed in a turbulent channel flow. For a given shear Reynolds number, ${\text{Re}}_{\tau }=300$, and a constant bubble volume fraction, $\mathrm{\Phi }\simeq 5.4\%$, we perform a campaign of direct numerical simulations of turbulence coupled with a phase-field method accounting for interfacial phenomena. For each simulation, we vary the Weber number (We, ratio of inertial to surface tension forces), the density ratio (${\rho }_r$, ratio of bubble density to carrier flow density) and the viscosity ratio (${\eta }_r$, ratio of bubble viscosity to carrier flow viscosity). Specifically, we consider two Weber numbers, $\text{We}=1.50$ and $\text{We}=3.00$, four density ratios, from ${\rho }_r=1$ down to ${\rho }_r=0.001,$ and five viscosity ratios, from ${\eta }_r=0.01$ up to ${\eta }_r=100$. Our results show that density differences have a negligible effect on breakage and coalescence phenomena, while a much stronger effect is observed when changing the viscosity of the two phases. Increasing the bubble viscosity with respect to the carrier fluid viscosity damps turbulence fluctuations, makes the bubble more rigid, and strongly prevents large deformations, thus reducing the number of breakage events. Local deformations of the interface, on the contrary, depend on both density and viscosity ratios: as the bubble density is increased, a larger number of small-scale deformations, small dimples and bumps, appear on the interface of the bubble. The opposite effect is observed for increasing bubble viscosities: the interface of the bubbles become smoother. We report that these effects are mostly visible for larger Weber numbers, where surface forces are weaker. Finally, we characterize the flow inside the bubbles; as the bubble density is increased, we observe, as expected, an increase in the turbulent kinetic energy (TKE) inside the bubble, while as the bubble viscosity is increased, we observe a mild reduction of the TKE inside the bubble and a strong suppression of turbulence.

The coating of rotating objects with varying surface curvature is an important manufacturing step for a wide variety of products. To efficiently examine the flow of liquid coatings on such objects, we develop a lubrication-theory-based model for flow on 2D cross sections of rotating noncircular cylinders whose variations in the radius of curvature are comparable to the characteristic cylinder radius. Good quantitative agreement is found between model predictions and Galerkin finite-element method simulations when the coating thickness is small, whereas qualitative agreement is found for thicker coatings. Encouraged by this agreement, we conduct a parametric study to examine coating behavior on rotating elliptical cylinders. Four regimes of coating behavior are found spanning gravity-dominated and surface-tension-dominated regimes. The parameter space yielding smooth coatings on elliptical cylinders is small, suggesting the need for additional steps such as the addition of surfactant to widen this coating window.

The generation of tsunamis by landslides has been the object of a lot of studies, focusing in particular on the wave maximum amplitude ${\eta }_{0,\max }$ to quantitatively assess the damage which these events may cause. The literature has long identified that this amplitude ${\eta }_{0,\max }$ is correlated to a Froude number ${\mathrm{Fr}}_{\max }$ proportional to a maximum slide front velocity ${\dot{x}}_{f,\max }$. Yet the dynamics of the slide needs to be determined from initial conditions to allow prediction of the maximum amplitude ${\eta }_{0,\max }$. Based on a canonical initial configuration, the aim of the present work is thus to better understand the transient physics connecting the landslide to the wave growth leading to the prediction of the wave maximum amplitude. In particular, the collapse of a Newtonian slide from air to water is considered here, investigating the role of two key ingredients: the slide inertia and viscous dissipation. The parameter space is systematically varied beyond laboratory and geophysical estimations to gain understanding on the fundamental process of wave formation, with two-dimensional three-phase numerical simulations using Basilisk. Results show that the column collapse of a Newtonian slide allows us to capture most of the physics of wave formation, and the correlation between ${\eta }_{0,\max }$ and the Froude number ${\mathrm{Fr}}_{\max }\propto {\dot{x}}_{f,\max }$ is recovered. A dynamical model of collapse reveals how the interplay between inertia and dissipation controls the slide dynamics through a Reynolds number $\mathrm{Re}\left(t\right)$ which, in turn, determines the kinematics of slide-water interface as quantified by the Froude number $\mathrm{Fr}\left(t\right)$. A simple model based on an idealised evolution of the collapse dynamics and volume conservation allows us to explicitly determine ${\mathrm{Fr}}_{\max }$ and ${\eta }_{0,\max }$ from the initial condition. This model allows us to capture results obtained from the numerical simulations and in accordance with empirical correlations usually found in the literature.

We report hydrodynamic interaction between droplets and the interface of a pair of co-flowing immiscible streams in a microchannel revealing droplet migration and interfacial deformation. We find small droplets of confinement ratio, i.e., ratio of drop size to the suspending stream width, $\beta <1$, exhibit lateral migration—while smaller droplets of $\beta <0.5$ migrate towards the co-flow interface, unexpectedly larger droplets of $0.5<\beta <1$ drift away from the interface. The size-based contrasting migration behavior is attributed to the interplay between the hitherto unexplored wall-directed negative lift force and the well-established center-directed noninertial lift force. We also find large droplets of $\beta >1$ cause deformation waves in an initially stable and flat interface that propagate downstream akin to traveling peristaltic waves. Numerical simulations reveal that interfacial deformation is a consequence of the distinctive pressure jumps across the co-flow interface at the upstream and downstream of a droplet. Our study reveals the amplitude of the deformation wave associated with a droplet grows spatially downstream but remains the same for a train of droplets crossing a fixed location, indicating convective instability. The effects of co-flow interfacial tension, viscosity contrast, confinement ratio, and droplet spacing on the deformation wave amplitude and its variation along the flow direction are studied. The experimental results are verified using a simple theoretical model. Our study presents an unexplored droplet-driven interfacial deformation wave that may find relevance in droplet microfluidics.

The investigation of the spanwise modulation of the Reynolds shear stress (RSS) distributions of a turbulent boundary layer modified by miniature vortex generators (MVGs) is performed, using an approach on a time-resolved velocity data set. The methodology is based on quadrant analysis of RSS to first identify the spatial and temporal information of the RSS events. We then apply the spanwise Fourier mode decomposition and triple velocity decomposition to obtain various statistics of the decomposed RSS events, including their conditional mean structures and actual mean skin friction contributions. In addition, the spanwise modification of the MVG on the RSS has been characterized by the fundamental and subharmonic modes of motions that scale with the spanwise separation distance $\left({\mathrm{\Lambda }}_z\right)$ between MVG pairs. The interactions between the ${\mathrm{\Lambda }}_z^{+}$-scaled mode and subharmonic modes are further investigated using the scale-by-scale RSS transport equation [Kawata and Alfredsson, Phys. Rev. Lett. 120, 244501 (2018)]. Results show that the ${\mathrm{\Lambda }}_z^{+}$-scaled motion tends to strengthen due to the inverse cascade of its subharmonic modes of motions, allowing the ${\mathrm{\Lambda }}_z^{+}$-scaled motion to persist further downstream.

The parametric forcing of premixed flames is observed here in the geometry of a Hele-Shaw burner. Using a vibroacoustic coupling, we are able to study the thresholds of the parametric flattening (where the flame wrinkles are suppressed) and the parametric instability (where the flame wrinkles oscillate at twice the acoustic period) and compare the measured values to a low-frequency theory. It is shown that the dependency of the parametric threshold with equivalence ratio is lower than predicted, suggesting that the Markstein lengths are frequency dependent and that the flattening threshold is independent of the Markstein number and of the nondimensional forcing frequency, in agreement with the Bychkov limit.

A detailed numerical investigation of pattern selection for thermocapillary flow in rectangular containers in microgravity is presented. These dynamics are studied for liquid $n$-octadecane, an alkane with high Prandtl number $(\text{Pr}=52.53)$, due to its relevance to recent microgravity experiments. Pattern selection is analyzed in terms of the aspect ratio, $\mathrm{\Gamma }$, and the applied Marangoni number, Ma. In short containers, the bifurcation picture is characterized by a transition from steady thermocapillary flow to a standing wave (SW) oscillatory mode as Ma is varied. This transition takes the form of a primary subcritical Hopf bifurcation accompanied by a secondary saddle node; these two bifurcations delimit a region of bistability. In large containers, the dynamics is characterized by a supercritical Hopf bifurcation that marks the transition from steady flow to a traveling wave (TW) mode. The critical Ma for this transition increases with $\mathrm{\Gamma }$. In intermediate containers, a complex pattern selection scenario is found, where both steady and oscillatory convection, in the form of either TWs or SWs, can appear depending on $\mathrm{\Gamma }$ and Ma. Finally, we apply this bifurcation analysis to help explain recent results on thermocapillary flows during the melting of phase change materials in microgravity [Salgado Sánchez et al., Int. J. Heat Mass Transf. 163, 120478 (2020); Salgado Sánchez et al., J. Fluid Mech. 908, A20 (2021)]. The temporal evolution of the phase change is characterized by an effective $\mathrm{\Gamma }$ and Ma in the liquid phase. We find very good agreement between the flow transitions observed during melting and those predicted for the equivalent rectangular containers over the explored range of $1.5\le \mathrm{\Gamma }\le 16$.