We conduct direct numerical simulations of turbulence sustained in slowly precessing spheroids with the absolute value of the ellipticity $\eta$ being between zero (i.e., a sphere) and 0.2. Using a flexible grid generation algorithm, we can effectively simulate flows in an arbitrarily shaped container. This enables us to investigate the ellipticity dependence of the precession-driven flow in spheroids with the spin and precession axes being at a right angle. The numerical results are in excellent agreement with experimental data under the same flow conditions. In particular, we numerically realize hysteresis loops, which have been well known since the seminal experiments by Malkus [Science 160, 259 (1968)], connecting two qualitatively different states in a precessing spheroid with non-negligible ellipticity $\left|\eta \right|$ larger than about $10/\sqrt{\text{Re}}$ (where $\text{Re}$ denotes the Reynolds number defined by using the spin angular velocity). Our numerical simulations reveal the three-dimensional turbulent flow structures in these states. One is a high-energy state where the mean flow is approximated by a uniform-vorticity flow. The other is a low-energy state with twisted mean-flow streamlines, which lead to fully developed turbulence when the Reynolds number is high enough. The mean-flow structures in the low-energy state are common irrespective of the ellipticity; namely, the main component of the mean flow is a circulation about the axis perpendicular both to the spin and precession axes, but the torsion of the mean-flow streamlines is larger for smaller $\eta$. For sufficiently high Reynolds numbers, the low-energy state and therefore developed turbulence are sustained for the Poincaré number (the precession rate) larger than about $\left|\eta \right|/2$. On the other hand, stronger precession leads to the significant reduction of turbulence in a central region of the container. Hence, a container with smaller $\left|\eta \right|$ is adequate to sustain developed turbulence with weak precession.

We examine the waveforms of linear waves over a fully submerged, arbitrarily periodic bed, using the recent Floquet theory for gravity waves and extending it to the regime of capillary-gravity waves. The exact solutions illustrate the complex features of waveform geometry that are frequency dependent, including the modulation of propagating waveforms in space-time, spatially modulated standing waveforms, asymmetric waveforms over a symmetric bed profile, and high-curvature wave-crest forms. These features are in contrast to the trivial and invariant sinusoidal waveform of the ordinary linear waves on a flat bed, but reminiscent of nonlinear waveforms. The effect of surface tension is seen to counteract wave scattering by topography, tending to restore the waveform towards a symmetric and sinusoidal geometry. These features are the general characteristics of linear waves over a periodic bed since they are the properties of eigenmodes, and can inspire and guide applications.

There are many experimental works and analyses of gravity water surface waves in vibrating high-aspect-ratio rectangular tanks. In most cases, the waves are symmetric or antisymmetric in the direction along the short sides. Here we report an unusual alternately localized Faraday wave (ALFW) in this system which is neither symmetric nor antisymmetric along the short side direction. The peculiar feature is that close to the boundary there are a series of large oscillating regions and flat regions; i.e., the surface barely moves during the experiment. The large oscillating regions and the flat regions appear alternately not only in the direction along the long side of the tank, but also along the short side. The large surface deformation implies strong nonlinearities of the phenomenon. The spectrum of the discrete cosine transformation of the surface profile shows clearly that there are only two dominating modes. However, further analyses reveal that it is not simply a two-mode excitation through external driving, but a one mode excitation, then pumping the other mode excited through strong internal mode interactions in a leading-passive way. We use the phenomenological nonlinear mode competition model, which is a set of coupled nonlinear Mathieu equations, to reproduce the ALFW pattern. Theoretical analyses and numerical simulations indicate that both nonlinear internal mode interactions and nonlinear bounding effects account for this phenomenon. Phase locking and amplitude bounding can be reproduced quantitatively by the model. The instability boundary in the parameter space obtained by numerical simulations fits the one obtained by experiments very well.

Liquid-jet impingement on flat impermeable substrates is important for a multitude of applications ranging from electronic-equipment cooling to fuel atomization and erosion of solid surfaces. On a wettable horizontal surface, where a sufficient downstream liquid depth can be sustained after axisymmetric impingement, the jet forms a thin film on the substrate up to a radial distance where the film height suddenly increases, forming a hydraulic jump. On a superhydrophobic surface, where a downstream liquid depth is not naturally sustained, the thin film expands and breaks up into droplets, which are subsequently ejected in a random fashion outward, as carried by their radial momentum. In the present work, a facile, scalable, wettability-patterning approach is presented for delaying or even eliminating droplet breakup in the case of jet impingement on horizontal superhydrophobic surfaces. Analytical expressions for predicting the hydraulic jump and droplet breakup locations are developed to designate the proper wettability patterns that facilitate alteration and control of the postimpingement liquid behavior. The axisymmetric model is extended to evaluate the radial variation of the competing forces responsible for film breakup, and a design criterion for the effective wettability patterns is proposed.

Several results on sedimenting equal spheres obtained by resolved simulations with the Physalis method are presented. The volume fraction ranges from 8.7% to 34.9% and the particle Galilei number from 49.7 to 99.4. The results shown concern particle collisions, diffusivities, the mean free path, the particle pair distribution function, and other features. It is found that many qualitative trends found in earlier studies continue to hold in the parameter range investigated here as well. The analysis of collisions reveals that particles interact prevalently via their flow fields rather than by direct contacts. A tendency toward particle clustering is demonstrated. The time evolution of the shape and size of particle tetrads is examined.

The onset and growth of shear instability in large-amplitude internal solitary-like waves propagating in a quasi-two-layer stratification is studied using high-resolution direct numerical simulations with a spectral collocation method. These waves have a minimum Richardson numbers of approximately 0.08 and a length ratio $L_{\mathrm{Ri}}/L_{\text{wave}}$ between 0.80 and 0.88, where $L_{\mathrm{Ri}}$ is the length of high shear region with a local Richardson number $\mathrm{Ri}<0.25$ and $L_{\text{wave}}$ is the half-width of the wave. In the wave with $L_{\mathrm{Ri}}/L_{\text{wave}}\approx 0.88$, the onset of instability occurs spontaneously without interacting with any externally imposed physical noise. When $L_{\mathrm{Ri}}/L_{\text{wave}}\lesssim 0.86$, the onset of instability is limited by viscous effects, so that criteria for the onset also include the Reynolds number of the flow field and the amplitude of the external noise. In the wave with $L_{\mathrm{Ri}}/L_{\text{wave}}\approx 0.85$, the spontaneous instability is possible only when the Reynolds number is sufficiently large, whereas in the wave with $L_{\mathrm{Ri}}/L_{\text{wave}}\approx 0.80$, instability does not grow spontaneously but must be triggered by perturbations of finite amplitude. For instabilities triggered by externally imposed noise, the amplitude of the noise has a crucial influence on their growth, whether such noise is in the form of random perturbations or normal-mode disturbances. On the other hand, the importance of non-normal growth decreases as the length ratio $L_{\mathrm{Ri}}/L_{\text{wave}}$ increases and as the amplitude of perturbations increases. In the wave with $L_{\mathrm{Ri}}/L_{\text{wave}}\approx 0.88$, further perturbing the flow field with sufficiently large perturbations leads to the growth of instability on the upstream side of the wave's crest, a result close to the optimal transient growth, even though the perturbations are in the form of normal-mode disturbances.

The role of activity on the hydrodynamic dispersion of bacteria in a model porous medium is studied by tracking thousands of bacteria in a microfluidic chip containing randomly placed pillars. We first evaluate the spreading dynamics of two populations of motile and nonmotile bacteria injected at different flow rates. In both cases, we observe that the mean and the variance of the distances covered by the bacteria vary linearly with time and flow velocity, a result qualitatively consistent with the standard geometric dispersion picture. However, quantitatively, the motile bacteria display a systematic retardation effect when compared to the nonmotile ones. Furthermore, the shape of the traveled distance distribution in the flow direction differs significantly for both the motile and the nonmotile strains, hence probing a markedly different exploration process. For the nonmotile bacteria, the distribution is Gaussian, whereas for the motile ones, the distribution displays a positive skewness and spreads exponentially downstream akin to a $\mathrm{\Gamma }$ distribution. The detailed microscopic study of the trajectories reveals two salient effects characterizing the exploration process of motile bacteria: (1) the emergence of an “active” retention effect due to an extended exploration of the pore surfaces and (2) an enhanced spreading at the forefront due to the transport of bacteria along “fast tracks” where they acquire a velocity larger than the local flow velocity. We finally discuss the practical applications of these effects on the large-scale macroscopic transfer and contamination processes caused by microbes in natural environments.

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.

Shock-particle interaction is a fundamental problem in many engineering applications, with the dynamics being heavily influenced by the incident-shock Mach number and the particle volume fraction. In this paper we present fully resolved inviscid simulations of an incident-shock wave traveling through a bed of randomly distributed spherical particles. We vary the strength of the incident shock along with the particle volume fraction in order to study the complex wave interaction during shock-particle interaction. In this study we are interested in the early-time behavior during which the particles do not move and hence in our simulations all the particles are fixed in space. We compute the streamwise average of flow field quantities to generate the $x\text{−}t$ contour plots to study the unsteady oscillations inside the particle bed. We observe that the transmitted shock slows down under certain conditions and it is partly due to tortuosity and partly due to weakening caused by energy dissipation. We also present the force histories of the streamwise drag and lift forces for all the particles. The random distribution of particles leads to high variability in the drag force experienced by the particles. We compute the mean peak drag force as a function of the streamwise location to study the mean behavior of the transmitted shock. Based on our findings, we propose simple modifications to improve the current point-particle models used in Euler-Lagrange simulations of shock interacting with a bed of particles.

Laboratory experiments are performed examining the enhanced damping of surface waves by floating spherical particles. Without particles, wave amplitudes decay exponentially in time; with the particles, the dissipation is enhanced such that waves are arrested in finite time. Initially the decay is exponential with an e-folding time that is inversely proportional to the depth of the particle layer, but independent of particle size. At later times and lower amplitudes, the decay turns into a power law ${(t_s-t)}^q$, with exponent lying between $q\simeq 2$ and 3. The stopping time $t_s$ also decreases with increasing particle layer depth.

Upper bounds on the heat transport and other quantities of interest in Rayleigh-Bénard convection are derived in previous work from constraints resulting from the equations of time evolution for kinetic energy, the root mean square of temperature, and the temperature averaged over horizontal planes. Here we investigate the effect of a constraint derived from the time evolution equation for the advective heat transport. This additional constraint leads to improved bounds on the toroidal dissipation.

Direct numerical simulations of passive scalar transport in turbulent channel flow subject to spanwise rotation are carried out with two different boundary conditions for the scalar. In the first case the scalar transport is driven by an assigned scalar difference at the walls and in the second case by a constant mean streamwise scalar gradient. The Reynolds number $\text{Re}=U_{b}h/\nu$ is fixed at $14000$ and the rotation number $\text{Ro}=2\mathrm{\Omega }h/U_b$ is varied from 0 to 0.75, where $U_b$ is the mean bulk velocity, $h$ half the channel gap width, and $\mathrm{\Omega }$ the rotation rate. This work is a continuation of Brethouwer [J. Fluid Mech. 844, 297 (2018)] to further study the influence of rotation and also the influence of scalar boundary conditions on scalar transport in channel flow. Mean scalar profiles and other scalar statistics differ in the two cases with different boundary conditions but are similar in the near-wall region in terms of local wall units. The conclusion of Brethouwer that the Reynolds analogy for scalar-momentum transfer does not apply to rotating channel flow is independent of scalar boundary conditions. Rotation influences the turbulent scalar flux differently than the Reynolds shear stress and strongly reduces the turbulent Prandtl number on the unstable channel side, irrespective of the scalar boundary conditions. Scalar structures are larger than the turbulence structures in rotating channel flow, in contrast to nonrotating channel flow where these are similar.

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 series of laboratory experiments on the generation of internal waves by a short duration impulsive, turbulent, forced plume descending into a stratified layer has been conducted. After the plume descends to a maximum depth it rebounds to an equilibrium level where the ensuing oscillation results in the generation of a propagating internal wave field. The finite duration impulsive plumes exhibited two classes of behavior: (1) Plumes with a density that matched that of the bottom of the stratified layer had a constant fraction of the plume energy transferred to the internal wave field, with an average value of $E_{\mathrm{IW}}/E_P\cong 6\%$, independent of the duration of the plume release. In contrast, (2) plumes with lower densities, half that of the bottom of the stratified layer, exhibited a larger degree of coupling of the plume energy to the internal wave field that increased with the duration of the plume release, having an average value of $\cong 10\%$. The observed degree of internal wave energy coupling for impulsive plumes is in general agreement with prior studies of continuous convective plumes and descending buoyant parcels.

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.

As viscosity is increased, a liquid capillary jet accelerated by gravity stretches over increasingly large distances before eventually breaking up. This Newtonian behavior is profoundly altered for particulate suspensions. Adding solid particles to a liquid, which increases the effective viscosity, can paradoxically shorten the jet considerably [as first reported by Furbank and Morris, Phys. Fluids 16, 1777 (2004)]. This apparent contradiction is rationalized by considering finite-size effects occurring at the scale of a few particles. A model is presented which captures the breakup length of suspension jets observed experimentally for a broad range of liquid viscosities, particle sizes, and extrusion velocities of the jet and recovers the Newtonian case for vanishing particle sizes. These results can be readily extended to any stretched jet configuration and potentially to other fluid media having a granularity.

The onset of leading-edge stall on stationary, smooth, thin, two-dimensional airfoils with various blunt nose shapes of the form $y=\pm k{\left(ax\right)}^{\frac{1}{a}}$ (where $a\ge 2$ and $k$ is a constant) at moderately high chord Reynolds numbers (Re) is studied. A reduced-order, multiple-scale model problem is developed and is complimented by direct numerical simulations for low Re and numerical computations using a Reynolds-averaged Navier-Stokes (RANS) flow solver for moderately high Re. The asymptotic theory results in a description of the flow around a thin airfoil composed of an outer region about a majority of the airfoil's chord, and an inner region, surrounding the nose, that match each other. The classical thin airfoil theory dominates the outer region. The coordinates in the inner region are scaled with respect to a characteristic length of the nose and the Reynolds number is modified $\left({\text{Re}}_M\right)$ in order to account for the acute velocity changes in the inner region, where both near-stagnation and high-suction areas appear. The far field of the inner region is described by a symmetric effect due to nose shape and an asymmetric effect with a lumped circulation parameter $\left(\tilde{A}\right)$ due to angle of attack and camber. The inner flow problem is solved numerically using a transformation from the physical domain to a computational domain and a second-order finite-difference scheme for integrating the vorticity and stream function. The computed results demonstrate numerical convergence with mesh refinement. The inner region solutions reveal, for various values of $a$, the nature of the flow around the nose and the inception of global separation and stall as $\tilde{A}$ increases above a certain critical value, ${\tilde{A}}_s$, at fixed $a$ and ${\text{Re}}_M$. For $a\ge 2$, the value of ${\tilde{A}}_s$ decreases with ${\text{Re}}_M$ up to a limit value, ${\text{Re}}_{M,\lim }$, above which unsteady effects increase ${\tilde{A}}_s$ and delay the onset of stall. For airfoils with the same thickness ratio and position of maximum thickness, global stall is delayed to higher angles of attack as $a$ is increased above 2. The results of the RANS computations for various $a$ show matching with the asymptotic results in a certain region of ${\text{Re}}_M$ values, as well as extend the stall predictions of ${\tilde{A}}_s$ to higher ${\text{Re}}_M$. Parametric studies provide data for the design of novel airfoils with blunt noses and higher stall angles of attack at various Re.

The influence of various inlet swirling flow profiles on the manifold of steady axisymmetric states of flows in a straight, long circular pipe of a finite length $L$ and on flow dynamics is investigated. The study is motivated by the bifurcation diagrams originally studied by Leclaire and Sipp [B. Leclaire and D. Sipp, J. Fluid Mech. 645, 81 (2010)] and explores, in all of their inflow cases, the relationship between bifurcation and flow evolution. Steady circumferential and axial velocities and azimuthal vorticity are prescribed at the inlet. A parallel flow state is set at the outlet. The outlet state of the steady problem may be determined by solutions of the axially independent Squire-Long equation. For each of the incoming flows studied, the solutions include the base columnar flow solution, a decelerated flow along the centerline, an accelerated flow along the centerline, a vortex-breakdown solution, and a wall-separation solution. These solutions correspond to respective steady states in the pipe. Branches of higher-order noncolumnar states that bifurcate at a sequence of critical swirl levels are also presented. The theoretical predictions are numerically realized by unsteady and inviscid flow simulations. The simulations clarify the base flow stability and the dynamics of initial perturbations to various attracting states. Results demonstrate that, depending on the inlet flow profile, the global minimum state of the energy function $\mathcal{E}$ of the problem turns at a certain critical swirl level, denoted by ${\omega }_0+\epsilon \left(L\right)$ [where $0<\epsilon \left(L\right)\ll 1$ and tends to zero with an increase of $L]$, from the columnar state to become a centerline-decelerated flow state, a vortex-breakdown state, or a wall-separation state. The jump of the global minimum state of $\mathcal{E}$ at $\omega ={\omega }_0+\epsilon \left(L\right)$ together with the critical swirl of the columnar state at $\omega ={\omega }_1$ govern the evolution of pipe vortex flows. This analysis provides understanding of all possible axisymmetric flow evolution processes for various inlet profiles and swirl levels, and the domain of attraction of crucial states.

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.