Recently the dynamics of flows beneath ice cover has garnered much interest in the environmental fluid dynamics community. Of particular importance is understanding how heat introduced via solar radiation is transported within a body of cold fresh water (characteristic temperatures are below the temperature of maximum density), and how a subsurface current affects this process. In this study we present high-resolution numerical simulations of the interaction between cold water convection and a parallel shear flow. The results of this paper show that for a sufficiently strong shear current, the growth phase of instabilities generated by volumetric thermal forcing (which represents solar radiation) is nearly two-dimensional and that the transition to more vigorous three-dimensional motion is initialized by baroclinic production of vorticity by convective instabilities followed by a rapid increase in streamwise vorticity generated by vortex tilting and stretching. We describe how this process is modified by differences in shear strength and thermal forcing attenuation length.

The processing of thin-structured materials in a fluidic environment, from nearly inextensible but flexible graphene sheets to highly extensible polymer films, arises in many applications. So far, little is known about the dynamics of such thin sheets freely suspended in fluid. In this work, we study the dynamics of freely suspended soft sheets in uniaxial extensional flow. Elastic sheets are modeled with a continuum model that accounts for in-plane deformation and out-of-plane bending, and the fluid motion is computed using the method of regularized Stokeslets. We explore two types of sheets: “stiff” sheets that strongly resist bending deformations and always stay flat and “flexible” sheets with both in-plane and out-of plane deformability that can wrinkle. For stiff sheets, we observe a coil-stretch-like transition, similar to what has been observed for long-chain linear polymers under extension as well as elastic sheets under planar extension: In a certain range of capillary number (flow strength relative to in-plane deformability), the sheets exhibit either a compact or a highly stretched conformation, depending on deformation history. For flexible sheets, sheets with sufficiently small bending stiffness wrinkle to form various conformations. Here the compact-stretched bistability still occurs but is strongly modified by the wrinkling instability: A highly stretched planar state can become unstable and wrinkle, after which it may dramatically shrink in length due to hydrodynamic screening associated with wrinkling. Therefore, wrinkling renders a shift in the bistability regime. In addition, we can predict and understand the nonlinear long-term dynamics for some parameter regimes with linear stability analysis of the flat steady states.

We report nonlinear saturation of bubble evolution occurring in a two-dimensional single-mode stratified compressible Rayleigh–Taylor instability via direct numerical simulation (DNS). A range of Atwood number ($\text{At}=0.1\sim 0.9$) are tested at varying levels of density stratification, corresponding to a range of static compressibility quantified as a Mach number over $\text{Ma}=0.1\sim 1$. Density stratification is found to cause different bubble behaviors for different At, with a critical At of 0.25 at which nonlinear saturation of bubble growth is realized. A modified buoyancy-drag model for stratified compressible RTI is proposed giving an accurate analytical prediction on this DNS-obtained critical At. Of special interest, similar nonlinear saturation is uncovered for the bubble evolution at $\text{At}=0.9$ as the pistonlike effect that describes the compressing effects of the rising bubble of light fluid exerting on the heavy fluid ahead of its front is fully extracted. Furthermore, it is demonstrated that the acceleration of the heavy fluid compressed in front of the bubble characterizing the pistonlike effect is nearly constant for different Ma and its ratio to the external acceleration has a fascinating power law scaling as ${\text{At}}^{2.5}{\text{Ma}}^2$.

The interfacial instability and flow patterns of coaxial liquid cone in a coflow focusing (CFF) process are investigated through the integration of experiments and numerical simulations. Based on the flow fields obtained quantitatively in numerical simulations, the startup process of focused coaxial liquid cone is established, and the streamlines of focusing stream are further compared with the potential flow model. The effects of main process parameters, including liquid flow rates, physical properties of materials, and geometrical parameters of CFF device on the cone morphologies, are given experimentally and numerically, and the local competition between the viscous shear stress and the interfacial tension on inner and outer cone interfaces is analyzed qualitatively through nondimensional parametric analysis. Moreover, through the particle tracing method in CFF experiments, the flow fields inside the liquid cone are obtained, with much attention paid to the recirculation flow occurring inside the inner liquid cone. The results show that the variation of liquid flow rates can manipulate the size of recirculation flow, and the balance of tangential shear stress makes main contributions to the formation of recirculation flow. This study provides significant guidance for the generation of microcapsules by the CFF technique in practical applications.

Although liquid behaviors in micrometric scales can be observed optically and those below nanometric scales can be probed with atomic force microscopy, those in the ranges from tens to hundreds of nanometers have seldom been visualized due to limits in optical and electron microscopy. Here we report direct visualization of condensation and wicking of water on arrays of solid walls with gaps ranging from tens to hundreds of nanometers, by reducing electron-beam-induced heating in the environmental scanning electron microscopy. We find that the water condensing and wicking on hydrophilic nanopatterns exhibits little difference from what has been observed on micropatterns. However, the condensation behavior of water on hydrophobic nanopatterns is found not to follow the conventional capillary condensation theory. The hydrophobic grooves of 40–80 nm widths are observed to be completely wetted by condensing water vapor, but do not allow externally approaching liquid water to invade themselves. We expect our experiments to trigger further experimental attempts to observe nanoscale liquid menisci in various situations. In addition, those peculiar nanoscale behaviors of water reported here will broaden our knowledge of nanoscale wetting and feed empirical inputs for theoretical models.

We present a numerical study that investigates the fluid-structure interaction of a flexible cantilever cylinder with a uniform flow at low Reynolds numbers ($\text{Re}$). A fully coupled fluid-structure solver based on the three-dimensional Navier-Stokes equations and Euler-Bernoulli beam theory is employed to examine the coupled dynamics of the flexible cylinder. Of particular interest is to explore the possibility of flow-induced vibrations at laminar subcritical $\text{Re}$, i.e., no periodic vortex shedding, and assess the extent to which such a flexible cylindrical beam could sustain the vibrations at this $\text{Re}$ regime. We find that when certain conditions are satisfied, the flexible cantilever cylinder experiences sustained vortex-induced vibrations (VIVs), with the frequency of the transverse oscillations matching the first-mode natural frequency of the cylinder. The range of the frequency match, known as the lock-in regime, is found to have a strong dependence on the Reynolds number $\text{Re}$, mass ratio $m^{*}$, and reduced velocity $U^{*}$. Unlike the steady wake behind a stationary rigid cylinder, the wake of the flexible cantilever cylinder is shown to become unstable at Reynolds numbers as low as $\text{Re}=22$ when system parameters are within the lock-in regime. A combined VIV-galloping type instability is suggested as the mechanism behind the sustained unsteadiness in the wake and large-amplitude vibrations of the cylinder at laminar subcritical $\text{Re}$. These findings attempt to generalize our understanding of flow-induced vibrations in flexible cantilever structures and have a relevance to the development of novel bio-inspired flow-sensing devices.

In the current work, we numerically study the effect of traveling-wave surface morphing actuation. Although this actuation strategy has been studied at higher Reynolds numbers for an airfoil and a rectangular flat plate, its effects at low Reynolds numbers relevant to micro-air vehicles have not yet been investigated. We perform high-fidelity two-dimensional numerical simulations to study the effects of traveling wave surface morphing on the suction surface of NACA0012 at $\text{Re}=1000$. The kinematics of actuation are defined by wave number and wavespeed, both of which are varied over a wide range of values to include parameters that considerably change the lift dynamics as well as those that do not. We first study the effect of actuation at an angle of attack of $\alpha =5^{\circ }$, where the unactuated flow is steady. The lift dynamics are found to align with the surface morphing kinematics, and there is a low-pressure minimum shown to be introduced into the flow-field by morphing that advects at a speed agnostic to the morphing parameters. Lift benefits are found to be maximal when the morphing kinematics align with this intrinsic flow speed. We then investigate the role of morphing in the presence of an unsteady, separated baseline flow (with intrinsic vortex-shedding processes) at $\alpha ={15}^{\circ }$. At this higher angle of attack, we identify three distinct behavioral regimes based on the relationship between morphing and the underlying shedding frequency. Of these regimes, the most beneficial to mean lift is the lock-on regime, where the vortex-shedding dynamics align with the morphing kinematics. Lock-on was similarly found using this actuation strategy at higher Reynolds numbers, though in that setting the effect was to reduce separation, whereas at these lower Reynolds numbers the outcome is that vortex shedding persists with—in certain cases—significant lift benefits. We also identify other regimes where morphing can become out of phase with the vortex-shedding dynamics, termed here the interactive regime, and where morphing leaves the unactuated dynamics unaltered, termed here the superposition regime. At the higher angle of attack, parameters leading to lift benefits/detriments are explained in terms of the effect of morphing on the leading and trailing-edge vortex. Where appropriate, connections between the mechanisms at the higher angle of attack are drawn to the matching/disparity of timescales between morphing and lift-producing pressure signatures seen in the lower-angle-of-attack setting.

The Marangoni contraction of sessile droplets occurs when a binary mixture of volatile liquids is placed on a high-energy surface. Although the surface is wetted completely by the mixture and its components, a quasistationary nonvanishing contact angle is observed. This seeming contradiction is caused by Marangoni flows that are driven by evaporative depletion of the volatile component near the edge of the droplet. Here, we show that the composition of such droplets is governed by Taylor dispersion, a consequence of diffusion and strong internal shear flow. We demonstrate that Taylor dispersion naturally arises in a self-consistent long-wave expansion for volatile liquid mixtures. Coupled to diffusion-limited evaporation, this model quantitatively reproduces not only the apparent shape of Marangoni-contracted droplets, but also their internal flows.

The Pi Chamber is a cloud chamber at Michigan Technological University that utilizes moist turbulent Rayleigh-Bénard flow between two temperature-controlled, saturated plates to create cloud conditions in a controlled laboratory setting. This experimental apparatus has been the source of numerous scientific studies but also offers an advantageous platform with which to test numerical modeling approaches. In this study, the primary goal is to use direct numerical simulation (DNS) with Lagrangian aerosol/droplet microphysics to recreate, as realistically as possible, the conditions inside the Pi Chamber. The biggest discrepancies between the DNS and laboratory setups are the Rayleigh number ($\mathrm{Ra}=7.9\times {10}^6$ in the DNS) and the use of periodic lateral boundary conditions. Nonetheless, numerical experiments are conducted for two published Pi Chamber cases: steady aerosol injection and the resulting statistically steady-state cloud and transient conditions when aerosol injection is shut off. Generally speaking, the DNS is able to capture many of the salient features observed in the Pi Chamber experiments, both qualitatively and quantitatively, including microphysical details and influences on the fluctuating ambient saturation in the chamber. From the DNS, Lagrangian statistics are interrogated which are otherwise inaccessible from the experimental view. In particular, the supersaturation fluctuations seen by droplets are observed to deviate from a Gaussian distribution—a common assumption in stochastic modeling—and the probability distribution of droplet lifetime does not adhere to the expected behavior assuming solid particles settling in a quiescent medium.

Over a sufficiently long period of time, or from an appropriate distance, the motion of many swimmers can appear smooth, with their trajectories appearing almost ballistic in nature and slowly varying in character. These long-time behaviors, however, often mask more complex dynamics, such as the side-to-side snakelike motion exhibited by spermatozoa as they swim, propelled by the frequent and periodic beating of their flagellum. Many models of motion neglect these effects in favour of smoother long-term behaviors, which are often of greater practical interest than the small-scale oscillatory motion. While it may be tempting to ignore any yawing motion, simply assuming that any effects of rapid oscillations cancel out over a period, a precise quantification of the impacts of high-frequency yawing is lacking. In this study, we systematically evaluate the long-term effects of general high-frequency oscillations on translational and angular motion, cast in the context of microswimmers but applicable more generally. Via a multiple-scales asymptotic analysis, we show that rapid oscillations can cause a long-term bias in the average direction of progression. We identify sufficient conditions for an unbiased long-term effect of yawing, and we quantify how yawing modifies the speed of propulsion and the effective hydrodynamic shape when in shear flow. Furthermore, we investigate and justify the long-time validity of the derived leading-order solutions and, by direct computational simulation, we evidence the relevance of the presented results to a canonical microswimmer.

Space-Lagrangian random walk models conceptualize advective transport in terms of collections of particles undergoing fixed-length steps along flow streamlines. The statistics and correlation structure of the underlying flow velocity statistics determine the transit times of particles undergoing advective transport. Broad velocity distributions lead to broadly distributed step transit times, reproducing commonly observed anomalous transport features such as superdiffusive plume growth, which are not captured by classical Fickian theories. Early space-Lagrangian models considered uncorrelated velocities across steps. These approaches were later extended to account for correlations through a spatial-Markov process. Here, we compare longitudinal dispersion dynamics in an uncorrelated continuous-time random walk with fixed-space steps to a Bernoulli relaxation spatial-Markov model exhibiting exponential decay of spatial velocity correlations along streamlines. We provide rigorous theoretical derivations, validated against numerical simulations. We find that, although the scaling forms of asymptotic dispersion agree between the two models, exact asymptotic equivalence requires employing different correlation lengths, which depend on the underlying Eulerian velocity statistics. The two models become equivalent in the limit of very broad velocity distributions, corresponding to a new quasiballistic regime recently identified in unsaturated porous media, which we rigorously characterize here.

We systematically study the role of surface roughness in fluid flow through rough fractures by using direct numerical simulations. Random rough fractal surfaces are generated with different relative roughness, which are then decomposed using the wavelet analysis method. Different frequencies of surface topological information is filtered in a level-by-level procedure, while the large-scale waviness remains approximately unchanged. To explore the effects of surface roughness across a spectrum of length scales, simulations are carried out for each approximation level under different flow conditions and fracture spacing. Our results reveal the impact of relative roughness and roughness details at different length scales on the nonlinear flow behavior due to inertia associated with the formation of eddy flows. We further propose an error index to describe the relative error in permeability induced by limited resolution in surface profile description. Our analysis shows that the relative error in permeability from surfaces under different levels of approximation and relative roughness can be well described by the proposed index for a wide range of flow conditions and fracture apertures. This study provides insights into the role of multiscale roughness on the fluid flow through rough fractures.

Thin-film-based nanoporous membrane technologies exploit evaporation to efficiently cool microscale and nanoscale electronic devices. At these scales, when domain sizes become comparable to the mean-free path in the vapor, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of higher-order moment methods is called for. Two higher-order moment equations are considered; the linearized versions of the Grad 13 and Regularized 13 equations. These are applied to the problem of nanoporous evaporation, and results are compared to the NSF method and the method of direct simulation Monte Carlo (i.e., solutions to the Boltzmann equations). Linear and nonlinear versions of the boundary conditions are examined, with the latter providing improved results, at little additional computational expense, compared to the linear form. The outcome is a simultaneously accurate and computationally efficient method, which can provide simulation-for-design capabilities at the nanoscale.

The precise description of the motion of anisotropic particles in a flow rests on the understanding of the force and torque acting on them. Here, we study experimentally small, very elongated particles settling in a fluid at small Reynolds number. In our experiments, we can, to a very good approximation, relate the rate of rotation of cylindrical tungsten rods, of aspect ratios $\beta =8$ and $\beta =16$, settling in pure glycerol, to the torque they are experiencing. This allows us to compare the measured torque with expressions obtained either in the slender-rod limit or in the case of spheroids. Both theories predict a simple angle dependence for the torque, which is found to capture very well the experimental results. The slender-rod theory overestimates the results for the two aspect ratios considered, while the expression obtained for a spheroid provides a better approximation for $\beta =16$. Comparing our results with those of previous experiments provides further insight on the conditions of validity of the slender-rod theory. The translational dynamics is shown to be in qualitative agreement with the slender-rod and spheroid models, the former one being found to represent better the experimental data.

The linear stability analysis of a ferrofluid confined in a cylindrical annulus with a rotating inner cylinder and a resting outer cylinder is performed when a magnetic field and a radial temperature gradient are applied to the ferrofluid. The inhomogeneous magnetic field created by a stack of magnets inserted inside the inner cylinder interacts with the magnetization of the ferrofluid and produces the Kelvin force. The later contains, besides a conservative term, a nonconservative part which can be seen as a magnetic buoyancy with a corresponding magnetic gravity. The magnetic buoyancy generates a thermomagnetic convection in the cylindrical annulus at a critical value of the temperature difference. The threshold of the thermomagnetic convection depends on the radius ratio of the annulus and it is independent of the Prandtl number ($\mathrm{Pr}$). The centrifugal instability is affected by the magnetic buoyancy. The centrifugal buoyancy has been included in the analysis and its effects are very sensitive to the diffusive nature of the fluid, i.e., to $\mathrm{Pr}$. A weak rotation of the inner cylinder decreases the threshold for $\mathrm{Pr}<325$ and it increases it for $\mathrm{Pr}>325$. An energy analysis indicates the relative importance of the dominant mechanisms driving the destabilization of the ferrofluid flow.

In this study, the dynamical behavior of the vortex pair produced in the wake of a cylinder with a slanted afterbody, relevant to cargo aircraft applications, is examined experimentally through time-resolved particle image velocimetry (TR-PIV) and fast-response pressure sensitive paint (PSP). The vortex wandering phenomenon, characterstic of this wake, is measured with state of the art, time-resolved diagnostics at Reynolds numbers ranging from ${\text{Re}}_D=25000$ to $750000$ and a slant angle of $\varphi ={45}^{\circ }$. Spectral proper orthogonal decomposition reveals a consistent and narrow normalized frequency band ($0.56<{\text{St}}_D<0.64$) with significant energetic peaks in both surface pressure and near-field vortex velocity fields across all Reynolds numbers examined. Pressure sensitive paint measurements at free stream velocities ranging from 15 m/s (${\text{Re}}_D=150000$) to 75 m/s (${\text{Re}}_D=750000$) reveal a strong unsteady signature of the flow structures that are related to the vortex wandering at these normalized frequencies. These structures consist of traveling pressure waves at the surface that excite the helical mode of the vortex core. These pressure patterns could be detected at free-stream velocities as low as 15 m/s, where the pressure fluctuations are of the order of 20 Pa.

The dynamic interactions between pairs of swimming microorganisms underpin the collective behavior of larger suspensions, but accurately calculating pairwise collisions has typically required the use of numerical simulations in which hydrodynamic interactions are fully resolved. In this paper, we utilize analytical expressions for forces and torques acting on two closely separated spherical squirmers—accurate to second order in the ratio of cell-cell spacing to squirmer radius—to calculate their scattering dynamics. Attention is limited to squirmers whose orientation vectors lie in the same plane. We characterize the outgoing angles of pairs of bottom-heavy squirmers in terms of their incoming angles, the squirmer parameter $\beta$, and the strength of the external gravitational field, discovering transient scattering, stationary bound states, pairwise swimming motion, and circular orbits. These results compare well with full numerical solutions obtained using boundary element methods, highlighting the utility of lubrication theory. We expect these results will be useful for the foundations of mesoscale continuum models for suspensions of spherical microorganisms.

The role of mechanistic (shear stress) and thermal wall conditions on the scenario of finger-shaped flame acceleration at the early stages of burning in channels is studied by means of computational simulations of the reacting flow equations involving fully compressible hydrodynamics, transport properties (heat conduction, diffusion, and viscosity), and chemical kinetics imitated by a one-step Arrhenius reaction. Specifically, free-slip walls (i.e., no shear stress at the walls) or nonslip walls (with shear stress) are considered as the mechanistic conditions, while the options for the thermal boundaries include adiabatic walls or isothermal walls of various temperatures. The parametric study involves variations of the channel widths, the thermal expansion ratios, and isothermal wall temperatures for the cases of both slip and nonslip wall conditions. It is shown that the difference between the effects of slip and nonslip walls is generally small during the early stages of burning, before a flame skirt contacts a sidewall. Thereafter, wall friction may play the role; in particular, it may distort or even prevent the formation of a tulip flame front. As for the thermal boundaries, while the finger flame dynamics in adiabatic channels is oftentimes similar to that in isothermal ones, the wall temperature has an impact on flame acceleration such that a flame tends to accelerate faster in hotter channels. Moreover, for isothermal walls preheated to a high temperature, emergence and propagation of an octopuslike flame front are observed. This feature is devoted to the formation of the secondary flame segments near very hot sidewalls, due to a high wall temperature. The impact of thermal expansion on the flame acceleration rate is significant for any wall conditions; it is slightly stronger for isothermal walls, and the flame front approaches the sidewalls faster at a lower thermal expansion ratio. Variation of the channel width shows a small impact in the case of adiabatic walls as well as preheated isothermal walls, but it provides a significant influence on flame propagation in a channel with isothermal walls kept at an initial fuel temperature. At the same time, the role of the channel width is practically the same for both slip and nonslip walls. Overall, the present work verifies and underlines the limitations of the previous theoretical models and computational studies of finger flame acceleration that employed adiabatic slip walls.

Gradient-based optimization of chaotic acoustics is challenging for a threefold reason: (i) first-order perturbations grow exponentially in time; (ii) the statistics of the solution may have a slow convergence; and (iii) the time-averaged acoustic energy may physically have discontinuous variations, which means that the gradient does not exist for some design parameters. We develop a versatile optimization method, which finds the design parameters that minimize time-averaged acoustic cost functionals, and overcomes the three aforementioned challenges. The method is gradient-free, model-informed, and data-driven with reservoir computing based on echo state networks. First, we analyze the predictive capabilities of echo state networks in thermoacoustics both in the short- and long-time prediction of the dynamics. We find that both fully data-driven and model-informed architectures are able to learn the chaotic acoustic dynamics, both time-accurately and statistically. Informing the training with a physical reduced-order model with one acoustic mode markedly improves the accuracy and robustness of the echo state networks, while keeping the computational cost low. Echo state networks offer accurate predictions of the long-time dynamics, which would be otherwise expensive by integrating the governing equations to evaluate the time-averaged quantity to optimize. Second, we couple echo state networks with a Bayesian technique to explore the design thermoacoustic parameter space. The computational method is minimally intrusive because it requires only the initialization of the physical and hyperparameter optimizers. Third, we find the set of flame parameters that minimize the time-averaged acoustic energy of chaotic oscillations, which are caused by the positive feedback with a heat source, such as a flame in gas turbines or rocket motors. These oscillations are known as thermoacoustic oscillations. The optimal set of flame parameters is found with the same accuracy as brute-force grid search but with a convergence rate that is more than one order of magnitude faster. This work opens up new possibilities for nonintrusive (“hands-off”) optimization of chaotic systems, in which the cost of generating data, for example, from high-fidelity simulations and experiments, is high.

When the Rayleigh number is low, Rayleigh-Bénard convection in a nonrotating spherical shell with central gravity has symmetric solutions in terms of three-dimensional discrete rotation. All the known patterns with the regular polyhedral symmetries accompany reflection symmetry. We found an alternative type of steady convection in a nonrotating spherical shell by computer simulations. The pattern has the discrete rotational symmetry of a regular tetrahedron with no reflection symmetry. The convection consists of six pairs of spiral rolls placed on 12 faces of a spherical dodecahedron. Depending on the winding of the spirals, there are two possible configurations that are mirror images of one another.