Spatial variations in ice and snow characteristics imply that radiative forcing in late winter lakes is spatially heterogeneous. We present idealized, three-dimensional simulations of buoyancy-driven flows, driven in this setting with heterogeneous solar radiation intensity, comparing rectilinear and radial cases. In both cases, radiative forcing in fresh water at temperatures below $4{}^{\circ }\mathrm{C}$ initiates an unstable stratification near the surface, leading to Rayleigh-Taylor instabilities. The variations in radiative forcing intensity generates gravity current-like flow along the surface. The resulting flow interacts with developing three-dimensional Rayleigh-Taylor instabilities. We provide an in-depth analysis of the development and death of the gravity current-like flow in the two cases mentioned. We find that while the interaction of this current with radiatively driven convection does create instabilities along the leading edge and slow its propagation, it is mixing with the convective and warm return flow that leads to the cessation of propagation and eventual death of the current. Differences in geometry affect the depth of the shear layer between the current and return flow, determining the timing of when propagation ends.

Nonlinear axisymmetric shape oscillations of a Newtonian drop in a vacuum are investigated using two different theoretical methods, for fundamental interest and for the significance of the oscillations in transport processes across the drop surface. The extended discontinuous Galerkin method is contrasted to the weakly nonlinear theory. While the former allows large drop surface deformation amplitudes to be analyzed with high precision and drop volume errors below $0.11\%$ even at the largest deformations, the latter provides analytical insight into the origin of quasiperiodic time behavior of the oscillations and reveals the oscillation modes coupled in the nonlinear motion. Results from both methods for moderate initial deformation amplitudes at modes of initial drop deformation $m=2$, 3, and 4 are in excellent agreement, showing the time asymmetry of the oscillation and the decrease of the oscillation frequency with increasing deformation amplitude. The Fourier power spectra for the first oscillation period exhibit decreased dominant frequencies as compared to the linear results as well as the mode coupling as nonlinear effects. The numerical method is used to compute the oscillatory and damping behavior of viscous drops, as well as the interconversion of kinetic and surface energies during the oscillations at strong initial deformations.

For low enough flow rates, turbulent channel flow displays spatial modulations of large wavelengths. This phenomenon has recently been interpreted as a linear instability of the turbulent flow. We question here the ability of linear stability analysis around the turbulent mean flow to predict the onset and wavelengths of such modulations. Both the mean flow and the Reynolds stresses are extracted from direct numerical simulation (DNS) in periodic computational domains of different size. The Orr-Sommerfeld-Squire formalism is used here, with the turbulent viscosity either ignored, evaluated from DNS, or modeled using a simple one-point closure model. Independently of the closure model and the domain size, the mean turbulent flow is found to be linearly stable, in marked contrast with the observed behavior. This suggests that the one-point approach is not sufficient to predict instability, at odds with other turbulent flow cases. For generic wall-bounded shear flows we discuss how the correct models for predicting instability could include fluctuations in a more explicit way.

Multilayered porous media can be found widely in both natural and engineered systems. This type of heterogeneous porous structure can have a substantial influence on the effective flow and transport processes. This work aims to develop a hybrid analytical-numerical solution that elucidates the relationship between the scalar dynamics and media properties in a coupled system comprising a two-dimensional free-flow layer and a heterogeneous porous medium, operating under fully developed laminar flow conditions. In our study, we employ perturbation and homogenization methods to derive a set of one-dimensional upscaled equations for transport of a passive scalar. Subsequently, we develop an integral transform-based semianalytical solution that allows to relate the properties of the porous system to scalar mixing and spreading. To validate the newly developed solution for the upscaled system, we compare it with the numerical results for the two-dimensional scalar transport. The semianalytical solution is used to investigate the influence of the multilayered system on macroscopic transport by analyzing the scalar cloud's breakthrough curve, dispersion coefficient, and mixing. Our findings indicate that the semianalytical solution can be utilized to optimize and control dispersion of the scalar cloud. Our computational results show the potential of the solution to determine the arrangement of porous media properties to achieve a desired mixing objective.

The density of the ocean generally increases continuously with depth as a consequence of variations in salinity and temperature. In some regions, however, the density profile of the ocean adopts a (double diffusive) staircase structure in which successive layers of uniform density fluid are separated by rapid density jumps. Previous work has theoretically examined the transmission and reflection of periodic internal (gravity) waves incident upon a density staircase. This predicted the existence of transmission spikes (global modes) for certain combinations of frequency and horizontal wave number in which the incident waves transmit perfectly across a density staircase. It was hypothesized that the transmission spikes occur when the incident waves resonate with natural modes of disturbances in the staircase. Here we derive theory to investigate the interactions between incident internal waves and modes. We demonstrate a close correspondence between the frequency for incident waves at a transmission spike and the real part of the frequency of modes at the same horizontal wave number. However, the frequency of the corresponding modes has a negative imaginary part corresponding to exponential decay of the modes in time. We perform numerical simulations to examine the impact of this near-resonant coupling when a vertically localized, quasimonochromatic internal wave packet interacts with a density staircase. In a range of simulations with fixed incident wave frequency and varying horizontal wave number, the measured transmission coefficient does not exhibit transmission spikes, but decreases monotonically with increasing horizontal wave number about the critical wave number separating strong and weak transmission. We show this occurs because the incident wave excites modes that then slowly transmit energy above and below the staircase at a rate consistent with the predicted decay rate of the modes. This rate is slower for staircases with more steps with the decay time increasing as the cube of the number of steps.

This work presents a methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated in four different study cases: the Lorenz system, a modified version of the Kuramoto-Sivashinsky equation, a streamwise-periodic two-dimensional channel flow, and a confined cylinder flow. Neural networks are trained as models to capture the complex system dynamics and estimate equilibrium points through a Newton method, enabled by back-propagation. These neural network surrogate models (NNSMs) are leveraged to train a second neural network, which is designed to act as a stabilizing closed-loop controller. The training process employs a recurrent approach, whereby the NNSM and the neural network controller are chained in closed loop along a finite time horizon. By cycling through phases of combined random open-loop actuation and closed-loop control, an iterative training process is introduced to overcome the lack of data near equilibrium points. This approach improves the accuracy of the models in the most critical region for achieving stabilization. Through the use of L1 regularization within loss functions, the NNSMs can also guide optimal sensor placement, reducing the number of sensors from an initial candidate set. The data sets produced during the iterative training process are also leveraged for conducting a linear stability analysis through a modified dynamic mode decomposition approach. The results demonstrate the effectiveness of computationally inexpensive neural networks in modeling, controlling, and enabling stability analysis of nonlinear systems, providing insights into the system behavior and offering potential for stabilization of complex fluid systems.

Recent [Bose and Durbin, Phys. Rev. Fluids 1, 073602 (2016)] direct numerical simulations (DNS) of adverse- and zero-pressure-gradient boundary layers beneath moderate levels of free stream turbulence ($Tu\le 2\%$) revealed a mixed mode transition regime, intermediate between orderly and bypass routes. In this regime, the amplitudes of the Klebanoff streaks and instability waves are similar, and both can contribute significantly as these interact. Three-dimensional visualizations of transitional eddies revealed a helical pattern, quite distinct from the sinuous and varicose forms seen in pure bypass transition. This raises the fundamental question of whether the helical pattern could be attributed to a previously unknown instability mode. In the present work, based on stability analyses, we show that it is indeed the case. Two-dimensional stability analyses are performed herein for base flows extracted from DNS flow fields. The three-dimensional structure of the eigenfunction of the most unstable mode indeed reveals a helical pattern. The instability arises well upstream of the appearance of helical structures in flow visualizations. In DNS, fluctuations at wavelengths corresponding to the instability modes have negligible energy in the upstream region. Due to their high growth rates, these instability modes develop into helical patterns in the transition region, which quickly break down. The streak configuration leading to the formation of the helical mode instability is different from those leading to sinuous and varicose modes, analyzed in previous studies of pure bypass transition. Thus, the mixed mode precursor is the distinctive cause of helical mode transition.

Flying insects can achieve remarkable and robust flapping aerodynamic performance and flight stability in various environments partially owing to the passive mechanisms of their wings and bodies, but a careful analysis associated with flexible wing hinge for forward flight is missing. Here we develop a fluid-structure interaction model that couples the one-torsional-spring-based elastic wing-hinge dynamics with the flapping aerodynamics to study the aerodynamics and flight stability of the hawkmoth, Manduca sexta, with flexible wing hinge at various flight velocities. The results show that the leading-edge vortex, the body vortex, and their interactions are responsible for augmenting the vertical force production interactively at all flight velocities, enabling a $6.5\%$ increase at fast flight speeds. The elastic storage enabled by the flexible wing hinge exhibits a $J$ curve, achieving high power efficiency at intermediate forward flight velocities. We verify that the realistic wing-hinge stiffness leads to optimal aerodynamic performance in terms of vertical force production and power cost. External disturbance rejection based on the flexible wing hinge is highly robust in multiple directions, independent of the forward flight velocity. This study highlights the importance and significance of flexible wing hinges in biomimetic designs for flapping micro aerial vehicles.

Droplet breakup is frequently observed in natural and industrial processes and has been considered as a promising approach for increasing productivity and adjusting droplet size in the microfluidic production of emulsions. Although valuable insights on the breakup mechanisms of single-phase droplets in microchannels have been provided over the past decades, the breakup physics of complex emulsions is still poorly understood. Spatially asymmetric Janus microdroplets, distinct from single-phase or double emulsion droplets possessing one uniform interface with the ambient phase, are anticipated to show unique breakup behaviors, which has not been explored. Here, we conduct both microfluidic experiments and three-dimensional lattice Boltzmann simulations to investigate the dynamic breakup of ionic liquid (IL)-water Janus droplets in an assembled 3D-printed microchannel with a bifurcation. Three different flow regimes are identified: (i) division into two daughter Janus droplets, (ii) breakup into a single-phase droplet and a smaller Janus droplet, and (iii) nonbreakup. A map of the breakup modes of Janus droplets is constructed based on the average capillary numbers (${\mathrm{Ca}}_{\mathrm{av}}$) of the continuous phase and the normalized droplet equivalent diameters. We find that the strong constraint effect of the main channel and large ${\mathrm{Ca}}_{\mathrm{av}}$ values are essential to the symmetrical breakup of Janus droplets. The tunnel between the mother droplet and the wall of the main channel, which allows the lateral shift of the Janus droplet, and moderate flow rates facilitate the breakup of the IL single-phase portion of Janus droplets. Through 90° rotation of the splitting microchannel, we elucidate the distinctions in Janus droplet behaviors under two baffle orientations. Potential impacts of the oblique flow characteristic of $\left[\mathrm{bmim}\right]\mathrm{Fe}{\mathrm{Cl}}_4$-water Janus droplets on the droplet breakup are discussed.

Suppression of the coffee ring effect is desirable in many industrial applications which utilize colloidal deposition from an evaporating liquid. Here we focus on the role of particle arrest at the liquid-air interface (surface capture) which occurs at high evaporation rates. It is known experimentally that this phenomenon inhibits particles from reaching the contact line, leading to a deposit which is closer to uniform. We are able to describe this effect using a simple 1D modeling framework and, utilizing asymptotic theory, parametrize our model by the ratio of the vertical advection and diffusion timescales. We show that our model is consistent with existing frameworks for small values of this parameter, but also predicts the surface layer formation seen experimentally at high evaporation rates. The formation of a surface layer leads to a deposit morphology which mimics the evaporative flux density and so is closest to uniform when evaporation has a constant strength across the liquid-air interface.

We present an experimental investigation of the turbulent entrainment in non-Boussinesq steady plumes, focusing on three helium releases issued from an axisymmetric source, and with increasing Reynolds number. Two-dimensional instantaneous velocity fields, measured using particle image velocimetry (PIV), are exploited to compute first- and second-order velocity statistics focusing on the near field, i.e., up to a distance of a few tens of source radii. Flow visualizations and velocity statistics profiles are investigated to describe the flow transition from a quasilaminar zone, governed by Rayleigh-Taylor instability, to a more distinctly turbulent region. The vertical evolution of the integral fluxes, the Richardson number, and the entrainment coefficient are presented enlightening the influence of an increasing Reynolds number at the source. The plume characteristic density is reconstructed based on the assumption, sustained by recent literature data, of a null-divergence flow. Making use of the entrainment decomposition, we investigate the contribution of the different physical mechanisms involved in the mixing process at varying distances from the source, with a focus on the effect of the local density ratio. Our results show that the variations of the entrainment coefficient in the turbulent region are primarily affected by the near-field generation of turbulent kinetic energy and by a rising contribution of buoyancy effects. Both features do not exhibit a clear dependence on local variations of the density ratio.

Long, flexible fibers transported by a turbulent channel flow sample nonlinear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them toward the center of the flow, similar to pole vaulting. As a result, the fibers migrate away from the walls, leading to depleted regions near the boundaries and more concentrated regions in the bulk. These higher concentrations in the center of the channel result in a greater net flux of fibers than what was initially imposed by the fluid. This effect becomes more pronounced as fiber length increases, especially when it approaches the channel height.

We study the drainage of a viscous liquid film coating the outside of a solid horizontal cylinder, where gravity acts vertically. We focus on the limit of large Ohnesorge numbers $\text{Oh}$, where inertia is negligible compared to viscous effects. We first study the evolution of the axially invariant draining flow, initiated at rest with uniform film thickness $\delta$. Nonlinear simulations indicate that for each $\delta$, there is a threshold in the Bond number ($\mathrm{Bo}$), which compares the gravitational effects with surface tension, above which the draining liquid bulk ruptures. This critical $\mathrm{Bo}$ is found to scale inversely with $\delta$, and defines the existence of a quasistationary pendant liquid curtain remaining sustained below the cylinder by surface tension. The interface of the pendant curtain is unconditionally linearly unstable and is prone to Rayleigh-Plateau-like, capillarity-driven, and Rayleigh-Taylor, gravity-driven, instabilities. The linear stability of the quasistatic state along with an energy analysis of the unstable mode illustrates that while the Rayleigh-Taylor instability is always present, capillary effects dominate the instability at small $\mathrm{Bo}$, which promotes the formation of pearls enveloping the cylinder. In contrast, at large $\mathrm{Bo}$, capillarity acts in a stabilizing way and the instability is purely gravity driven, forming underside modulations. We present the asymptotic energy repartition representing the different physical mechanisms at play in the instability of the saturated curtains for a wide range of $\{\mathrm{Bo},\delta \}$. The results of the linear analysis agree with the preexisting experiments of de Bruyn [Phys. Fluids 9, 1599 (1997)] and nonlinear simulations of Weidner et al. [J. Colloid Interface Sci. 187, 243 (1997)] in the limit of a thin film and extend the results for thick films. Additionally, based on the volume made available for droplet growth by the development of the most linearly amplified wavelength, we build a tentative regime diagram that predicts the final patterns emerging from the pendant curtain, namely,  an array of saturated pearls or pendant drops or the onset of three-dimensional droplet pinch-off. Furthermore, a transient growth analysis accounting for the time evolution of the base state towards a saturated curtain conclusively demonstrates that the initial flow evolution does not result in altering the most amplified wavelength, thus rationalizing a posteriori the asymptotic analysis to predict the fate of the three-dimensional patterns.

The Fluctuating Force Fluctuating Torque (F3T) model is developed and evaluated for the dynamics of a turbulent particle-gas suspension of rough spherical particles in a turbulent Couette flow in the limit where the viscous relaxation time of the particles and the time between collisions are much larger than the integral time for the fluid turbulence. The fluid force/torque exerted on the particles comprises a steady part due to the difference in the particle velocity/angular velocity and the fluid mean velocity/rotation rate, and a fluctuating part due to the turbulent velocity/vorticity fluctuations. The fluctuations are modeled as Gaussian white noise whose variance is determined from the fluid velocity and vorticity fluctuations. The smooth and rough inelastic collision models are considered for particle-particle and particle-wall collisions. The results show that inclusion of roughness is important for accurately predicting the particle dynamics; the second moments of the velocity fluctuations for rough particles are higher than those for smooth particles by a factor of 2–10, while the second moments of the angular velocity fluctuations are higher by 1–2 orders of magnitude. The F3T model quantitatively predicts the number density, mean and root-mean-square velocity and angular velocity profiles, and the distribution functions for the particle velocity and angular velocity, even though a Gaussian model is used for the highly non-Gaussian distributions for the force and torque fluctuations.

When turbulent flow is laden with negatively buoyant particles, their mean distribution in the direction of gravity can induce stable density gradients that penalize turbulent fluctuations. This effect is studied numerically for shear-driven flow with dilute noninertial sediment. The turbulent dynamics and sediment transport depend critically on particle settling velocity $v_s$, splitting into two regimes: homogeneous weakly stratified turbulence and flow with developed turbulence atop an intermittent boundary layer. At intermediate $v_s$, neither state can be sustained and the flow laminarizes.

In this work, a numerical study on the inertial migration of particle suspension in a circular pipe with thermal effect is performed by means of the lattice Boltzmann method and the discrete element method. Both constant temperature and varied temperature conditions are taken into consideration. The migration behavior and the heat transfer are well characterized in terms of the circumferential and radial positions as well as the Nusselt number. The results show that particles tend to migrate toward the pipe bottom due to the thermal buoyancy when the fluid's temperature is higher than the particle's. For a single particle with constant temperature, it is shown that the variation of circumferential equilibrium position can be well regressed by the Richardson number and divided into three zones, i.e., an inertial lift dominating zone, a transition zone, and a buoyancy dominating zone. Both the radial equilibrium position and the Nusselt number are sensitive to the Reynolds number and increase consistently with the Grashof number. For particle suspension with constant temperature, similar migration behavior is observed with an enlarged transition zone. However, a nonmonotonic variation of the radial equilibrium position as well as the Nusselt number is discovered, which is attributed to the particle crowding effect. For varied temperature conditions, the migration process is affected by the heat capacity ratio and the Prandtl number, which determine the heating rate of the particle. Nevertheless, the radial equilibrium position is irrelevant with the thermal effect, which only depends on the Reynolds number and resembles the isothermal condition.

An expected statistical law of passive scalar turbulence subjected to high Schmidt numbers is studied with the Hessian-based Lagrangian renormalized approximation (HBLRA), a self-consistent closure theory recently developed for passive scalar turbulence. Without relying on any empirical parameters, HBLRA derives the scalar variance spectrum proportional to $k^{-1}$ in the viscous-convective range predicted by Batchelor. Thanks to improvements in the physical description, HBLRA yields quantitatively better predictions of the scalar variance spectrum and its universal constant in comparison with pioneering closure theories. Our results suggest that the turbulence motion of only a limited scale range may contribute to the scalar flux within the viscous-convective range. Numerical solutions for finite Schmidt numbers ($\text{Sc}=10$–$100000$) are obtained, where a clear viscous-convective range appears with a well-developed inertial-convective range.

Hydrofoils with symmetric oscillations can generate asymmetric vortex wakes. This surprising asymmetry has been widely reproduced, but a simple metric to predict its onset has remained elusive. Here, using a combination of vortex modeling and water channel experiments, we show that vortex wake deflection is well predicted by the “relative dipole angle.” In addition to offering a predictive physics-based metric, our results show that a hydrofoil's wake can converge much slower than previously thought (more than 200 oscillation cycles), and that the wake's asymmetry is more than a memory of the hydrofoil's initial condition—it is an instability inherent to the vortex street.

We study transport in synthetic, bidisperse porous structures, with arrays of microchannels interconnected by a nanoporous layer. These structures are inspired by the xylem tissue in vascular plants, in which sap water travels from the roots to the leaves to maintain hydration and carry micronutrients. We experimentally evaluate transport in three conditions: high pressure-driven flow, spontaneous imbibition, and transpiration-driven flow. The latter case resembles the situation in a living plant, where bulk liquid water is transported upwards in a metastable state (negative pressure), driven by evaporation in the leaves; here we report stable, transpiration-driven flows down to $\sim -15$ MPa of driving force. By varying the shape of the microchannels, we show that we can tune the rate of these transport processes in a predictable manner, using a simple analytical (effective medium) approach and numerical simulations of the flow field in the bidisperse media. We also show that the spontaneous imbibition behavior of a single structure—with fixed geometry—can behave very differently depending on its preparation (filled with air vs evacuated), because of a dramatic change in the conductance of vapor in the microchannels; this change offers a second way to tune the rate of transport in bidisperse, xylemlike structures by switching between air-filled and evacuated states.

This work explores the dynamic response of a turbulent boundary layer to large-scale reactive opposition control, at a friction Reynolds number of ${\text{Re}}_{\tau }\approx 2240$. A surface-mounted hot-film is employed as the input sensor, capturing large-scale fluctuations in the wall-shear stress, and actuation is performed with a single on/off wall-normal blowing jet positioned $2.4\delta$ downstream of the input sensor, operating with an exit velocity of $v_{\mathrm{j}}=0.4U_{\infty }$. Our study builds upon the work of Abbassi et al. [Int. J. Heat Fluid Flow 67, 30 (2017)] and includes a control-calibration experiment and a performance assessment using PIV- and PTV-based flow field analyses. With the control-off calibration-experiment conducted a priori, a transfer kernel is identified so that the velocity fluctuations that are to-be-controlled can be estimated. The controller targets large-scale high-speed zones in an “opposing” mode and low-speed zones in a “reinforcing” mode. A desynchronized mode was tested for reference and consisted of a statistically similar control mode, but without synchronization to the incoming velocity fluctuations. An energy-attenuation of about 40 % is observed for the opposing control mode in the frequency band corresponding to the passage of large-scale motions. This proves the effectiveness of the control in targeting large-scale motions: an energy-intensification of roughly 45% occurs for the reinforcing control mode instead, while no change in energy, within the wall-normal range targeted, appears with the desynchronized control mode. Moreover, direct measures of the skin-friction drag are inferred from PTV data. Results indicate that the opposing control logic yields the lowest wall-shear stress (3% lower than the desynchronized control, and 10% lower than the uncontrolled flow). Finally, a FIK-decomposition of the skin-friction coefficient revealed that the off-the-wall turbulence follows a consistent trend with the PTV-based wall-shear stress measurements, although biased by an increased shear in the wake of the boundary layer given the formation of a plume due to the jet-in-crossflow actuation.