In this numerical study on Rayleigh-Bénard convection, we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers ${10}^5\le \text{Ra}\le {10}^9$ for a fixed Prandtl number of Pr = 4.3. We find that the global heat transfer can be enhanced up to $18\%$, and locally around $800\%$. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for $\text{Ra}={10}^8$.

A scale-by-scale kinetic energy budget is analyzed near the turbulent/nonturbulent interfacial (TNTI) layer with direct numerical simulations (DNSs) of a local turbulent front evolving without mean shear (shear-free turbulence). A local volume average is used to decompose the flow variables into their large-scale and small-scale components near the TNTI layer. The kinetic energy and interscale energy flux from large to small scales of motion are shown to be severely depleted for small scales within the viscous superlayer. The forward interscale energy transfer from large to small scales near the TNTI layer is mostly caused by the velocity gradient in the interface normal direction while the velocity gradient in the tangential direction transfers, on average, the energy from small to large scales. The velocity gradients that cause the forward energy transfer near the TNTI layer are associated with a compressive motion in the interface normal direction and a shearing motion due to the velocity in the tangential direction. The pressure diffusion increases the kinetic energy near the interface except at small scales within the TNTI layer. The averaged pressure diffusion term at the small scales within the TNTI layer has negative values, which are consistent with the presence of small-scale vortices within the TNTI layer. The transports by turbulent diffusion and interaction between large and small scales are negatively correlated even near the TNTI layer, and their effects are locally canceled by each other as also observed in other turbulent flows.

The mechanism of poloidal flow suppression in an electrovortex flow (EVF) is verified in a liquid metal experiment and supported by numerical simulations. Beyond a certain threshold of azimuthal forcing, a strong poloidal EVF flow develops only transiently, before the centrifugal forces of the slowly generated swirl compensate the EVF-driving forces. This result shows that EVFs can become of particular importance in large-scale liquid metal batteries, especially during the switch-on regime when the transient poloidal flows can be up to two orders of magnitude stronger than those expected in the saturated regime.

Periodic surface microtextures of different shapes such as $\mathsf{V}$ grooves, semicircular grooves, or rectangular grooves have been studied under laminar and turbulent flow conditions to offer guides for designing optimized low-friction surfaces. In this work we investigate the efficacy of periodic streamwise-aligned surface features in reducing the torque exerted on a steadily rotating cylinder in Taylor-Couette flow. Using three-dimensional printed riblet-textured rotors and a bespoke Taylor-Couette cell, which can be mounted on a controlled stress rheometer, we measure the evolution in the torque acting on the inner rotor as a function of three different dimensionless parameters: (i) the Reynolds number characterizing the flow, (ii) the sharpness of the riblets, as defined by their aspect ratio (height to wavelength), and (iii) the axial scale of the riblets with respect to the size of the overall Taylor-Couette cell (the ratio of the riblet wavelength to the gap of the Taylor-Couette cell). Our experimental results in the laminar viscous flow regime show a reduction in torque up to 10% over a wide range of Reynolds numbers that is a nonmonotonic function of the aspect ratio of the grooves and independent of ${\mathrm{Re}}_d$ (the gap-based Reynolds number). However, after the transition to the Taylor vortex regime, the modification in torque also becomes a function of the Reynolds number while remaining a nonmonotonic function of the aspect ratio. Using finite-volume simulation of the three-dimensional swirling flow in the annular gap, we discuss the kinematic changes to the Taylor-Couette flow in the presence of the riblets compared to the case of smooth rotors and compute the resulting torque reduction as a function of the parameter space defined above. Good agreement between experiments and computational predictions is found for both azimuthal Couette flow and the Taylor vortex regime.

The effect of partial slip flow on airfoil performance at high Reynolds numbers is analyzed in this paper. The link between the physical mechanism of drag reduction attained by many devices and the slip length concept has been well assessed in the literature. A slip length model is therefore here adopted in large eddy simulations to quantify the effect of slip flow on airfoil performance. The possibility to adopt a slip flow boundary condition to simulate riblets on airfoil is verified. Their effectiveness in reducing friction drag in turbulent flow has been well assessed since the end of the last century. Both theory and experiments proved that the effect of riblets only depends on the local Reynolds number. However, some experiments showed an increased effectiveness of riblets in the presence of pressure gradient. This secondary effect is still being debated and a physical explanation has not been found. This paper has the aim to provide a contribution to the understanding of this phenomenon. Large eddy simulations of flows around airfoils are proposed with an extensive analysis of riblet performance, obtained by a proper slip flow boundary condition. It is shown that riblets reduce the boundary layer displacement thickness inducing small but significant modifications to the pressure distribution, in particular in the adverse pressure gradient region. The reduced thickening of the equivalent body is the reason for the reduced form drag.

Generation of monodisperse droplets by a large droplet impacting a mesh array is a common technique in microfluidic engineering, materials science, and drug production. Understanding the dynamic mechanism behind this is critical to controlling this process. This work uses a nonorthogonal multiple-relaxation-time lattice Boltzmann (LB) method to simulate a droplet impacting a mesh array. By varying the droplet viscosity and surface tension, a comprehensive parametric study is carried out to investigate the influence of droplet properties on the dynamic process of droplet impact, penetration, and fragmentation. The results indicate that the inertial effect dominates the spread stage of droplet impact. At later stages, the viscous drag and surface tension act to prevent the spread of the droplet, which results in different maximum spreading diameters. The penetration of the droplet through the mesh initially leads to the formation of a liquid jet, the length of which is determined by the competition between the dynamic pressure and capillary pressure. Different jet breakup lengths are observed for various Weber numbers. The maximum spreading diameter and jet breakup length are predicted by an extended model over a wide range of liquid properties, in good agreement with the LB simulation results. An analysis is also conducted from an energy perspective. It is found that the surface energy significantly decreases after the fragmentation of the high-viscosity droplet, which is caused by the merge of satellite droplets after the jet breakup.

Lattice Boltzmann simulations of fully developed rotating turbulent flow in rectangular ducts are performed. The rectangular ducts are rotated along the spanwise direction at a constant angular speed $\mathrm{\Omega }$. The Reynolds number ${\mathrm{Re}}_{\tau }=u_{\tau }h/\nu$ and rotation number ${\mathrm{Ro}}_{\tau }=2\mathrm{\Omega }h/u_{\tau }$ are fixed at 150 and 2.5, respectively, where $u_{\tau }$ denotes the friction velocity and $h$ is the half duct width. A rotating Boltzmann formulation is adopted combined with a shear-improved subgrid-scale model for large eddy simulation. In order to clarify the sidewall effect, the duct aspect ratio (AR) varies from 1 to 6 and then ∞ (channel). Code validations for a square duct $(\mathrm{AR}=1)$ are conducted by comparing the present results with previous direct numerical simulation data from Navier-Stokes solvers. Good agreement is found, which confirms the applicability of the rotating lattice Boltzmann model for predicting wall-bounded turbulent flows subject to rotation induced centrifugal and Coriolis forces. With increasing aspect ratio, it is further observed that there exists a critical $\mathrm{AR}=4$, beyond or below which the peak of the mean velocity profile is skewed to the suction or pressure side. The same critical value of AR also appears in the anisotropic invariant map indicated by the turbulence state in the duct center. Furthermore, the Ekman layer transport is persistent temporally and spatially in all duct flows and its influence on the core region decreases with increasing AR.

The turbulent flow within short canopy gaps was experimentally investigated using planar particle image velocimetry. The gaps were situated in the fully developed region of dense homogeneous canopies in shallow submergence at a Reynolds number of $20000$, based on the flow depth and the free-stream velocity. The flow was studied for gaps with lengths $L/h=0.5$, 1, 2, 3, and 4, where $h$ denotes the canopy height. The results suggest that dense canopies behave as one unit despite the presence of a short gap following a long upstream patch; this is supported by the lack of upward flow deflection and the minimal disruption to in-plane vortical activity at the leading edge of the downstream patch. Across the five gaps, a recirculation zone, noted in the time-averaged flow field, forms past the upstream patch. Flow reattachment occurs at the trailing edge of the $L/h=4$ gap and within the downstream patch for the other gaps. Building on previous studies, the results presented here reveal the importance of the length of the upstream patch in setting the flow regime within the gaps. A thorough examination of the time-averaged streamwise and wall-normal velocities, shear layer growth, in-plane turbulent kinetic energy, Reynolds shear stress, and two-point correlations suggests a classification of the flow into two regimes: a skimming flow regime ($L/h=0.5$ and 1) and a shear layer growth regime ($L/h=2$, 3, and 4). In contrast with the skimming flow regime, the shear layer and enhanced turbulence exhibit deep penetration within the gaps and promote mixing in the shear layer growth regime. It is important to note that the presented results and conclusions are based on planar measurements and, therefore, do not capture any variations in the spanwise direction. Volumetric measurements are suggested to capture such variations and to provide a more detailed description of the flow field.

A closed-form solution is presented for the collective Marangoni-induced motion of a two-dimensional periodic array, or “flotilla,” of Marangoni boats on deep water at zero Reynolds, capillary, and surface Péclet numbers. The physical setup is identical to the model of Marangoni propulsion proposed by Lauga and Davis [J. Fluid Mech. 705, 120 (2012)], but now accounts for interaction effects between boats and is in a simpler two-dimensional setting. The boats are modeled as identical thin floating strips, each self-actuated by a trailing edge surfactant source that lowers the surface tension there according to a linear equation of state. The collective Marangoni propulsion speed of a flotilla of boats is found to be ${\left(2\pi \mu \delta \right)}^{-1}\mathrm{\Delta }\sigma lnsec(\pi \delta /2)$, where $\delta$ is the meniscus coverage fraction, $\mu$ is the subphase fluid viscosity, and $\mathrm{\Delta }\sigma$ is the surfactant-induced surface tension disparity across each boat. The theoretical result exemplifies the mechanism for collective rectilinear motion due to Marangoni convection caused by the diffusion of the insoluble surfactant.

Hydrogels consist of a polymer skeleton hydrated by an aqueous solvent, and their hydrodynamics is often described by a coarse-grained poroelasticity model where the boundary conditions between the hydrogel and a surrounding solvent require careful consideration. Young et al. [Phys. Rev. Fluids 4, 063601 (2019)] used the energy dissipation principle to derive a set of boundary conditions regarding the velocity jumps at the interface. However, when applied to an external shear flow over a gel layer, these conditions predict no entrained flow inside the gel, in contrast to the prediction of a previous model by Minale [Phys. Fluids 26, 123102 (2014)]. We adapt the procedure of Young et al. to derive an alternative set of boundary conditions that does allow an external shear flow to induce shear inside the gel and compare the velocity profile to that of Minale. We also derive the limiting form of the boundary conditions in a Darcy medium.

Recently, advances in techniques for the detection of Lagrangian coherent structures (LCSs) have driven forward understanding of kinematics and particle transport in a variety of flows. One major shortcoming of these techniques, however, is the lack of an objective procedure for identifying time scales of interest, or an ability to characterize the lives, deaths, or age of coherent structures, especially when relevant flow time scales are larger than the time scales associated with coherence. Here, we address these issues by proposing a multiple object tracking framework frequently used in video analysis to extend the use of existing LCS detection algorithms, allowing coherence time scales to be considered independently of the overall flow evolution time scale and revealing dynamics of the LCSs. Our approach enables the detection of evolving Lagrangian coherent structures, which are created and destroyed throughout the larger time scales of analysis of complex flows.

The coherent structures in the turbulent wake of a disk at a moderately high Reynolds number ($\text{Re}$) of $50000$ are examined using spectral proper orthogonal decomposition (SPOD) which considers all three velocity components in a numerical database. The SPOD eigenvalues at a given streamwise ($x$) location are functions of azimuthal wave number ($m$), frequency ($\text{St}$), and SPOD index ($n$). By $x/D=10$, two specific modes dominate the fluctuation energy: (i) the vortex shedding (VS) mode with $m=1,\text{St}=0.135,n=1$, and (ii) the double helix (DH) mode with $m=2,\text{St}\to 0,n=1$. The VS mode is more energetic than the DH mode in the near wake but, in the far wake, it is the DH mode which is dominant. The DH mode, when scaled with local turbulent velocity and length scales, shows self-similarity in eigenvalues and eigenmodes while the VS mode, which is a global mode, does not exhibit strict self-similarity. Modes $m=0$, 3, and 4, although subdominant, also make a significant net contribution to the fluctuation energy, and their eigenspectra are evaluated. The reconstruction of turbulent kinetic energy (TKE) and Reynolds shear stress, $\langle u_x^{\prime }{u}_r^{\prime }\rangle$, is evaluated by varying $(m,\text{St},n)$ combinations. Higher SPOD modes contribute significantly to the TKE, especially near the centerline. In contrast, reconstruction of $\langle u_x^{\prime }{u}_r^{\prime }\rangle$ requires far fewer modes: $\left|m\right|\le 4, \left|\text{St}\right|\le 1$, and $n\le 3$. Among azimuthal modes, $m=1$ and 2 are the leading contributors to both TKE and $\langle u_x^{\prime }{u}_r^{\prime }\rangle$. While $m=1$ captures the slope of the shear-stress profile near the centerline, $m=2$ is important to capture $\langle u_x^{\prime }{u}_r^{\prime }\rangle$ at and near its peak. SPOD is also performed in the vicinity of the disk to describe the modal transition to the principal contributors in the wake. The leading SPOD modes show a high-frequency shear-layer peak close to the disk and the vortex shedding mode commences its initial dominance of the wake at the end of the recirculation region.

The drag wake of a dimpled sphere is studied experimentally using stereo particle image velocimetry at $\mathrm{Re}=5\times {10}^4$ to a downstream distance of $\sim 200$ diameters. The wake growth and velocity decay are analyzed and compared with self-similar decay laws. The measured exponents for the mean axial velocity field differ from the classical mean-field self-similar solution. This is consistent with other recent experimental observations of the near wake of axisymmetric bodies but is the first to show a full decade of scaling with nonclassical exponents, indicating the scaling is not merely a near-wake effect. The data also indicate that deviations from the classical solution may be due to the failure of the assumption that velocity fluctuations are in balance with production from the mean axial flow. Relaxing this assumption yields a family of self-similar decay solutions, one of which is consistent with the measured wake decay. The observed solution preserves the velocity fluctuation Reynolds number with downstream distance. The experimental data also show that individual wake realizations bear little resemblance to the mean flow, suggesting that mean flow solutions may have limited practical value.

Oscillation of sessile drops is important to many applications. In the present study, the natural oscillation of a sessile drop on flat surfaces with free contact lines (FCL) is investigated through numerical and theoretical analysis. The FCL condition represents a limit of contact line mobility, i.e., the contact angle remains constant when the contact line moves. In the numerical simulation, the interfaces are captured by the volume-of-fluid method and the contact angle at the boundary is specified using the height-function method. The oscillation frequencies for sessile drops with FCL are mainly controlled by the contact angle and the Bond number and a parametric study is carried out to characterize their effects on the frequencies for the first and high-order modes. Particular attention is paid to the frequency of the first mode, since it is usually the dominant mode. An inviscid theoretical model for the first mode is developed. The model yields an explicit expression for the first-mode frequency as a function of the contact angle and the Bond number, with all parameters involved fully determined by the equilibrium drop theory and the simulation. The predicted frequencies for a wide range of contact angles agree very well with the simulation results for small Bond numbers. The frequencies for both the first and high-order modes decrease with the contact angle and increase with the Bond number. For the high-order modes, the frequencies for different modes generally scale with the Rayleigh frequencies. The scaling relation performs better for small Bond numbers and large contact angles. A simple model is proposed to predict the frequencies of high-order modes for large contact angles and a good agreement with the simulation results is observed.

We present numerical simulations for computing the interface separating a ferrofluid droplet, surrounded by a nonmagnetic fluid, confined in a Hele-Shaw cell, and subjected to an in-plane, external radial magnetic field. The radial magnetic field destabilizes the interface, while surface tension tends to stabilize it. We focus our attention on investigating the advanced time, fully nonlinear behavior of the interface dynamics. By using a vortex sheet formalism, we employ an accurate boundary integral method to study the distinctive pattern formation resulting from this ferrohydrodynamic system. In this setting, we examine how the viscosity contrast $A$, a dimensionless surface tension parameter $B$, and the magnetic susceptibility $\chi$ impact the shape of the complex, emerging interfacial patterns. From the interplay of the controlling parameters $A$, $B$, and $\chi$, a gallery of visually striking pattern-forming morphologies is presented and discussed. The resulting radial magnetic-field-induced interface patterns assume various radially stretched, starlike shapes, typically having spiky fingers. These patterns are very different from ferrofluid structures usually obtained in Hele-Shaw cells for other magnetic field configurations. Simulation results are also compared to linear and weakly nonlinear stages of the dynamics. Reproduction of linear growth rates and early nonlinear tip-sharpening structures substantiate the validity of our numerical approach.

Turbulence modulation in particle-laden stationary homogeneous shear turbulence (HST) is investigated using one-dimensional turbulence (ODT), a low-dimensional stochastic flow simulation model. For this purpose, an ODT formulation previously used to study turbulence modulation in forced homogeneous isotropic turbulence (HIT) is extended, so that the model emulates the anisotropic character of HST and, potentially, anisotropic turbulence in general. This is done by limiting the kinetic-energy redistribution during an eddy event to an exchange involving two velocity components, where the three possible choices of the omitted component define three eddy types whose relative likelihoods control the anisotropy. Comparisons of ODT and direct-numerical-simulation results with reference to signatures of turbulence modulation are the basis of a broader ODT parameter study that is reported. Owing to the reduced dimensionality of ODT, it is found that the fidelity of the model for single-phase HST does not extend to particle effects on flow anisotropy, but for quantities averaged over components, parametric trends are captured. The consistent approach to case comparisons that was introduced in the HIT study to evaluate sensitivities to particle-phase parameters in a given flow configuration is extended here to a cross-comparison of HST and HIT model results, and its efficacy is again confirmed. The results provide an overall characterization of the potential for ODT to support the incorporation of particle-induced turbulence modulation into subgrid-scale closures of large-eddy simulations.

Diffusion controls a plethora of natural and industrial phenomena. Directly, as in intracellular transport and gas exchange in the lungs, or indirectly, in processes that are driven by the encounter of different entities through their mixing: e.g., microbes and nutrients or species involved in chemical reactions. When mixing happens in confined environments that are characterized by the presence of impermeable boundaries, the species spatial organization deviates from the one observed in unconfined systems. Here, we investigate the impact of confinement on mixing state and rate. We use the analytical solution of a one-dimensional diffusion equation for a finite spatial domain of size $\lambda$ to quantify the impact of confinement on several mixing measures, such as the concentration and gradients probability density function, scalar dissipation rate, and dilution index. We show that no-flux boundary conditions lead to a new timescale characterizing confinement-limited mixing controlled by diffusion, ${\lambda }^2/\left(D{\pi }^2\right)$, which is significantly shorter (one order of magnitude shorter) than the characteristic diffusive timescale, ${\lambda }^2/D$, in an unconfined domain. These observations show that the diffusive homogenization mechanism is enhanced by the presence of impermeable boundaries and, thus, mixing happens much faster under confinement.

In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification, with the goal of quantifying and parametrizing the impact of stratification on timescales that describe the delay in rising. These experiments confirm the significant slowdown observed in past literature of settling and rising particles and droplets in stratification, and these are the first experiments to study single liquid droplets as opposed to solid particles or bubbles. By tracking the motion of the droplets as they rise through a stratified fluid, we identify two new timescales which quantitatively describe this slowdown: an entrainment timescale and a retention timescale. These timescales measure dynamics that were not captured in previous timescale discussions, which primarily focused on the timescale to the velocity minimum $\left(U_{\text{min}}\right)$. The entrainment timescale is a measure of the time that a droplet spends below its upper-layer terminal velocity and relates to the duration over which the droplet's rise is affected by entrained dense fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. These two timescales are interconnected by the magnitude of the slowdown $(U_u-U_{\text{min}})$ relative to the upper-layer terminal velocity $\left(U_u\right)$, as well as a constant that reflects the approximately universal form of the recovery of a droplet's velocity from $U_{\text{min}}$ to $U_u$. Both timescales are found to depend on the Froude and Reynolds numbers of the system, Fr $=U_u/\left(Nd\right)$ and Re $={\rho }_u{U}_{u}d/\nu$. We find that both timescales are only significantly large for Fr $\lesssim 1$, indicating that trapping dynamics in a relatively sharp stratification arise from a balance between drop inertia and buoyancy. Finally, we present a theoretical formulation for the force enhancement $\mathrm{\Gamma }$, the ratio between the maximum stratification-induced force and the corresponding drag force on the droplet, based on a simple force balance at the point of the velocity minimum. Using our experimental data, we find that our formulation compares well with recent theoretical and computational work by Zhang et al. [J. Fluid Mech. 875, 622 (2019)] on the force enhancement on a solid sphere settling in a stratified fluid, and provides the first experimental data supporting their approach.

The dynamics of branched polymers in semidilute solutions are thought to depend on a coupling between polymer chain architecture, intermolecular excluded volume interactions, and long-range hydrodynamic interactions (HI). However, it has been challenging to quantitatively understand these phenomena due to the influence of intra- and intermolecular HI and chain-chain interactions for nonlinear polymer topologies in flow. In this work, we directly observe the relaxation dynamics of comb-shaped polymers in semidilute solutions of linear polymers using single molecule experiments and molecular simulations. Experimental results are directly complemented by coarse-grained simulations of comb polymers in semidilute solutions of linear polymers including long-range HI and excluded volume interactions. Our results show an unexpected nonmonotonic dependence of comb polymer relaxation time on branch density that arises due to a subtle yet important interplay between hydrodynamic shielding and polymer architecture.

We examine a mechanism of locomotion of active particles whose surface is uniformly coated with mobile enzymes. The enzymes catalyze a reaction that drives phoretic flows but their homogeneous distribution forbids locomotion by symmetry. We find that the ability of the enzymes to migrate over the surface combined with self-phoresis can lead to a spontaneous symmetry-breaking instability whereby the homogeneous distribution of enzymes polarizes and the particle propels. The instability is driven by the advection of enzymes by the phoretic flows and occurs above a critical Péclet number. The transition to polarized motile states occurs via a supercritical or subcritical pitchfork bifurcations, the latter of which enables hysteresis and coexistence of uniform and polarized states.