This work studies the aggregation of colloids under depletion attraction focusing on the effect of hydrodynamic interactions on cluster kinetics and average structures. Our numerical study is based on a variant of the immersed boundary method (inertial coupling method) which solves the solvent fluctuating hydrodynamics and instantaneously couples the particle and the fluid momentum transfer. Comparison is made with Langevin dynamics and Monte Carlo methods, which do not include hydrodynamics. We consider a small system (20 and 40 particles) which reproduces the system considered by Whitmer and Luijten [J. Phys. Chem. B 115, 7294 (2011)] (analyzed by multiparticle rotation dynamics). In that work, the authors report substantial hydrodynamic effects altering the cluster sizes and shapes. By contrast, within statistical error, we have not found any hydrodynamic effect on the average clusters structure. We also analyze the time-evolution of the aggregation kinetics, revealing a slowing down of the process due to the reduction of the mobility close to the clusters. The time correlation of the cluster number, shape, and size reveals two characteristic times: a decay at short times faster than the single-particle diffusion time $t_D$, followed by a slower exponential decay at long times with a typical time of several $t_D$.

A scaling formula for the mean velocity and wall distance in compressible turbulent wall-bounded flows is developed. The development is both physics- and data-driven: universality in the viscous sublayer and of the Morkovin-scaled shear stress is analytically enforced, after which the remaining two free parameters are determined from direct numerical simulation data. The scaling formula is calibrated on four boundary layers up to Mach 6, and validated on seven boundary layers up to Mach 14. The proposed transformation shows an improved collapse of the mean velocity profile across different Reynolds numbers, Mach numbers, and wall thermal conditions when compared to existing ones.

Periodic winds acting on a stratified waterbody can amplify normal modes of motion and enhance the basin-scale circulation via resonance. Here, we use idealized large-eddy simulations to investigate the flow features and quantify the horizontal transport in periodically wind-forced stratified basins. Motivated by observations in lakes, we focus on systems in which daily winds either resonate with the second vertical basin-scale internal mode, V2H1 (case 1), or the first vertical basin-scale internal mode, V1H1 (case 2). In particular, we analyze the case when strong nonlinearities affect the evolution of the V2H1 mode (case 3). To achieve these three resonance scenarios, we hold the basin morphology and the periodic forcing invariant, but change the background stratification. Our results show that a quasilinear V2H1 modal response has more active mass transport in the boundary regions than does the quasilinear V1H1 case. This difference arises from the lack of midlayer horizontal transport in the V1H1 mode, whereas the midlayer current in the V2H1 mode intensifies the transport along the slopes in both directions by splitting the flow into two branches, one running upslope and one running downslope. Nonlinear dynamics further amplify the along-slope transport in case 3, in which a second mode, an undular borelike wave, emerges from the periodic forcing. This study shows that the horizontal transport under wind-induced resonance is sensitive to the amplified mode of motion in the stratified basin and that nonlinear flow dynamics can considerably enhance mass transport in sloping regions.

The filling of small cavities with liquids plays a central role in numerous settings including imprint lithography, gravure printing, microfluidics, lubricant-impregnated surfaces, and porous-media flow. Air entrapment resulting from incomplete filling may be detrimental for certain applications. Although wetting dynamics can be complicated by liquid rheology, the influence of non-Newtonian behavior is not well understood. To develop fundamental understanding, two-dimensional numerical simulations are used to study liquid filling in two model problems involving a stationary trapezoidal cavity and a horizontal plate above the cavity. In these model problems, liquid is driven into the cavity by (i) an imposed pressure gradient and (ii) a combination of horizontal plate motion and an imposed pressure gradient. Shear-thinning liquids described by a Carreau-type expression are considered, and the nonlinear governing equations with inertia and gravity neglected are solved using the Galerkin finite-element method. For both model problems, it is found that increasing cavity width and wettability, decreasing wall steepness, or lowering the capillary number generally improves filling by allowing the contact line on the cavity to slip more. Shear thinning enhances contact-line motion via reduced viscosities near the dynamic contact line and, as a consequence, leads to improved cavity filling.

The forced Korteweg–de Vries equation is commonly used to describe transcritical flow over localized topography, with the well-known outcome that undular bore is generated both upstream and downstream, connected by a steady hydraulic solution over the topography for positive forcing (obstacle) or an unsteady solution for negative forcing (hole). Here we examine the same problem using the forced extended Korteweg–de Vries equation, in which a cubic nonlinear term has been included as well as the usual quadratic nonlinear term. We consider both signs of this cubic nonlinear term and both signs of the forcing. Overall, the outcome is qualitatively similar to that from the forced Korteweg–de Vries equation when the additional cubic nonlinear term is small, but interesting differences emerge as the magnitude of the cubic nonlinear term increases.

The dissolution of a body into quiescent water leads to density stratifications at the interfaces that drive buoyant flows. Where the stratification is unstable, the flow destabilizes into convective solute plumes. By analogy with the Rayleigh-Bénard instability where concentration replaces temperature, this phenomenon is known as the solutal Rayleigh-Bénard instability. Here we report experiments of the dissolution of inclined rectangular blocks made of salt, caramel, or plaster in aqueous solutions of various concentrations. The solute flows along the block while forming plumes before they detach and sink. This flow along the block organizes the emission of plumes within longitudinal parallel stripes with a well-defined millimeter-scale wavelength. The instability of the flow reflects on the concentration field in the boundary layer, which engraves longitudinal grooves onto the block. These grooves interact with the flow and turn into a paving of three-dimensional, cuplike patterns that grow in size and propagate upstream. These bedforms are reminiscent of the scallop bedforms observed on the walls of cave or icebergs. Whereas the block interface is highly dynamical and evolves through time, it remains flat on the global scale and recedes at a stationary rate. We derive scaling laws for the receding velocity and the pattern genesis at the inclined interface that are based on a concentration boundary layer of constant thickness, which is controlled by the flow instability but where neither the patterns nor the flow along the block play any role. We apply these results to the formation of sublimation patterns.

Our study involved an experimental investigation of a homogeneous bubble-swarm past a circular cylinder, of which the size is more than five times larger than that of a bubble, while varying the upstream volume void fraction, $\langle \overline{\alpha }\rangle$, in a small-to-moderate range and cylinder diameter, $D$. The Reynolds number of rising bubbles is approximately ${10}^3$. We focused on the way in which the preferred concentration of bubbles past a cylinder is established and how its wake is induced. We measured the gas- and liquid-phase velocity fields simultaneously by using a high-speed two-phase particle image velocimetry technique. Depending on the void distribution in the wake region, two regimes are classified. In the first regime (smaller $\langle \overline{\alpha }\rangle$), the bubbles tend to accumulate downstream of the side of the cylinder (along the shear-layer region), which is attributed to the mitigated lateral migration of bubbles via the balance between the drag force with the pressure gradient and shear-induced lift forces acting on them. As $\langle \overline{\alpha }\rangle$ increases, in the second regime, the shear-induced lift force becomes sufficiently strong to move the bubbles toward the center of the cylinder, resulting in the void fraction exhibiting a broad peak at this position. Based on the void distribution, the liquid flow forms an interesting wake structure behind the cylinder. For example, a wake-defect-like streamwise velocity profile and skew-symmetric Reynolds stress distribution are induced; however, the distortion by the circular cylinder is restored quite fast (within $5D$ along the streamwise direction). Increasing the cylinder size, however, delays the recovery of uniform flow statistics and reduces the turbulence level in the wake. Finally, we propose a model for bubble-induced fluctuation (Reynolds stress) that includes the contributions of the gradients of liquid velocity, void distribution, and bubble velocity. The model, which is an extension of the well-known eddy-diffusivity model, considers the effects of bubble-induced flow and multiple bubbles (void fraction). The bubble-induced Reynolds stress estimated by the present model is in a reasonably good agreement with the data measured downstream of the circular cylinder.

The effects of a perforated bottom wall on the unsteadiness of a turbulent offset attaching jet are experimentally investigated for a jet with a Reynolds number of 14 600 initially offset one jet height. The effects of two independent control parameters, the open area of the perforated wall and the depth of the air cavity underneath the wall, are considered. Two distinct flow patterns are observed. In the first, when either the open area or the cavity depth is small, the recirculating flow is largely above the perforated plate and there is only slight change in the jet trajectory. In the second, when the open area and the cavity depth are both large, the perforated plate and cavity serve as a channel for flow to recirculate upstream with a large amount of flow penetrating the perforated plate in the reattachment region, traveling upstream in the cavity, and flowing into the recirculation bubble near the jet exit. Jet trajectories become much more parallel to the wall. The flow patterns can be distinguished from the change in the base static pressure and the jet curvature. In both flow patterns, the lower-frequency motion becomes much more in phase in the spanwise direction due to the attenuation of the spanwise varying disturbances.

Spatial artificial neural network (ANN) models are developed for subgrid-scale (SGS) forces in the large eddy simulation (LES) of turbulence. The input features are based on the first-order derivatives of the filtered velocity field at different spatial locations. The correlation coefficients of SGS forces predicted by the spatial artifical neural network (SANN) models with reasonable spatial stencil geometry can be made larger than 0.99 in an a priori analysis, and the relative error of SGS forces can be made smaller than $15\%$, much smaller than that of the traditional gradient model. In a posteriori analysis, a detailed comparison is made on the results of LES using the SANN model, implicit large eddy simulation (ILES), the dynamic Smagorinsky model (DSM), and the dynamic mixed model (DMM) at grid resolution of ${64}^3$. It is shown that the SANN model performs better than the ILES, DSM, and DMM models in the prediction of the spectrum and other statistical properties of the velocity field, as well as the instantaneous flow structures. These results suggest that artificial neural network with consideration of spatial characteristics is a very effective tool for developing advanced SGS models in LES of turbulence.

We investigate the effect of cooperative interactions in an ensemble of microorganisms, modeled as self-propelled disklike and rodlike particles, in a three-dimensional turbulent flow and show flocking and nematic ordering as an emergent phenomenon. Building on the work by Choudhary et al. [Europhys. Lett. 112, 24005 (2015)] for two-dimensional systems, and combining ideas from active matter and turbulent transport, we show that nontrivial correlations between the flow and individual dynamics are essential for the microorganisms to flock in, for example, a turbulent three-dimensional marine environment. Our results may have implications especially in the modeling of artificial microswimmers in a hostile environment.

Electro-osmotic flow is a well-established and efficient method for driving microchannel flows that relies on the interaction of an externally applied electric field with charge arising at the interface between the liquid and the channel walls. However, its relatively low velocities together with its dependence on the $p\mathrm{H}$ of the liquid severely limit its utility. Here we experimentally demonstrate fast electro-osmotic flow over microstructured superhydrophobic surfaces. By suspending the electrolyte in a Cassie-Baxter state over hierarchical surfaces, we create stable gas-liquid interfaces on which we induce charge through a gate electrode. We provide a detailed investigation and characterization of the electro-osmotic velocity as a function of the surface geometry by utilizing particle tracking velocimetry in a microfluidic device and show that the resulting electro-osmotic velocity scales with the ratio of slip length to double-layer thickness. Compared to no-slip surfaces, we demonstrate an order of magnitude enhancement in velocity and complete $p\mathrm{H}$ independence, enabling wider utility of electro-osmotic flow in manipulation of microscale flows.

The initial state of terrestrial planets was partly determined, during accretion, by the fall of metal drops in a liquid magma ocean. Here we perform systematic numerical simulations in two-dimensional cylindrical axisymmetric geometry of these falling dynamics and associated heat exchanges at the scale of one single drop for various initial sizes and ambient viscosities. We explore Reynolds number in the range 0.05–48, viscosity ratios in the range 50–4000, Weber number in the range 0.04–5, and Peclet number in the range 70–850. We show that heat exchange between the two phases occurs predominantly at the front section of the drop. Our systematic, parametric study shows that the thermal boundary layer thickness, the depth and time for equilibration, the Nusselt number, and the magma ocean volume affected by thermal exchanges all scale as power laws of the Peclet number. Because of drop distortions, these scaling laws deviate from the classical balances considering only heat diffusion through a laminar thermal boundary layer. Finally, when considering a temperature-dependent viscosity of the ambient fluid, we show that a low-viscosity layer surrounds the drop, which influences the thermal evolution of nondeformable, low-Reynolds-number drops only and decreases the breakup distance for some limited breakup modes.

Highly swirling flows are often prone to precessing instabilities, with an azimuthal wave number of $m=-1$. We carry out a weakly nonlinear analysis to determine the response behavior of this instability to harmonic forcing. An incompressible flow is considered, where an annular inlet provides a swirling flow into a cylindrical region. For high swirl a vortex breakdown is induced, which is found to support an $m=-1$ instability. By expanding about the Reynolds number where this instability first occurs, a Stuart-Landau equation for the critical mode amplitude can be found and the effect of forcing can be assessed. Two types of forcing are considered. First, a Gaussian forcing confined to the inlet nozzle is used to study $m=0$ and $m=-1$ forcings. Second, optimal forcings (measured by the two-norm) with azimuthal wave numbers in the range $-3\le m\le 3$ are considered. It is found that modal stabilization is highly dependent on the azimuthal wave number $m$, which governs whether the forcing is counter- or corotating with the direction of swirl. Counterrotating forcings are able to stabilize the mode for a wide range of forcing frequencies, while corotating forcings fail to yield a stable flow. In all cases, it is the base-flow modification induced by the forced response that is the dominant underlying feature responsible for the observed stabilization. This base-flow modification seeks to reduce axial momentum near the recirculation region for corotating forcings and increase it for counterrotating forcings, thus changing the size of the recirculation bubble and producing the two distinct response behaviors.

Velocity potential contours have been used to demarcate the boundary between the interior and exterior of a plume, this for the case of adjacent plumes subject to merger [Rooney, J. Fluid Mech. 771, R1 (2015)]. Whereas Rooney's theory is restricted to cases where the plume source is much smaller than the distance between neighboring plume centers, the modification suggested herein allows individual plumes to originate from an area source of arbitrary size. In the present theory, the height at which two plumes fully merge is defined as the location where the combined plume boundary is no longer concave. Referencing the plume boundary curvature, we introduce an alternative, simpler entrainment formulation that does not involve the flux-balance parameter used in Rooney's revised model. The present model is applied to adjacent cooling tower plumes and generates satisfactory agreement with previous model predictions, including those that adopt a quite different criterion for plume merger.

From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the $4/5\mathrm{ths}$ law holds in an intermediate range of scales and that the second-order exponent over the same range of scales is anomalous, departing from the self-similar value of $2/3$ and approaching a constant of 0.72 at high Reynolds numbers. We compare to some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order $n$, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large $n$, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about 2 at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.

The heat transfer and flow structure in rotating Rayleigh-Bénard convection are strongly influenced by the Rayleigh (Ra), Prandtl (Pr), and Rossby (Ro) numbers. For $\text{Pr}\gtrsim 1$ and intermediate rotation rates, the heat transfer is increased compared to the nonrotating case. We find that the regime of increased heat transfer is subdivided into low- and high-Ra-number regimes. For $\text{Ra}\lesssim 5\times {10}^8$ the heat transfer at a given Ra and Pr is highest at an optimal rotation rate, at which the thicknesses of the viscous and thermal boundary layers are about equal. From the scaling relations of the thermal and viscous boundary layer thicknesses, we derive that the optimal rotation rate scales as $1/{\text{Ro}}_{\mathrm{opt}}\approx 0.12{\text{Pr}}^{1/2}{\text{Ra}}^{1/6}$. In the low-Ra regime the heat transfer is similar in a periodic domain and cylindrical cells with different aspect ratios, i.e., the ratio of diameter to height. This is consistent with the view that the vertically aligned vortices are the dominant flow structure. For $\text{Ra}\gtrsim 5\times {10}^8$ the above scaling for the optimal rotation rate does not hold anymore. It turns out that in the high-Ra regime, the flow structures at the optimal rotation rate are very different than for lower Ra. Surprisingly, the heat transfer in the high-Ra regime differs significantly for a periodic domain and cylindrical cells with different aspect ratios, which originates from the sidewall boundary layer dynamics and the corresponding secondary circulation.

The present paper describes a microfluidic oscillator based on facing impinging jets and operating in laminar flow conditions. Using appropriate microchannel configurations, pulsatile liquid flows are generated at the microscale from steady and equal inlet flow conditions and without moving parts or external stimuli. An experimental campaign has been carried out, using oscillator structures manufactured in silicon using conventional microfabrication techniques. This allowed us to study in detail the impact of the main geometric parameters of these structures on the oscillation frequency. The observed range of regular oscillations was found to depend on the geometry of the output channels, with highly regular oscillations occurring over a very large range of Reynolds numbers (Re) when an expansion of the output channel is added. The evolution of the self-oscillating frequency was shown to be dependent on the distance separating the impinging jets and on the average speed of the jets. Direct numerical simulations have been performed using a spectral element method. The computed dye concentration fields and nondimensional self-oscillation frequencies compare well with the experiments. The simulations enable a detailed characterization of the self-oscillation phenomenon in terms of pressure and velocity fields.

Particle image velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on rapid distortion theory (RDT) and Taylor's hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forward and backward in time using the PIV snapshots as initial conditions. The flow field in the intervening period is then reconstructed by taking a weighted sum of the forward and backward estimates. This spatiotemporal weighting function is designed to account for the advective nature of the RDT and TH equations. Reconstruction accuracy is evaluated as a function of spatial resolution and reconstruction time horizon using direct numerical simulation data for turbulent channel flow from the Johns Hopkins Turbulence Database. This method reconstructs single-point turbulence statistics well and resolves velocity spectra at frequencies higher than the temporal Nyquist limit of the acquisition system. Reconstructions obtained using a characteristics-based evolution of the flow field under TH prove to be more accurate compared to reconstructions obtained from numerical integration of the discretized forms of RDT and TH. The effect of measurement noise on reconstruction error is also evaluated.

We present a combined theoretical-experimental investigation of the downslope propagation of a gravity current sustained by a source. The current propagates first on a horizontal bottom, then on a downslope. We focus on the case when the current at the ridge (point where donwslope begins) has a stable interface ($\text{Ri}>0.25$) and is critical with $F=1$, where Ri and $F$ are the bulk Richardson and flow Froude numbers. We derive the equations that govern the nose propagation and speed using a shallow-water (SW) model, in which the nose is a jump matched to characteristics emitted at the ridge. This provides a self-contained prediction for the speed of propagation $u_N$ and position ${\xi }_N$ of the nose. The predicted $u_N$ increases with time and distance $\xi$ from the ridge. Since Ri decreases with $\xi$ in the tail behind the nose, appearance of instabilities at a certain traveled distance determines the domain of validity of the SW solution. A good agreement is reported with various experiments with different initial conditions at the ridge and slope angles (both fixed and changing with distance from the ridge). It is shown that the nose velocity is always less than the maximum velocity within the current head, which corresponds to the speed of the characteristics released at the ridge that catch on the current head.

Vortex gradient stretching is believed to be the mechanism that generates large vorticity gradients at small scales and consequently maintains the enstrophy cascade to small scales in two-dimensional turbulence. In this work, using particle tracking measurements of two-dimensional turbulence in a soap-film flow, we show experimental evidence that in the direct enstrophy cascade range, the vorticity gradient is preferentially perpendicular to the instantaneous stretching direction. We also show that in regions where the stretching direction and the vorticity gradient are perpendicular to each other, the enstrophy flux is on average from large to small scales, while it is from small to large scales in other regions. Moreover, when observing the angle between stretching and the vorticity gradient in a coordinate system following a fluid particle trajectory, i.e., in the Lagrangian view, we observe that the vorticity gradient direction responds to but lags behind the stretching direction. Therefore, we observe a stronger alignment between the vorticity gradient direction with the stretching direction at an earlier time. At all scales in the direct cascade range, the evolution of the angle between the vorticity gradient and the stretching direction displays a time scale given by the mean enstrophy, independent of the scale, providing direct experimental support for the theoretical argument that vorticity is nearly constant in the direct cascade range.