This paper details the statistical and time-resolved analysis of the relationship between the near-field pressure fluctuations of unforced, subsonic free jets ($0.4\le M\le 0.6$) and their far-field sound emissions. Near-field and far-field microphone measurements were taken on a conical array close to the jets and an azimuthal ring at ${20}^{\circ }$ to the jet axis, respectively. Recent velocity and pressure measurements indicate the presence of linear wave packets in the near field by closely matching predictions from the linear homogenous parabolized stability equations, but the agreement breaks down both beyond the end of the potential core and when considering higher order statistical moments, such as the two-point coherence. Proper orthogonal decomposition (POD), interpreted in terms of inhomogeneous linear models using the resolvent framework allows us to understand these discrepancies. A new technique is developed for projecting time-domain pressure measurements onto a statistically obtained POD basis, yielding the time-resolved activity of each POD mode and its correlation with the far field. A single POD mode, interpreted as an optimal high-gain structure that arises due to turbulent forcing, captures the salient near-field–far-field correlation signature; further, the signatures of the next two modes, understood as suboptimally forced structures, suggest that these POD modes represent higher order, acoustically important near-field behavior. An existing Green's-function-based technique is used to make far-field predictions, and results are interpreted in terms of POD/resolvent modes, indicating the acoustic importance of this higher order behavior. The technique is extended to provide time-domain far-field predictions.

The results of a fully resolved simulation of up to 2000 spheres suspended in a vertical liquid stream are analyzed by a method based on a truncated Fourier series expansion. It is shown that, in this way, it is possible to identify continuity (or kinematic) waves and to determine their velocity, which is found to closely agree with the theory of one-dimensional continuity waves based on the Richardson-Zaki drag correlation.

The present work proposes the use of anisotropically permeable substrates as a means to reduce turbulent skin friction. We conduct an a priori analysis to assess the potential of these surfaces, based on the effect of small-scale surface manipulations on near-wall turbulence. The analysis, valid for small permeability, predicts a monotonic decrease in friction as the streamwise permeability increases. Empirical results suggest that the drag-reducing mechanism is however bound to fail beyond a certain permeability. We investigate the development of Kelvin-Helmholtz-like rollers at the surface as a potential mechanism for this failure. These rollers, which are a typical feature of turbulent flows over permeable walls, are known to increase drag and their appearance is known to limit the drag-reducing effect. We propose a model, based on linear stability analysis, that predicts the onset of these rollers for sufficiently large permeability and allows us to bound the maximum drag reduction that these surfaces can achieve.

In this work we derive the image flow fields for point force singularities placed outside a stationary drop covered with an insoluble, nondiffusing, and incompressible surfactant. We assume the interface to be Newtonian and use the Boussinesq-Scriven constitutive law for the interfacial stress tensor. We use this analytical solution to investigate two different problems. First, we derive the mobility matrix for two drops of arbitrary sizes covered with an incompressible surfactant. In the second example, we calculate the velocity of a swimming microorganism (modeled as a Stokes dipole) outside a drop covered with an incompressible surfactant.

This study numerically investigates the internal jetlike mixing upon the coalescence of two initially stationary droplets of unequal sizes by employing the volume of fluid method with an adaptive mesh refinement algorithm. The emergence of the internal jet is attributed to the formation of a main vortex ring, as the jetlike structure shows a strong correlation with the main vortex ring inside the merged droplet. By tracking the evolution of the main vortex ring together with its circulation, we identified two mechanisms that are essential to the internal-jet formation: the vortex-ring growth and the vortex-ring detachment. Recognizing that the initiation of the vortex-ring-induced jet energetically relies on the merged interface but the manifestation of the jet physically relies on the competition between the convection and viscous dissipation of the vortex ring, we further developed and substantiated a vortex-ring-based Reynolds number $\left(\mathrm{R}{\mathrm{e}}_J={\mathrm{\Gamma }}_{\mathrm{VD}}/4\pi \nu \right)$ criterion, where ${\mathrm{\Gamma }}_{\mathrm{VD}}$ is the circulation of the detached main vortex ring and $\nu$ is the liquid kinematic viscosity, to interpret the occurrence of the internal jet at various Ohnesorge numbers and size ratios. For the merged droplet with apparent jet formation, the average mixing rate after jet formation increases monotonically with $\mathrm{R}{\mathrm{e}}_J$, which therefore serves as an approximate measure of the jet strength. In this respect, stronger internal jet is responsible for enhanced mixing of the merged droplet.

One of the most prominent dynamical features of turbulent, rapidly rotating convection is the formation of large-scale coherent structures, driven by Reynolds stresses resulting from the small-scale convective flows. In spherical geometry, such structures consist of intense zonal flows that are invariant along the rotation axis. In planar geometry, long-lived, depth-invariant structures also form at large scales, but, in the absence of horizontal anisotropy, they consist of vortices that grow to the domain size. In this work, through the introduction of horizontal anisotropy into a numerical model of planar rotating convection by the adoption of unequal horizontal box sizes (i.e., $L_x\le L_y$, where the $xy$ plane is horizontal), we investigate whether unidirectional flows and large-scale vortices can coexist. We find that only a small degree of anisotropy is required to bring about a transition from dynamics dominated by persistent large-scale vortices to dynamics dominated by persistent unidirectional flows parallel to the shortest horizontal direction. When the anisotropy is sufficiently large, the unidirectional flow consists of multiple jets, generated on a time scale smaller than a global viscous time scale, thus signifying that the upscale energy transfer does not spontaneously feed the largest available mode in the system. That said, the multiple jets merge on much longer time scales. Large-scale vortices of size comparable with $L_x$ systematically form in the flanks of the jets and can be persistent or intermittent. This indicates that large-scale vortices, either coexisting with jets or not, are a robust dynamical feature of planar rotating convection.

We compare the stability of a static pendent drop under two types of control, volume control and pressure control. The drops are taken to be pinned to curves of arbitrary shape. The two types of control introduce integrals into the eigenvalue problems that determine the points of instability. We show that these integrals are solely responsible for the possible occurrence of bifurcation points, depending only on the Bond number. We then show that the points of instability for either type of control can be related to one another and predicted precisely from the eigenvalues of, yet, a third problem, one that is devoid of any integrals. If the curves of attachment are symmetric, we can derive a result that predicts the instability point and associated pattern, all without solving any eigenvalue problem.

Eddy energy transport in rotating two-dimensional turbulence is investigated using numerical simulation. Stochastic forcing is used to generate an inhomogeneous field of turbulence and the time-mean energy profile is diagnosed. An advective-diffusive model for the transport is fit to the simulation data by requiring the model to accurately predict the observed time-mean energy distribution. Isotropic harmonic diffusion of energy is found to be an accurate model in the case of uniform, solid-body background rotation (the $f$ plane), with a diffusivity that scales reasonably well with a mixing-length law $\kappa \propto V\ell$, where $V$ and $\ell$ are characteristic eddy velocity and length scales. Passive tracer dynamics are added and it is found that the energy diffusivity is $75\%$ of the tracer diffusivity. The addition of a differential background rotation with constant vorticity gradient $\beta$ leads to significant changes to the energy transport. The eddies generate and interact with a mean flow that advects the eddy energy. Mean advection plus anisotropic diffusion (with reduced diffusivity in the direction of the background vorticity gradient) is moderately accurate for flows with scale separation between the eddies and mean flow, but anisotropic diffusion becomes a much less accurate model of the transport when scale separation breaks down. Finally, it is observed that the time-mean eddy energy does not look like the actual eddy energy distribution at any instant of time. In the future, stochastic models of the eddy energy transport may prove more useful than models of the mean transport for predicting realistic eddy energy distributions.

According to Kirkinis and Davis [J. Fluid Mech. 746, R3 (2014)], the motion of a contact line can produce a sequence of moving eddies, commonly known as Moffatt vortices. In this work, we extend the formulation given in Kirkinis and Davis for the moving contact line between two viscous fluids and a nonzero static contact angle, and we consider the flow structure in the corner between the interface and the wall. In particular, we discuss the condition for observing Moffatt vortices and we demonstrate that an infinite series of Moffatt vortices cannot be observed considering a Navier-slip boundary condition.

The near wake of a flow past a multiscale array of bars is studied by means of particle image velocimetry (PIV). The aim of this research is to understand the nature of multiscale flows, where multiple coherent motions of nonuniform sizes and characteristic frequencies (i.e., sheddings of particular bars in our considered case) interact with each other. The velocity fields acquired from the experiments are triple decomposed into their mean, a number of coherent fluctuations, and their stochastic part according to a triple decomposition technique introduced recently by Baj et al., Phys. Fluids 27, 075104 (2015). This nonstandard approach allows us to monitor the interactions between different coherent fluctuations representative of sheddings of the particular bars. Further, additional equations governing the kinetic energy of the recognized velocity components are derived to provide better insight into the dynamics of these interactions. Interestingly, apart from the coherent fluctuations associated with sheddings, some additional, secondary coherent fluctuations are also recognized. These seem to appear as a result of nonlinear triadic interactions between the primary shedding modes when the two shedding structures of different characteristic frequencies are in close proximity to one another. The secondary coherent motions are almost exclusively supplied with energy by the primary coherent motions, whereas the latter are driven by the mean flow. It is also found that the coherent fluctuations play an important role in exciting the stochastic fluctuations, as the energy is not fed to the stochastic fluctuations directly from the mean flow but rather through the coherent modes.

The concave curvature effect for an impinging jet flow is discussed in this paper. To do so, a submerged axisymmetric isothermal impinging jet at a Reynolds number (based on the nozzle diameter and the bulk velocity at the nozzle outlet) $\text{Re}=23000$ and for a nozzle to plate distance of two jet diameters $H=2D$ is considered. This investigation is done numerically using a wall-resolved large-eddy simulation. Two geometrical arrangements are studied. These correspond to a jet impinging on a flat plate and a jet impinging on a hemispherical concave plate with a relative curvature $D/d=0.089$, where $d$ is the concave plate diameter. A detailed comparison shows that both flow configurations are very similar in terms of flow dynamics and heat transfer behaviors. The same mechanisms, coming from the initial jet instability and driving the heat transfer at the wall, are found for both geometries. However, a reduction of the mean wall heat transfer is reported for the jet impinging on the concave surface when compared to the flat plate impingement. This reduction mainly comes from the alleviation of the secondary peak. The deterioration of wall heat transfer is shown to be caused by a reduction in the intensity of the intermittent cold fluid injections generated by the secondary structures. These weaker events are assumed to be the consequence of the stabilizing normal pressure gradient, in the outer layer of the wall jet, induced by the concave curvature of the plate. This result goes against the current consensus, inherited from boundary layer studies, that is to say, that concave curvature enhances the heat transfer rate at the wall due to the formation of Görtler vortices. In an attempt to explain the contradictory result of the present study, a discussion is proposed in this paper showing that the commonly used analogy with boundary layer results must be made with care owing to several inherent differences between impinging jet and boundary layer flows.

In an electrically conducting fluid, vortices stretch out a weak, large-scale magnetic field to form strong current sheets on their edges. Associated with these current sheets are magnetic stresses, which are subsequently released through reconnection, leading to vortex disruption, and possibly even destruction. This disruption phenomenon is investigated here in the context of two-dimensional, homogeneous, incompressible magnetohydrodynamics. We derive a simple order of magnitude estimate for the magnetic stresses—and thus the degree of disruption—that depends on the strength of the background magnetic field (measured by the parameter $M$, a ratio between the Alfvén speed and a typical flow speed) and on the magnetic diffusivity (measured by the magnetic Reynolds number $\mathrm{Rm})$. The resulting estimate suggests that significant disruption occurs when $M^2\mathrm{Rm}=O\left(1\right)$. To test our prediction, we analyze direct numerical simulations of vortices generated by the breakup of unstable shear flows with an initially weak background magnetic field. Using the Okubo-Weiss vortex coherence criterion, we introduce a vortex disruption measure, and show that it is consistent with our predicted scaling, for vortices generated by instabilities of both a shear layer and a jet.

Heat or mass transfer around an evaporating drop or condensing vapor bubble is a complex issue due to the interplay between the substrate properties, diffusion- and convection-driven mass transfer, and Marangoni effects, to mention but a few. In order to disentangle these mechanisms, we focus here mainly on the convective mass transfer contribution in an isothermal mass transfer problem. For this, we study the case of a millimetric carbon dioxide bubble which is suspended under a substrate and dissolved into pure liquid water. The high solubility of ${\mathrm{CO}}_2$ in water makes the liquid denser and promotes a buoyant-driven flow at a high (solutal) Rayleigh number ($\text{Ra}\sim {10}^4$). The alteration of $p\mathrm{H}$ allows the concentration field in the liquid to be imaged by laser fluorescence enabling us to measure both the global mass flux (bubble volume, contact angle) and local mass flux around the bubble along time. After a short period of mass diffusion, where the boundary layer thickens like the square root of time, convection starts and the ${\mathrm{CO}}_2$ is carried by a plume falling at constant velocity. The boundary layer thickness then reaches a plateau which depends on the bubble cross section. Meanwhile the plume velocity scales like ${\left(dV/dt\right)}^{1/2}$ with $V$ being the volume of the bubble. As for the rate of volume loss, we recover a constant mass flux in the diffusion-driven regime followed by a decrease in the volume $V$ like $V^{2/3}$ after convection has started. We present a model which agrees well with the bubble dynamics and discuss our results in the context of droplet evaporation, as well as high Rayleigh convection.

The dynamic drying process is studied in spatially heterogeneous film-forming latex suspensions across a wide range of dispersion concentrations using optical imaging techniques. Systematic changes in latex suspension concentration are found to affect lateral drying heterogeneity and surface topology. A nonmonotonic decay in contact angle is observed at the edges of drying droplets by continuously monitoring evaporation dynamics, which is quantitatively characterized by the peak strain and peak formation time. An analytical model is developed to explain the nonmonotonic contact-angle decay by considering a transient dilational stress imposed on a viscoelastic solid model for the particle network. Importantly, the latex concentration dependence of this phenomenon provides evidence for a smooth transition from fluid-line pinning to fluid-line recession behavior during drying, leading to ringlike to volcanolike deposition patterns, respectively. Using experimental data for drying heterogeneity, we quantitatively explore the influence of Marangoni flow and capillary pressure on drying behavior. Moreover, our results show that latex concentration and particle packing can also be strategically used to reduce contact-line friction, thereby affecting fluid-line recession. Taken together, these results show that studying latex suspensions in seemingly simple droplet geometries provides insight into the emergent spatially heterogeneous viscoelastic properties during film formation.

The statistics of fluctuating velocity components are studied in the riser of a closed-loop circulating fluidized bed with fluid catalytic cracking catalyst particles. Our analysis shows distinct similarities as well as deviations compared to existing theories and bench-scale experiments. The study confirms anisotropic and non-Maxwellian distribution of fluctuating velocity components. The velocity distribution functions (VDFs) corresponding to transverse fluctuations exhibit symmetry, and follow a stretched-exponential behavior up to three standard deviations. The form of the transverse VDF is largely determined by interparticle interactions. The tails become more overpopulated with an increase in particle loading. The observed deviations from the Gaussian distribution are represented using the leading order term in the Sonine expansion, which is commonly used to approximate the VDFs in kinetic theory for granular flows. The vertical fluctuating VDFs are asymmetric and the skewness shifts as the wall is approached. In comparison to transverse fluctuations, the vertical VDF is determined by the local hydrodynamics. This is an observation of particle velocity fluctuations in a large-scale system and their quantitative comparison with the Maxwell-Boltzmann statistics.

The draw resonance effect appears in fiber spinning processes if the ratio of take-up to inlet velocity, the so-called draw ratio, exceeds a critical value and manifests itself in steady oscillations of flow velocity and fiber diameter. We study the effect of surface tension on the draw resonance behavior of Newtonian fiber spinning in the presence of inertia and gravity. Utilizing an alternative scaling makes it possible to visualize the results in stability maps of highly practical relevance. The interplay of the destabilizing effect of surface tension and the stabilizing effects of inertia and gravity lead to nonmonotonic stability behavior and local stability maxima with respect to the dimensionless fluidity and the dimensionless inlet velocity. A region of unconditional instability caused by the influence of surface tension is found in addition to the region of unconditional stability caused by inertia, which was described in previous works [M. Bechert, D. W. Schubert, and B. Scheid, Eur. J. Mech B 52, 68 (2015); Phys. Fluids 28, 024109 (2016)]. Due to its importance for a particular group of fiber spinning applications, a viscous–gravity–surface-tension regime, i.e., negligible effect of inertia, is analyzed separately. The mechanism underlying the destabilizing effect of surface tension is discussed and established stability criteria are tested for validity in the presence of surface tension.

We revisit the longstanding question of the onset of sediment transport driven by a turbulent fluid flow via laboratory measurements. We use particle-tracking velocimetry to quantify the fluid flow as well as the motion of individual grains. As we increase the flow speed above the threshold for sediment transport, we observe that an increasing fraction of grains is transported downstream, although the average downstream velocity of the transported grains remains roughly constant. However, we find that the fraction of mobilized grains does not vanish sharply at a critical flow rate. Additionally, the distribution of the fluctuating velocities of nontransported grains becomes broader with heavier tails, meaning that unambiguously separating mobile and static grains is not possible. As an alternative approach, we quantify the statistics of grain velocities by using a mixture model consisting of two forms for the grain velocities: a decaying-exponential tail, which represents grains transported downstream, and a peaked distribution centered at zero velocity, which represents grains that fluctuate due to the turbulent flow but remain in place. Our results suggest that more sophisticated statistical measures may be required to quantify grain motion near the onset of sediment transport, particularly in the presence of turbulence.

We study numerically the settling of a porous sphere in a density-stratified ambient fluid. Simulations are validated against prior laboratory experiments and compared to two mathematical models. Two main effects cause the particle to slow down as it enters a density gradient: lighter fluid within the particle and entrainment of the density-stratified ambient fluid. The numerical simulations accurately capture the particle retention time. We quantify the delay in settling due to ambient fluid entrainment and lighter internal fluid becoming denser through diffusion as a function of the Reynolds, Péclet, and Darcy numbers, as well as the thickness of the transition layer and the ratio of the density difference between the lower and upper fluid layers to the density difference between the particle and the upper layer. A simple fitting formula is presented to describe the settling time delay as a function of each of those five nondimensional parameters.

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.