We experimentally investigate the amplitude of the common sound heard when we pour water, tea, or coffee on a filled receptacle. Using water jets from circular nozzles, we find that pouring is audible when the nozzle distance from the free surface is above one-third of the jet breakup length. The sound amplitude increases with the steepness of the jet corrugation, informing that thin jets are louder than thick ones for a given pouring height. Since the jet corrugation is related to the air entrainment rate, the sound of pouring can serve as a practical noninvasive probe in aeration processes. After the jet breaks up into drops impacting on the free surface, the pouring sound amplitude increases with the nozzle diameter, unlike before breakup.

The efficient transport of fluids through disordered media requires a thorough understanding of how the driving rate affects two-phase interface propagation. Despite our understanding of front dynamics in homogeneous environments, as well as how medium heterogeneities shape fluid interfaces at rest, little is known about the effects of localized topographical variations on large-scale interface dynamics. To gain physical insights into this problem, we study here oil-air displacements through an “imperfect” Hele-Shaw cell. Combining experiments, numerical simulations, and theory, we show that the flow rate dramatically alters the interface response to a porous constriction as one approaches the Saffman-Taylor instability, strictly under stable conditions. This gives rise to asymmetric imbibition–drainage hysteresis cycles that feature divergent extensions and nonlocal effects, all of which are aptly captured and explained by a minimal free boundary model.

We develop a theory of fluid-structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit. We consider the canonical geometries of a two-dimensional channel with a deformable top wall and an axisymmetric deformable tube. Focusing on the hydrodynamics, we employ a linear relationship between wall displacement and hydrodynamic pressure, which has been shown to be suitable for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, and the flow rate is related to the pressure gradient (and the tube or wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without a priori assumptions on the magnitude of the oscillation frequency (i.e., at arbitrary Womersley number). We find that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. We find good agreement between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number.

Turbulent scalar mixing occurs within a wide variety of natural and engineering flows. Predicting and controlling the scalar concentration(s) within these flows can yield immediate benefits to numerous applications across many fields. To that end, a better understanding of the effects of scalar-field initial conditions on the evolution(s) of scalar fields is required to either promote or delay the rate at which mixing occurs. Direct numerical simulations are employed herein to simulate the evolution in time of the hydrodynamic and (passive) scalar fields within a fully developed turbulent channel flow. The effects of the scalar field initial conditions are studied by analyzing the evolution of the scalar field subject to three different initial conditions with interfaces oriented normal to the streamwise, wall-normal, and transverse directions. Particular emphasis is placed on the scalar variance and dissipation rate budgets, including the evolutions of their constituent terms. The fastest mixing occurs for the initial condition in which the interface is aligned normal to the mean velocity vector. The rapid mixing in this case is associated with higher rates of production and destruction of the scalar dissipation, as well as strong advection and stretching of the interface by the mean flow. In addition to better mixing arising from the stronger turbulence near the wall, enhanced mixing is correlated with having the edge of an interface along a channel wall, such that a large distortion of the initial interface arises from the combined effects of the no-slip condition at the channel walls with the advection of the interface by the mean flow in the region between the walls. To maximize this effect, it is recommended that scalar interfaces be aligned normal to the mean velocity vector to promote mixing within internal flows.

Switchable and adaptive substrates emerged as valuable tools for controlling wetting and actuation of droplet motion. Here, we report a computational study of the dynamics of an unstable thin liquid film deposited on a switchable substrate, modeled with a space- and time-varying contact angle. For a sufficiently large rate of wettability variation, a topological transition appears. Instead of breaking up into droplets, as expected for a substrate with multiple wetting minima, a metastable rivulet state emerges. A criterion discriminating whether or not rivulets occur is identified in terms of a single dimensionless parameter. Finally, we show and derive theoretically how the film rupture times, droplet shape, and rivulet lifetime depend on the pattern wavelength and speed.

A previous model of a two-dimensional, stratified dipole is applied to a cylindrical vortex of dense fluid traveling across the lower boundary of a semi-infinite, unstratified ambient. The vortex is semicircular in profile. The model is derived from the Boussinesq-Euler equations and hence is an idealization neglecting the effects of viscosity, density diffusion, and friction. This is similar to other idealized models of dense fluid flow. The flow maintains a steady state through a balance of positive and negative vorticity generation as the dense fluid travels around the vortex. Numerical experiments are performed to investigate the stability and behavior of isolated and interacting vortices of this type.

In this study, wind and water tunnel experiments of turbulent wakes in a scaled floating wind farm are performed. Scaling of a floating wind farm with a scaling ratio of 1:400 is made possible by relaxing geometric scaling of the turbine platform system, such that the dynamic response can be correctly matched, and to allow for relaxing Froude scaling such that the Reynolds number can be kept large enough. Four dimensionless parameters, describing the relative importance of wind and wave loads compared to turbine inertia, are used to guide the scaled floater design. Free decay tests of the pitch and heave response confirm that the dimensionless natural frequency of the scaled model is in the typical range for full-scale floating turbines when matching the proposed four dimensionless parameters. The response and performance of a single turbine scaled model are characterized for different wind and wave conditions. Subsequently, a wind farm experiment is performed with twelve floating turbine models, organized in four rows and three columns. Particle image velocimetry measurements of the wake of the middle turbine in the third row reveal distinct differences in wake properties for different wave conditions. Conditional averaging confirms a synchronization of wake deflection with the traveling waves in the wind farm. The power outputs show distinct peaks at the wave frequencies and its harmonics, due to motions triggered by complex wave-turbine-wake interactions. The power spectrum of the aggregate power of three streamwise aligned turbines exhibits anticorrelation of motions at the wave frequency due to wave speed induced phase lag, and spatiotemporal correlations of power outputs at the frequency corresponding to the wind-convective time between two rows. These experiments using an appropriately scaled floating wind farm in a wind tunnel setup confirm distinct impacts of turbine motion on wake recovery and meandering, and measurement results highlight the intricate interactions between wave topology and wake meandering.

Ciliary flows are generated by a vast array of eukaryotic organisms, from unicellular algae to mammals, and occur in a range of different geometrical configurations. We employ a point torque—or “rotlet”—model to capture the time-averaged ciliary flow above a planar rigid wall. We demonstrate the advantages (i.e., accuracy and computational efficiency) of using this, arguably simpler, approach compared to other singularity-based models in Stokes flows. Then, to model ciliary flows in confined spaces, we extend the point torque solution to a bounded domain between two plane parallel no-slip walls. The flow field is resolved using the method of images and Fourier transforms, and we analyze the role of confinement by comparing the resultant fluid velocity to that of a rotlet near a single wall. Our results suggest that the flow field of a single cilium is not changed significantly by the confinement, even when the distance between the walls is commensurate with the cilium's length.

Magnetic resonance imaging (MRI) experiments have been performed in conjunction with direct numerical simulations (DNS) to study neutrally buoyant particle-laden pipe flows. The flows are characterized by the suspension liquid Reynolds number (${\mathrm{Re}}_s$), based on the bulk liquid velocity and suspension viscosity obtained from Eilers' correlation, the bulk solid volume fraction (${\varphi }_b$), and the particle-to-pipe diameter ratio ($d/D$). Six different cases have been studied, each with a unique combination of ${\mathrm{Re}}_s$ and $\varphi$, while $d/D$ is kept constant at 0.058. The selected cases ensure that the comparison is performed across different flow regimes, each exhibiting characteristic behavior. In general, an excellent agreement is found between experiment and simulation for the average liquid velocity and solid volume fraction profiles. Root-mean-square errors as low as 1.7% and 5.3% are found for the velocity and volume fraction profiles, respectively. This study presents accurate and quantitative velocity and volume fraction profiles of semidilute up to dense suspension flows using both experimental and numerical methods. Three different flow regimes are identified, based on the experimental and numerical solid volume fraction profiles. These profiles explain observations in the drag change. For low bulk solid volume fractions a drag increase (with respect to an equal ${\mathrm{Re}}_s$ single-phase case) is observed. For moderate volume fraction distributions the drag is found to decrease, due to particle accumulation at the pipe center. For high volume fractions the drag is found to decrease further. For solid volume fractions of 0.4 a drag reduction higher than 25% is found. This drag reduction is linked to the strong viscosity gradient in the radial direction, where the relatively low viscosity near the pipe wall acts as a lubrication layer between the pipe wall and the dense core.

This paper reports on a numerical study of the reciprocating flow through a double bifurcation. Its aim is to quantify the potential gas transport in flows similar to those in the human airway during high-frequency ventilation, a medical ventilation technique that uses fast, yet shallow, inflations to minimize pressure and volume variation in the lungs and therefore protect lungs from ventilator-induced lung injury. The shallow inflations mean that gas transport is not achieved by bulk advection and other mechanisms must be used. Here we focus on nonlinear mean streaming and turbulent diffusion. We show that both of these mechanisms are driven by the formation of Dean vortices due to centrifugal instability in the curved sections of the bifurcation. We report the impact of the upstream and downstream conditions on both of these during both inhalation and exhalation portions of the reciprocating flow; in particular, we show that the development of turbulence in a given airway vessel is influenced by downstream conditions and not simply by the local flow conditions. This result highlights the importance of using a geometry of appropriate complexity for the modeling of physiological flows, particularly if the results are to be parameterised for use in larger-scale but lower-order models.

In the presence of shear-enhanced diffusion (Taylor dispersion), flame propagation is effectively anisotropic. This study focuses on the influence of the direction of a shear flow relative to the direction of propagation on the diffusional-thermal instabilities of premixed flames. The problem is addressed analytically using large activation energy asymptotics, complemented by numerical simulations, in the framework of a constant density two-dimensional model. The model, obtained by depth averaging of the governing equations in a Hele-Shaw configuration, accounts for shear-enhanced diffusion. A linear stability analysis is carried out analytically, leading to a dispersion relation involving three parameters: the Lewis number Le; the Taylor-dispersion coefficient $p$, which is proportional to the Péclet number; and the angle $\varphi$ between the direction of propagation of the unperturbed planar flame and the flow direction. Based on the dispersion relation, stability diagrams are determined in terms of the parameters, along with bifurcations curves identifying the nature of the instabilities observed. It is shown that cellular instabilities expected when $\text{Le}<1$ can now occur as a result of Taylor dispersion in $\text{Le}>1$ mixtures, provided the angle $\varphi$ exceeds a critical value approximately equal to ${75}^{\circ }$. In general, it is found that an increase in $\varphi$ from $0^{\circ }$ to ${90}^{\circ }$ has a stabilizing effect in subunity Lewis number mixtures $\text{Le}<1$ and a destabilizing effect when $\text{Le}>1$. Particular attention is devoted to the cellular long-wave instability encountered, which is found to be described by a modified Kuramoto-Sivashinsky equation. The equation involves the three aforementioned parameters and includes a dispersion term (a third-order spatial derivative) as well a drift term (first-order derivative) whenever $\varphi \ne 0^{\circ }$ and $\varphi \ne {90}^{\circ }$, which is whenever the direction of the shear flow is neither parallel nor perpendicular to the direction of flame propagation.

Quasistatic Rayleigh-Bénard convection with an imposed horizontal magnetic field is investigated numerically for Chandrasekhar numbers up to $Q={10}^6$ with stress-free boundary conditions. Both $Q$ and the Rayleigh number (Ra) are varied to identify the various dynamical regimes that are present in this system. We find three primary regimes: (i) a two-dimensional (2D) regime in which the axes of the convection rolls are oriented parallel to the imposed magnetic field; (ii) an anisotropic three-dimensional (3D) regime; and (iii) a mean flow regime characterized by a large scale horizontal flow directed transverse to the imposed magnetic field. The transition to 3D dynamics is preceded by a series of 2D transitions in which the number of convection rolls decreases as Ra is increased. For sufficiently large $Q$, there is an eventual transition to two rolls just prior to the 2D-3D transition. The 2D-3D transition occurs when inertial forces become comparable to the Lorentz force, i.e., when $\sqrt{Q}/\text{Re}=O\left(1\right)$; 2D, magnetically constrained states persist when $\sqrt{Q}/\text{Re}\gtrsim O\left(1\right)$. Within the 2D regime, we find heat and momentum transport scalings that are consistent with the hydrodynamic asymptotic predictions of Chini and Cox [Phys. Fluids 21, 083603 (2009)]: the Nusselt number (Nu) and Reynolds number (Re) scale as $\text{Nu}\sim {\text{Ra}}^{1/3}$ and $\text{Re}\sim {\text{Ra}}^{2/3}$, respectively. For $Q={10}^6$, we find that the scaling behavior of Nu and Re breaks down at large values of Ra due to a sequence of bifurcations and the eventual manifestation of mean flows.

In this work, baroclinic instability in a current-undercurrent system is analyzed using the biglobal instability analysis (BIA). Idealized model flows are considered and the flow parameters are estimated from the Western North Pacific circulation system. Compared with the prevailing one-dimensional linear stability analysis (1D-LSA), BIA can deal with the basic flow of continuously nonuniform vertical shear and strong horizontal variation within the framework of the Boussinesq equation to account for nongeostrophic effects. The basic velocity gradually changes from the vertically linear Eady type to a more realistic distribution, which destabilizes the Phillips-type mode due to the strengthening of the vertical shear. With an increasing zonal velocity variation, the mode is more of a barotropic type in the long-wave range and is more of a baroclinic type in the short-wave range. Moreover, the high vertical shear near the vertical boundaries supports a series of Charney-type modes in the confined boundary region. The Charney modes are severely affected by the boundary constraint, leading to a wide unstable wave-number range deep into the small-scale region and enhanced ageostrophic motions. The top and bottom boundary layers due to viscosity and diffusivity can be destabilizing and sustain the modal growth for short waves. In comparison, 1D-LSA can overestimate the growth rate of baroclinic modes and cannot quantify the coupling effects with the horizontal shear for the present case.

Buoyancy-driven dissolution of the solid phase is common in natural processes and subsurface applications, such as geomorphology, solution mining, and geological ${\mathrm{CO}}_2$ storage. When an external horizontal flow is imposed, the dissolution dynamics are controlled by the interplay between buoyancy-driven and forced convections. The reshaping of the solid surface due to this interplay is not well understood. Here, we fabricate a soluble microfluidic chip with a horizontal channel to investigate the pore-scale dissolution dynamics in a gravity field. We observe that the wave number and the surface roughness factor of the upper solid-liquid interface initially increases with the flow rate (Péclet number Pe) and then decreases, indicating two dissolution regimes, namely, Regimes I and II. Microparticle-image-velocimetry-based imaging reveals that the eddy evolution occurring in the flow-dissolution system controls the local dissolution rate and the geometry evolution of the solid-liquid interface. Through the quantification of the eddies (or troughs) for the whole channel, the number of the eddies increases with Pe in Regime I and decreases with Pe in Regime II, indicating that the buoyancy-driven convection is enhanced in Regime I and suppressed in Regime II by the forced convection. Finally, by performing a theoretical analysis of the density gradient, we obtain a scaled critical aperture, i.e., the critical aperture normalized by a characteristic length, for the onset of unstable dissolution of the solid-liquid interface. Such a scaled critical aperture is constant for both dissolution regimes. In this paper, we elucidate the crucial role of eddies in the flow-dissolution system in a gravity field. Moreover, we improve our understanding of the interplay between buoyancy-driven and forced convections in etching the solid surface.

This study considers advective and diffusive transport of passive scalar fields by spatially varying incompressible flows. Prior studies have shown that the eddy diffusivities governing the mean-field transport in such systems can generally be nonlocal in space and time. While for many flows nonlocal eddy diffusivities are more accurate than commonly used Boussinesq eddy diffusivities, nonlocal eddy diffusivities are often computationally cost prohibitive to obtain and difficult to implement in practice. We develop a systematic and more cost-effective approach for modeling nonlocal eddy diffusivities using matched moment inverse operators. These operators are constructed using only a few leading-order moments of the exact nonlocal eddy diffusivity kernel, which can be easily computed using the inverse macroscopic forcing method [Mani and Park, Phys. Rev. Fluids 6, 054607 (2021)]. The resulting reduced-order models for the mean fields that incorporate the modeled eddy diffusivities often improve Boussinesq-limit models because they capture leading-order nonlocal effects. But more importantly, these models can be expressed as partial differential equations that are readily solvable using existing computational fluid dynamics capabilities rather than as integropartial differential equations.

We study the Reynolds-number effects on the outer region of moderate adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) and find that their small-scale (viscous) energy reduces with increasing friction Reynolds number (${\mathrm{Re}}_{\tau }$). The trend is based on analyzing APG TBL data across $600\lesssim {\mathrm{Re}}_{\tau }\lesssim 7000$ and contrasts with the negligible variation in small viscous-scaled energy noted for canonical wall flows. The data sets considered include those from a well-resolved numerical simulation [Pozuelo et al., J. Fluid Mech. 939, A34 (2022)], which provides access to an APG TBL maintained at near-equilibrium conditions across $1000\lesssim {\mathrm{Re}}_{\tau }\lesssim$ 2000, with a well-defined flow history, and a new high-${\mathrm{Re}}_{\tau }$ ($\sim 7000$) experimental study from the large Melbourne wind tunnel, with its long test section modified to permit development of an APG TBL from a “canonical” upstream condition. The decrease in small-scale energy with ${\mathrm{Re}}_{\tau }$ is revealed via decomposing the streamwise normal stresses into small- and large-scale contributions, based on a sharp spectral cutoff. The origin for this trend is traced back to the production of turbulent kinetic energy in an APG TBL, the small-scale contribution to which is also found to decrease with ${\mathrm{Re}}_{\tau }$ in the outer region. The conclusion is reaffirmed by investigating attenuation of streamwise normal stresses due to changing spatial resolutions of the numerical grid or hotwire sensors, which reduces with increasing ${\mathrm{Re}}_{\tau }$ and is found to be negligible at ${\mathrm{Re}}_{\tau }\sim 7000$ in this study. The results emphasize that new scaling arguments and spatial-resolution corrections should be tested rigorously across a broad ${\mathrm{Re}}_{\tau }$ range, particularly for pressure gradient TBLs.

We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven cavity in two spatial dimensions. We benchmark our solution against published reference data for low Reynolds numbers and find excellent agreement. In addition, we investigate the short-time dynamics of the flow at high Reynolds numbers for the lid-driven and doubly-driven cavities. We represent the velocity components by matrix product states and find that the bond dimension grows logarithmically with simulation time. The tensor network algorithm requires at most a few percent of the number of variables parametrizing the solution obtained by direct numerical simulation, and approximately improves the runtime by an order of magnitude compared to direct numerical simulation on similar hardware. Our approach is readily transferable to other flows, and paves the way towards quantum computational fluid dynamics in complex geometries.

Sheared granular materials spontaneously develop heterogeneous and transient kinematic fields which resemble turbulence. We focus here on characterizing the length scale of these heterogeneities. We simulate plane-shear flows and measure the local grain velocity, velocity fluctuation, shear rate, vorticity, and dilation rate. The results show that these quantities are widely distributed, even more so at low inertial numbers. We relate this effect to spatial correlations that develop at low inertial numbers, where the flow becomes partitioned into “cold” patches with lower than average strain rate and “hot” zones where the strain rate is concentrated. We finally extract a characteristic length scale for the size of these heterogeneities, corresponding to the size of a representative elementary volume. This size is found to vary from a few grain diameters at high inertial number to a few dozen grain diameters at low inertial number, following a characteristic power law. These insights into. representative elementary volume (REV) size may be of importance to further develop continuum models for granular flows, capturing local and nonlocal effects.

The wing structure of several insects, including dragonflies, is not smooth, but corrugated; its vertical cross section consists of a connected series of line segments. Some previous studies have reported that corrugated wings exhibit better aerodynamic performance than flat wings at low Reynolds numbers $[\text{Re}\simeq \mathit{O}\left({10}^3\right)]$. However, the mechanism remains unclear because of the complex wing structure and flow characteristics. A corrugated structure modifies the formation and behavior of aerodynamic flow features arising during unsteady wing motion, such as the leading-edge vortex (LEV). These modifications can be key to lift enhancement in many insects, though the details of these benefits remain imperfectly understood. In this study, we analyzed the flow around a two-dimensional corrugated wing model that started impulsively by direct numerical simulations. We focused on the period between the initial generation of LEVs and subsequent interactions before detachment. For the flat wing, it is known that a secondary vortex with a sign opposite to that of the LEV, the $\lambda$ vortex, develops and erupts to discourage lift enhancement. For corrugated wings, such an eruption of the $\lambda$ vortex can be suppressed by the corrugation structure, which enhances the lift. The detailed mechanism and its dependence on the angle of attack are also discussed.

Constitutive relations are needed to predict the behavior of complex fluids in nonviscometric flows. This is an area that is largely unexplored for yield stress materials because of the difficulty describing the elastoviscoplastic behavior for arbitrary flows. Here, we measure the shear and extensional rheology of a simple tunable yield stress system: emulsions with different oil volume fractions that allow one to vary the flow properties over a large range. We propose universal concentration scaling laws that produce master curves for the shear and extensional rheology with a minimal number of known emulsion parameters. The extensional viscosity is obtained experimentally using a theory for inelastic shear-thinning materials, demonstrating that elastic stresses are unimportant in the pinching dynamics, and the elastic normal stress differences contribute minimally to the von Mises yield surface. Hence, this shows that material elasticity is unimportant, and an explicit constitutive equation of, for example, Criminale-Ericksen-Filby type, with a Herschel-Bulkley viscosity and a modulus equal to the Laplace pressure is adequate to describe the behavior of such concentrated soft-sphere systems in general steady and low Deborah number unsteady Eulerian and Lagrangian flows.