Turbulence in a wall-bounded flow of supercritical fluid can be significantly modulated by nonuniform body forces. This study presents direct numerical simulations performed with a nonuniform streamwise body force varying in the wall-normal direction in a fully developed channel flow. A quasilaminar state and reorganized turbulence were obtained by changing the amplitude of the nonuniform body force which distorts the parabolic mean velocity profile and thus alters the turbulence production due to mean shear. Weak production of the flattened mean velocity profile leads to a relaminarization. In the quasilaminar state, all components of the Reynolds stress tensor are fairly weak except the streamwise fluctuations distant from the wall, which indicates the collapse of the near-wall turbulence self-sustaining cycle. The remaining streamwise fluctuations away from the wall exhibit elongated streaks, which is shown by premultiplied spectra. In the recovered turbulence regime, the Reynolds shear stress has a negative range in the bulk connected with a positive range near the wall. This corresponds to the nonmonotonic shear stress resulting from an M-shaped velocity profile. In a subsequent quadrant analysis of the Reynolds shear stress, the sweep and ejection events are found to dominate near the wall only while inward $Q_1$ and outward $Q_3$ motions are significant in the bulk. Both kinds of high-speed events can be attributed to the velocity maxima of the M-shaped mean velocity profile and are found to penetrate towards the wall and the channel center. Interestingly, the flow topology shows the typical teardrop shape once turbulence recovered. Our study contributes to the understanding of flow relaminarization in mixed convection and assists in developing further flow control techniques.

Doubly diffusive convection driven by horizontal gradients of temperature and salinity is studied in a three-dimensional enclosure of square horizontal cross section and large aspect ratio. Previous studies focused on the primary instability and revealed the formation of subcritical branches of spatially localized states. These states lose stability because of their twist instability, thereby precluding the presence of any related stable steady states beyond the primary bifurcation and giving rise to spontaneous temporal complexity for supercritical parameter values. This paper investigates the emergence of this behavior. In particular, chaos is shown to be produced at a crisis bifurcation located close to the primary bifurcation. The critical exponent related to this crisis bifurcation is computed and explains the unusually abrupt transition. The construction of a low-dimensional model highlights that only a few requirements are necessary for this type of transition to occur. As a consequence, it is believed to be observable in many other systems.

We investigate through numerical simulations of the Navier-Stokes equations the influence of the surface roughness on the fluid flow through fracture joints. Using the Hurst exponent $H$ to characterize the roughness of the self-affine surfaces that constitute the fracture, our analysis reveals the important interplay between geometry and inertia on the flow. Precisely, for low values of Reynolds numbers, Re, we use Darcy's law to quantify the hydraulic resistance $G$ of the fracture and show that its dependence on $H$ can be explained in terms of a simple geometrical model for the geometric tortuosity $\tau$ of the channel. At sufficiently high values of Re, when inertial effects become relevant, our results reveal that nonlinear corrections up to third order to Darcy's law are approximately proportional to $H$. These results imply that the resistance $G$ to the flow follows a universal behavior by simply rescaling it in terms of the fracture resistivity and using an effective Reynolds number, namely, $\mathrm{Re}/H$. Our results also reveal the presence of quasi-one-dimensional channeling, even considering the absence of shear displacement between upper and lower surfaces of the self-affine fracture.

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the nonlinear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well-resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12{288}^3$, and the Taylor-scale Reynolds number is in the range 140–1300. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_{\lambda }$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_{\lambda }$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

We consider the use of probabilistic neural networks for fluid flow surrogate modeling and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (i) the shallow-water equations, (ii) a two-dimensional cylinder flow, (iii) the wake of a NACA0012 airfoil with a Gurney flap, and (iv) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow surrogate model but also systematically quantifies the uncertainty therein to assist with model interpretability.

Flow-reversal phenomena in a classical two-dimensional (2D) Rayleigh-Bénard convection, in a square enclosure, are usually explained through growth and merging of diagonally opposite counterrotating corner rolls. To probe further the corner-roll growth dynamics, we have altered the square enclosure edges by additional slanted conduction walls, so that the enclosure resembles an octagonal shape. We have performed a series of 2D numerical simulations by varying the slanted wall inclination angle ($\alpha$) from $0^{\circ }$ to ${45}^{\circ }$, to construct a detailed flow map in thermal convection in a range $5\times {10}^5\le \text{Ra}\le {10}^8$ and $0.8\le \text{Pr}\le 2.0$, where $\text{Ra}$ is the Rayleigh number and $\text{Pr}$ is the Prandtl number. Depending on $\text{Ra}$, $\text{Pr}$, and $\alpha$, flow features in the octagonal enclosure can exist in the form of a uniform circulation, a two-roll, a mixed, a periodic, a quasiperiodic, or multiple flow states superimposed on each other. The flow reversals in the octagonal enclosure take place in several ways, for example, by the ejection of mushroom-shaped plumes alternatively from the opposite slanted walls at low $\text{Ra}$ ($\approx {10}^5$) and high $\text{Pr}$ ($\approx 2$), by the corner-roll growth at high $\text{Ra}$ ($\approx {10}^8$) and low $\text{Pr}$ ($\approx 1.2$), and by the dipole at high $\text{Ra}$ ($\approx {10}^8$) and high $\text{Pr}$ ($\approx 2$). Strikingly, the dimensionless flow-reversal frequency scales linearly with an increase in $\alpha$, and the slope varies from 1.04 at low $\text{Ra}=5\times {10}^5$ to 0.328 at high $\text{Ra}={10}^8$. We have shown the flow reversals are a consequence of competition between the dipole (a two-roll state where a cold roll sits above a hot roll) and the quadrupole (the four corner rolls) modes with the monopole mode. A uniform circulation with flow-reversal results if the quadrupole mode wins, and a two-roll state with a reversal results, if the dipole wins. At high $\text{Ra}(\ge {10}^8)$, the dipole strengthens, and the core bulk region shows hydrodynamic instabilities in the form of turbulent-like engulfments. We have uncovered the mechanism responsible for the observed engulfments due to the increase in turbulence production in the core bulk region by the buoyancy. As a result, we have observed that total heat transport also increases up to $14\%$ when $\alpha$ is varied from $0^{\circ }$ to ${45}^{\circ }$.

The proliferation of turbulence in subcritical wall-bounded shear flows involves spatially localized coherent structures. Turbulent spots correspond to finite-time nonlinear responses to pointwise disturbances and are regarded as seeds of turbulence during transition. The rapid spatial decay of the turbulent fluctuations away from a spot is accompanied by large-scale flows with a robust structuration. The far-field velocity field of these spots is investigated numerically using spectral methods in large domains in four different flow scenarios (plane Couette, plane Poiseuille, Couette-Poiseuille, and a sinusoidal shear flow). At odds with former expectations, the planar components of the velocity field decay algebraically. These decay exponents depend only on the symmetries of the system, which here depend on the presence of an applied gradient, and not on the Reynolds number. This suggests an effective two-dimensional multipolar expansion for the far field, dominated by a quadrupolar flow component or, for asymmetric flow fields, by a dipolar flow component.

In this paper, particle image velocimetry and electrochemical measurements were applied simultaneously to examine the relationship between wall shear stress and the three-component velocity field in pipe flow. Moreover, the large-scale motions in the velocity field were separated into very-large-scale motions (VLSMs) and large-scale motions (LSMs) to investigate their respective influences on the wall shear stress fluctuations. The conditional velocity field during negative wall shear stress fluctuations confirmed the existence of the “footprints” of the streamwise and wall-normal velocity components in VLSMs. Further, a pair of counter-rotating roll modes was found to appear in the VLSMs, exhibiting length scales of ${\lambda }_x>3R$, where ${\lambda }_x$ is the streamwise wavelength and $R$ is the pipe radius. In contrast, in LSMs, which exhibit length scales of $0.6R<{\lambda }_x<3R$, counter-rotating vortex pairs were not observed. In this paper, the length-scale threshold for generating counter-rotating vortex pairs in pipe flow was found to be $3R$. This threshold value is higher than the value reported for turbulent boundary layers, which is $1\delta$, where $\delta$ is the boundary-layer thickness. Two-point correlations of wall shear stress, which are associated with the conditional spanwise velocity in the $\theta -x$ plane, revealed the effect of spanwise meandering features on the near-wall region.

Speech is a potent route for viral transmission in the COVID-19 pandemic. Informed mitigation strategies are difficult to develop since no aerosolization mechanism has been visualized yet in the oral cavity. Here we show with high-speed imaging how phonation of common stop consonants, found in most of the world's spoken languages, form and extend salivary filaments in a few milliseconds as moist lips open or when the tongue separates from the teeth. Both saliva viscoelasticity and airflow associated with the plosion of stop consonants are essential for stabilizing and subsequently forming centimeter-scale thin filaments, tens of microns in diameter, that break into speech droplets. Moreover, these plosive consonants induce vortex rings that drive meter-long transport of exhaled air, tying this mechanism to transport associated with speech. We demonstrate that a similar mechanism of aerosolization occurs during the vibration of reeds in wind instruments and may occur during the flapping of the glottis folds. Finally, our research suggests a mitigation of droplet production during speech by using a lip balm.

For a family of oscillatory Stokes layers, the spatiotemporal evolution of impulsively excited disturbances is investigated, using direct numerical simulations of the linearized Navier-Stokes equations. The semi-infinite planar Stokes layer is modified to incorporate a low-amplitude, high-frequency harmonic, which provides a simplified model of the external noise found in physical experiments. For the unmodified Stokes layer, impulsively excited disturbances are known to form family-tree-like structures, composed of multiple wave packets. The long-term behavior that is encompassed within these structures is studied, together with the effects upon them of the alterations to the base flow. In the absence of any base-flow modification, the disturbances are discovered to exhibit a subharmonic pattern of temporal growth, with a periodicity that is twice that of the basic state. It is also shown that when linear instability first arises, it takes an absolute rather than a convective form. Inclusion of a high-frequency harmonic into the basic state is found to have a strong and destabilizing impact upon the impulse response. The development of the family-tree-like disturbance structure can be disrupted, changing the character of the absolute instability and promoting its appearance at much reduced Reynolds numbers.

In this paper, we investigate drainage and oscillation behaviors of sessile drops caused by capillary drainage through a hole. When a water drop is deposited on a hole drilled on a superhydrophobic plate in contact with a bath of water from the bottom side, the liquid in the drop will transport into the bath and a jet is then produced. We focus on the evolution of the drop diameter $D\left(t\right)$ with time $t$. For a small drop, a scaling relation $D\left(t\right)\sim t^{2/7}$ is observed, arising from the competition between the surface tension and inertia. In addition, due to the initial perturbation arising from the deposition, both the drop and the jet show oscillation behaviors. It is observed that the amplitude of the drop oscillation decreases with time while the frequency increases, and we attribute these behaviors to the variable drop mass as well as the competition between the capillary force and the inertia. Considering the present system as a damped harmonic oscillator with variable mass, theoretical models are proposed, which predict well the experimental results. Moreover, we develop a way to suppress the initial perturbation, which allows us to create drops with very large volumes. Our results show that the scaling regime asymptotically reaches $D\left(t\right)\sim t^{1/2}$ when the drop becomes a puddle.

Gradients of chemical potentials in a multiphase system induce mass transport and thus motion of liquid-liquid interfaces. We probe the displacement of oil on a solid substrate immersed in water through this osmosis phenomenon by using two experimental microfluidic systems. The first one, based on glass capillary, is used to quantify the permeability to water of oils sandwiched between two different salt solutions that set the water flux and thus oil motion dynamics. In the context of oil recovery, in particular in the case of low-salinity water flooding, we show that the presence of asphaltenes increases the flux of water and thus the velocity of oil. The second system involves microfabricated cavities that play the role of dead-end pores where oil is trapped in the presence of a salt crystal. The salt crystal allows nucleation of a water drop inside the microcavities that swells under osmosis, thus moving oil out of the dead-end pore model. The efficiency of oil removing from the model crevice is shown to be a function of geometrical and wetting properties, including heterogeneities of surface features. Counterintuitively, it is less probable for oil to move out from a hydrophilic cavity than from a hydrophobic one. Experimental observations are rationalized by geometrical arguments.

Highly resolved numerical simulations by the immersed boundary method are used to study neutrally buoyant spherical particle motion when carried by fluid approaching a wall. The carrying flow studied is the Hiemenz-Homann (HH) axisymmetric straining flow into a stagnation point at a flat rigid wall, with a boundary layer of thickness $3\delta =3\sqrt{\nu /B}$, with $B$ the strain rate of the flow and $\nu$ the kinematic viscosity of the fluid. The pressure in the carrying flow increases on approach to the stagnation point, as a result of the deceleration of the fluid. A single particle moving toward a smooth wall along the axis of the HH flow was studied by Li et al. [Li et al., J. Fluid Mech. 892, A32 (2020)]. Results for the particle and fluid motion from this prior work are coupled here with numerical analysis of the impact using a simple model of roughness effects, with contact allowed at a radius slightly larger than the hydrodynamic radius, but with no detailed analysis of roughness otherwise considered. Solid contact is modeled for particle-wall separations below a threshold of order 1% of the particle radius, while the abruptly changing fluid flow during the collision is resolved numerically. The model is validated against existing experimental results of heavy particle settling and rebound, allowing for variation of the scale of the contact threshold. One particle impacting on the wall and two particles impacting each other as well as the wall are studied for neutrally buoyant particles in the stagnation point flow. Defining the Reynolds number based on the particle radius $a, \text{Re}=2{\mathrm{Ba}}^2/\nu =2{(a/\delta )}^2$, and the Stokes number as $\text{St}=\text{Re}/9$, the influence of inertia is related to the particle size relative to the boundary layer thickness. For one particle of $a/\delta <1$, the particle asymptotically comes to rest at the wall without rebound. Impact begins for $a/\delta \approx 1.3–1.6$ for particle roughness (onset of impact) from 6% to 4% of $a$, respectively, with progressively stronger impact as $a/\delta$ increases beyond the threshold. The particle collision dynamics and the collision time deduced from this model are presented. For pairs of particles constrained to remain on the flow axis, a range of initial separations and sizes are studied. For the case when impact of the pair occurs before the closer particle reaches the wall, an impulse from the trailing particle to the leading one results in a much stronger collision than seen with a single particle, and multiple collisions are predicted to occur before the particles come to rest. A surprising contactless rebound of the particle closer to the wall is found, as the pressure variation associated with the carrying flow pushes this particle away from the wall while it is shielded from drag by the farther particle.

We present a theoretical investigation of liquid imbibition into capillaries with axially varying geometry. We show that using appropriate geometry and wettability, converging capillaries, in principle, can act as a liquid diode. We explain the underlying mechanics and conditions that make a converging capillary a liquid diode. Further, we describe a methodology to enhance the rate of liquid imbibition into the proposed diode. We mathematically show that creating a wettability gradient along the axial length of the capillary diode enhances the rate of liquid imbibition compared to a capillary diode with uniform wettability. Our mathematical model predicts that using a wettability gradient along the axial length of the capillary diode decreases the imbibition time by more than 30% compared to a capillary diode with uniform wettability.

When an object impacts the free surface of a liquid, it ejects a splash curtain upwards and creates an air cavity below the free surface. As the object descends into the liquid, the air cavity eventually closes under the action of hydrostatic pressure (deep seal). In contrast, the surface curtain may splash outwards or dome over and close, creating a surface seal. In this paper, we experimentally investigate how the splash curtain dynamics are governed by cavity pressure difference, gravity, and surface tension, and how their interplay controls the occurrence, or not, of the surface seal. Based on the experimental observations and measurements, we develop an analytical model to describe the trajectory and dynamics of the splash curtain. The model enables us to reveal the scaling relationship for the dimensionless surface seal time and discover the existence of a critical dimensionless number that predicts the occurrence of the surface seal. This scaling indicates that the most significant parameter governing the occurrence of a surface seal is the velocity of the airflow rushing into the cavity, which is in contrast to the current understanding that considers the impact velocity as the determinant parameter.

We analyze the interfacial instability of a thin film confined between a rigid surface and a prestretched elastic sheet, triggered by nonuniform electro-osmotic flow. We derive a nonlinear $\text{viscous}-\text{elastic}$ equation governing the deformation of the elastic sheet, describing the balance between viscous resistance, the dielectric and electro-osmotic effects, and the restoring effect of elasticity. Our theoretical analysis, validated by numerical simulations, shows several distinct modes of instability depending on the electro-osmotic pattern, controlled by a nondimensional parameter representing the ratio of electro-osmotic to elastic forces. We consider several limiting cases and present approximate asymptotic expressions predicting the electric field required for triggering of the instability. Through dynamic numerical simulations of the governing equation, we study the hysteresis of the system and show that the instability can result in an asymmetric deformation pattern, even for symmetric actuation. Finally, we validate our theoretical model with finite-element simulations of the two-way coupled Navier equations for the elastic solid, the unsteady Stokes equations for the fluid, and the Laplace equation for the electric potential, showing very good agreement. The mechanism illustrated in this work, together with the provided analysis, may be useful in toward the implementation of instability-based soft actuators for lab-on-a-chip and soft-robotic applications.

This experimental laboratory study presents a detailed analysis of the surface oscillations inside a square cavity connected laterally to an open channel. For an approaching steady and one-dimensional main stream with a high (subcritical) Froude number, interaction with the dead water volume in the cavity area triggers high-amplitude free-surface oscillations, denoted seiches. In the present study, the length of the square cavity equals half of the combined width of the cavity and the main channel. This particular geometry enables two-dimensional or bidirectional seiching with standing waves being excited in both directions simultaneously. In this work, the (relative) magnitude of the different seiching modes (transverse and longitudinal) is measured and analyzed for a range of flow conditions with varying Froude number. The current experimental results confirm earlier findings indicating that the magnitude and dominance of the longitudinal seiching mode (with respect to the transverse mode) grows with increasing Froude number of the main stream. Additionally, a wavelet analysis in the time and frequency domains reveals that the amplitude of the two modes fluctuates significantly in the course of a single experiment, such that seiching cannot be considered a steady phenomenon. Therefore, two alternative strategies are presented to quantify the amplitude of both modes using a more time-localized approach that is less affected by the intermittent behavior of seiching. Although more research is necessary to fully understand what determines the dominant mode at a given moment, an in-depth analysis of the surface recordings at multiple locations in the cavity suggests that the transition from transverse to longitudinal seiching (and vice versa) is related to the phase difference between the bidirectional seiching waves at the (inner) corners of the cavity.

We demonstrate that two surface waves propagating at a small angle $2\theta$ to each other generate large-scale (compared to the wavelength) vertical vorticity owing to hydrodynamic nonlinearity in a viscous fluid. The horizontal geometric structure of the induced flow coincides with the structure of the Stokes drift in an ideal fluid, but its steady-state amplitude is larger and it penetrates deeper into the fluid volume as compared to the Stokes drift. In an unbounded fluid, the steady-state amplitude and penetration depth are increased by the factor of $1/sin\theta$ and the evolution time of the induced flow can be estimated as $1/\left(4\nu k^2{sin}^2\theta \right)$, where $\nu$ is the fluid kinematic viscosity and $k$ is the wave number. Also, we study how the finite depth of the fluid and a thin insoluble liquid film that possibly covers the fluid surface due to contamination effect the generation of large-scale vorticity and discuss the physical consequences of this phenomenon in the context of recent experiments.

It is known that a horizontal two-layer liquid film heated from above is subject to a long-wave oscillatory Marangoni instability. The action of a time-periodic modulation of interfacial heat consumption on the temporal dynamics of nonlinear Marangoni waves is investigated. The problem is studied numerically in the framework of long-wave amplitude equations. We focus on the phenomenon of synchronization between instability-induced oscillations and external parameter modulation. It is found that the time-periodic heat consumption modulation can create either a time-periodic regime (synchronization) or a quasiperiodic regime (no synchronization). Diagrams of regimes are constructed.

Linear damping is widely applied in experiments and fluid models to describe the large-scale dissipation that absorbs upscale energy transfers in two-dimensional (2D) turbulence. However, in many systems, it is not justified that linear damping is a good model and it is hard to obtain the damping coefficient from directly measurable quantities. Based on the forcing-scale resolving structure-function theory of homogeneous isotropic 2D turbulence derived by Xie and Bühler [J. Fluid Mech. 851, 672 (2018)], we propose a procedure that simultaneously obtains the magnitude of energy flux, the energy injection scale, and the damping coefficient by fitting the measurable second- and third-order velocity structure functions. Also, a test function based on the structure-function theory is proposed to justify the form of linear damping on each scale. The validity of this procedure is tested against data obtained from numerical simulations.