Wall vortex occurs when a cavitation bubble oscillates far from a single rigid wall (at a dimensionless standoff distance of ${\gamma }_r>1.3$). This study reveals that introducing a water surface expands the wall vortex regime. A wall vortex in an expanded new regime forms instead of a free vortex at a smaller ${\gamma }_r$ value. Because of the influence of the water surface, a broader jet pierces the bottom of a bubble. This causes the bubbles to expand easily along the wall and form a flat shape during the second cycle. Here an outwards flow forms instead of an upward flow after the bubble recollapses. This study investigates the formation and development of a wall vortex in the new expanded regime via a combination of experiments, numerical simulations, and theoretical modeling. To this end, a theoretical model describing the radial motion $R$ and centroid position $h$ of the bubble between the boundaries is developed using Lagrangian formulation. Two infinite sets of image bubbles are used to satisfy the conditions of the water surface and rigid wall based on image theory. The criteria for the vortex flow patterns are proposed based on the direction of the centroid migration $\dot{h}\left(t_c\right)$ of the bubble at the beginning of the second cycle $t_c$. A free vortex occurs when the upward flow dominates $[\dot{h}\left(t_c\right)>0]$, whereas a downwards flow dominates the wall vortex $[\dot{h}\left(t_c\right)<0]$. A phase diagram of the vortex flows is obtained from the theoretical model and is verified using the experimental results. Numerical analysis reveals that the wall vortex flow with the influence of the water surface contributes to a greater wall shear stress and larger area, thereby increasing the potential for surface cleaning. These findings provide new insights for engineering applications such as ultrasonic cleaning.

Plane Couette flow with constant wall transpiration, i.e., constant blowing from below and constant suction from above, is a solution of the Navier-Stokes equations in terms of exponentials. It is characterized by two Reynolds numbers Re and ${\text{Re}}_V$, where Re parametrizes the moving wall and ${\text{Re}}_V$ describes the influence of the transpiration. For this flow the modified Orr-Sommerfeld equation admits one of the very few exact solutions in terms of hypergeometric functions. Based on this, we solve the stability problem, though for the main part focus on temporal stability. For small wall-transpiration rates up to ${\text{Re}}_V\simeq 6.71$, the flow remains unconditionally stable, analogous to the classical Couette flow for arbitrary Reynolds numbers Re. By further increasing ${\text{Re}}_V$ an instability sets in and a minimum critical Reynolds number of $\text{Re}=668350.491$ is reached at ${\text{Re}}_V=9.799$. Hence, around this point, the destabilizing effect of blowing outweighs the stabilizing effect of suction. By further increasing the transpiration rate beyond this point, the corresponding critical Reynolds number Re increases again and continues to grow. This limiting case is accompanied by the development of a strong boundary-layer-like velocity profile near the upper wall and the flow transitions to the asymptotic suction boundary layer (ASBL). Thus, the present analysis comprises the whole range from classical Couette flows extended by transpiration to the ASBL, which is known to have a strongly stabilizing effect.

In the present study, the effects of density variations on structures developing in an isotropic incompressible turbulent flow are investigated. Statistical analyses are carried out on data sets obtained from direct numerical simulations of forced turbulence. The discretized variable-density incompressible Navier-Stokes equations are time advanced with a Fourier-Fourier spectral solver coupled with a semi-implicit second order in time Runge-Kutta scheme. Turbulence is forced using an extension of the Lundgren method to the variable-density equations including mass diffusion effects. Numerical evidence shows that the introduction of a variable-density field into a turbulent field modifies the coherent structures and the energy spectrum in the inertial range. The analysis of probability density functions of velocity gradients and Lagrangian acceleration suggests an increase in time and space intermittency beyond a threshold density ratio associated with the two-fluid mixture. These modifications are not captured by the classical scaling laws of skewness and flatness factors given in the literature for the constant-density flow case. The energy spectra preserve the Kolmogorov slope while exhibiting an energy level alteration within the smallest scales of the inertial range. This region corresponds to the range of modes where the energy levels of the Rayleigh-Taylor instability criterion are the highest, giving some physical arguments that the aforementioned structural modifications may be attributed to Rayleigh-Taylor-like instabilities.

A model for the structure function constant associated with the index of refraction fluctuations in Rayleigh-Bénard turbulence is developed. The model is based upon the following assumptions: (1) the turbulence is homogeneous and isotropic at or near the midplane, (2) the rate of production is in balance with the rate of dissipation, (3) an inertial region exists, and (4) estimates for the rate of dissipation of temperature fluctuations and of turbulent kinetic energy can be made by assuming that the large-scale turbulence is dissipated in one eddy turnover time. From these assumptions, the dependence of the structure function on the geometry, heat flux, and the properties of the fluid is obtained. The model predicts that the normalized structure function constant is independent of the Rayleigh number. To verify the model, numerical simulations of Rayleigh-Bénard turbulence were performed using two different approaches: an in-house code based on a pseudospectral method, and a finite volume code which employs a model for the smallest scales of the turbulence. The model was found to agree with the results of the simulations, thereby lending support for the assumptions underlying the theory.

The interaction between a vortex and an impacting body which is oriented normally to it is complex due to the interaction of inviscid and viscous three-dimensional mechanisms. To model this process, direct numerical simulations of a thin cylinder intersecting a columnar vortex oriented normally to it are conducted. By varying the impact parameter and the Reynolds number, the two regimes of interaction mentioned in the literature are distinguished: the weak and strong vortex regimes. Low impact parameters, representing strong vortices, led to ejection and interaction of secondary vorticity from the cylinder's boundary layer, while high impact parameters, representing weak vortices, led to approximately inviscid interaction of the cylinder with the primary vortex through deformations. No significant effect of the Reynolds number in the overall phenomenology is found, even if larger Reynolds numbers lead to the formation of increasingly smaller and more intense vortex structures in the parameter range studied. Finally, the hydrodynamic force curves on the cylinder are analyzed, showing that intense forces could be locally generated for some parameter regimes, but that the average force on the cylinder does not substantially deviate from baseline cases where no vortex was present. Our results shed light on the underlying mechanisms of vortex-body interactions and their dependence on various parameters.

We carry out a numerical study of swept shock wave/turbulent boundary layer interaction in the hypersonic regime. Starting from a numerical/experimental benchmark case of a nearly adiabatic two-dimensional hypersonic interaction, a crossflow velocity component is added to the incoming flow to mimic three-dimensional interactions with cylindrical symmetry. We observe, for a fixed streamwise Mach number, monotonic increase of the extent of the interaction region for the swept cases. An attempt at extending the free-interaction theory to hypersonic swept interactions is made, which is found to apply only to the initial part of the interaction region. The spatiotemporal dynamics of wall pressure on mean separation line features large-scale pressure corrugations, which are advected at a phase speed which is a fraction of the mean crossflow velocity, if present. The characteristic wavelength of the corrugation is found to be a multiple of the separation bubble size. The numerically estimated peak frequencies well conform with the previously introduced formula for swept supersonic interactions [Ceci et al., J. Fluid Mech. 956, R1 (2023)]. Proper orthogonal decomposition is applied to investigate the spatial structure of the corrugation at the separation point and educe phase relations between the flow structure and pressure oscillations at the reattachment point. The present analysis leads us to conclude that the same phenomenology found in swept supersonic interactions also holds in the hypersonic case.

Here we discuss how the use of textured liquid-infused solids can expedite the dynamics of spreading of viscous drops, when the subjacent oil layer is less viscous. We characterize the nature and amplitude of the effect, and the laws governing the spreading at short time. More generally, our findings affirm the universality of the early dynamics of viscous contact, found to hold for drops that coalesce, spread, or even, like here, slip on their substrate.

In this paper a formulation of the incompressible Navier-Stokes equations is introduced which allows one to model boundary-layer flows induced by the motion of a deforming surface. Such a formulation may be used to model flows relevant in a wide variety of industries from polymer processing to glass manufacturing. We show that for particular sheet geometries and velocities, similarity solutions may be obtained that account for sheet thinning (or thickening) and roughness patterns observed in extrusion-type processes.

The transverse flow-induced vibration (FIV) of an elastically supported elliptical cylinder-plate assembly is investigated numerically for a laminar flow at a Reynolds number of 100. The aspect ratio (AR) of the elliptical cylinder is varied over a range of values (namely, $\text{AR}=0.5$, 0.67, 0.75, 1, 1.5, and 2). In addition, two normalized splitter-plate lengths, $L_{\text{SP}}/D=0.75$ and 2.5, are investigated (where $L_{\text{SP}}$ is the splitter-plate length, and $D$ is the equivalent diameter of the elliptical cylinder). A low mass ratio of 10 and zero structural damping are used in the numerical simulations to induce larger oscillations in the assembly. The numerical results show that all cases investigated exhibit a FIV over an unlimited range of reduced velocity. An increase in the AR promotes the vibrations of the assembly through a reduction in the reduced velocity associated with the onset of FIV and a concomitant increase in the vibration amplitude. In addition, a larger AR facilitates the transition from a pure galloping (for $\text{AR}\le 1$) to an integrated VIV-galloping response (for $\text{AR}>1$) for an assembly with $L_{\text{SP}}/D=0.75$. Moreover, a larger AR significantly decreases the onset velocity of galloping for an assembly with $L_{\text{SP}}/D=2.5$. The AR determines the nature and width of the synchronization branch in the amplitude response. In general, a larger AR leads to the inception of higher-order synchronization branches in the amplitude response and to the suppression of some branches (e.g., still and initial galloping branches) for assemblies with long splitter plates. Finally, with respect to the flow dynamics associated with an unlimited FIV, increasing AR promotes the shedding of more complex vortices in the wake of the assembly (e.g., the emergence of a tail-shaped vortex and a slender vortex)—despite this, the wake mode remains unaltered.

Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10% of the number of modes that describes the full flow field, indicating that the method introduced here is capable of identifying complicated forcing mechanisms from a relatively small collection of observations. In addition to demonstrating the efficacy of this method on turbulent flow data generated by simulations of the two-dimensional Navier-Stokes equations, we also rigorously justify convergence of the derived algorithm. Beyond the practical applicability of such an algorithm, the reliance of this method on the dynamical evolution of the system yields physical insight into the turbulent cascade.

Interfacial waves arising in a two-phase swirling flow driven by a low-frequency rotating magnetic field (RMF) are studied. At low RMF frequencies, on the order of 1–$10\mathrm{Hz}$, the oscillatory part of the induced Lorenz force becomes comparable to the time-averaged one and cannot be neglected. In particular, when free surfaces or two-liquid stably stratified systems are subject to a low-frequency RMF, induced pressure variations necessarily excite free-surface/interfacial waves, which can improve mass transfer in different metallurgical processes. In this paper we formulate a linear wave model and derive explicit analytical solutions predicting RMF-driven wave patterns that closely resemble hyperbolic paraboloids. These theoretical predictions are validated against experiments based on a nonintrusive acoustic measurement technique, which measures liquid-liquid interface elevations in a two-phase KOH-GaInSn stably stratified system. A good quantitative agreement is found for nonresonant wave responses in the vicinity of the fundamental resonance frequency. The experiments reveal the additional excitation of several higher harmonics superimposing the fundamental wave oscillation, which are visible even in the linear wave regime.

While heat transport by baroclinic turbulence in oceans and planetary atmospheres is well described by a two-layer model, the relative depth of the two layers varies greatly depending on the situation of interest, making it an important parameter governing the transport properties of the system. Focusing on the low-drag turbulent regime, we extend the vortex-gas scaling theory to address the case of arbitrary layer depths. To wit, we map the arbitrary-layer-depth system onto an equivalent equal-depth system with rescaled parameters, establishing the asymptotic validity of the mapping for weak bottom drag. This approach leads to quantitative predictions for the turbulent transport by two-layer baroclinic turbulence with arbitrary layer depths, without additional free parameters. We validate these predictions using an extended suite of numerical simulations with either linear or quadratic bottom drag.

We investigate the inertial and non-inertial dynamics of three-dimensional elastic capsules flowing through a square channel presenting a sharp corner. Our study analyzes the trajectory, surface area, velocity, and membrane stress of the capsules in the case of a single capsule, a system of two interacting capsules, and a train of ten capsules released upstream of the corner. The channel Reynolds number Re ranges from 0.01 to 50 and the Capillary number Ca, which measures the ratio of the viscous and elastic stresses, ranges from 0.075 to 0.35. We find that in the inertial regime, the membrane stretch and stress increase dramatically as compared to the non-inertial case, and that the velocity overshoot inside the corner is also enhanced. The maximum capsule deformation is observed to depend nearly linearly on Ca and Re. Additionally, we report a repelling mechanism between two confined capsules when their initial interspacing distance $d$ is smaller than a critical value $d_c$. The deformation of the leading capsule is found to be mitigated by the presence of the following capsule. In the case of multiple capsules flowing through the corner, we observe that the increase in the maximum surface area of the trailing capsules eventually saturates at the tail of the train. Moreover, we find that the corner tends to separate the capsules regardless of their upstream interspacing distances $d$. This study contributes to the elaboration of practical guidelines for controlling capsule breakup and predicting throughput in both inertial and non-inertial microfluidic experiments.

The angular motion of a forebody-gimbaled axisymmetric cylindrical bluff body wind tunnel model that is free to pitch, yaw, and roll in a uniform stream in response to flow-induced aerodynamic loads is modified by fluidic actuation of its near wake. The model is anchored at its leading edge by a low-friction gimbal coupling attached to a wire-mounted short streamwise sting where each of the eight support wires is connected to a servo actuator for position and attitude control of the sting. Aerodynamic moments on the model and thereby its angular motions are controlled in a closed loop using fluidic modification of its near wake by azimuthally segmented flow attachment over its aft end. Actuation is effected using fourfold symmetrically distributed and independently activated synthetic jet actuators. Coupled effects of actuation-induced transitory changes in the attitude of the model are measured by an image-tracking system and the evolution of the near wake captured using high-speed stereo particle image velocimetry (SPIV). Dynamic mode decomposition (DMD) of the time-dependent near-wake flow field indicates that suppression or amplification of the natural oscillations of the model are associated with controlled changes in the symmetry and spectral content of the primary dynamic modes. It is shown that these controlled wake interactions can be harnessed to tune the temporal attitude response of the model, with natural oscillation suppression of $>50-65\%$ in pitch and 75–85% in yaw across the entire investigated range of Reynolds numbers of $1.32\times {10}^5$ to $1.92\times {10}^5$. In addition, an example of amplification of the natural oscillations of $>150\%$ is illustrated at a Reynolds number of $1.62\times {10}^5$.

We consider fluid flows, governed by the Navier-Stokes equations, subject to a steady symmetry-breaking bifurcation and forced by a weak noise acting on a slow timescale. By generalizing the multiple-scale weakly nonlinear expansion technique employed in the literature for the response of the Duffing oscillator, we rigorously derive a stochastically forced Stuart-Landau equation for the dominant symmetry-breaking mode. The probability density function of the solution, and of the escape time from one attractor to the other, are then determined by solving the associated Fokker-Planck equation. The validity of this reduced order model is tested on the flow past a sudden expansion for a given Reynolds number and different noise amplitudes. At a very low numerical cost, the statistics obtained from the amplitude equation accurately reproduce those of long-time direct numerical simulations.

We present experiments on the mixing of active particles—swimming Tetraselmis microbes—in a microfluidic vortex chain flow, driven magnetohydrodynamically. We track the microbes in the flow and interpret the resulting trajectories in terms of a theory of swimming invariant manifolds (SwIMs), a generalization of invariant manifold theories developed originally to characterize mixing of passive tracers. The experiments verify predictions that SwIMs act as barriers in a three-dimensional $(x,y,\theta )$ phase space. Projected onto $(x,y)$ position space, edges of the manifolds (SwIM-edges) are one-way barriers that impede the motion of the microbes in one direction but allow them to pass freely in the other. Pairs of SwIMs combine to form chutes that carry microbes between vortices. For short times, the experimentally measured intervortex flux agrees well with theoretical predictions based on the cross-sectional area of the chutes, despite experimental evidence of nonuniformities in the $(x,y,\theta )$ microbe density, due to deviations of the microbes from a perfect circular shape.

We conducted numerical simulations of passive scalar carried by noninertial particles convected by the isotropic turbulence at low to high Reynolds number up to $R_{\lambda }=550$ with infinitely large Schmidt numbers. In the numerical method, each particle has a scalar value ${\theta }_p$ that relaxes with a relaxation time ${\tau }_{\theta }$ independent of the turbulence and its evolution is computed along the Lagrangian trajectory, and the scalar is mapped onto the Eulerian grid points. In the limit of large ${\tau }_{\theta }$, the evolution equation for the mapped field $\theta$ converges to that in the Batchelor regime with an infinite Schmidt number. We investigated the two point statistics including the variance spectrum of the field $\theta$ and confirmed their consistency with the turbulence theory, such as the Batchelor spectrum, constancy of the transfer flux, and the Yaglom 4/3 law for the third-order structure function by parameter sweep simulations with various values of ${\tau }_{\theta }$. An explanation of the present numerical method from the view point of the turbulence physics is presented. The visualized scalar field shows features commonly seen in passive scalar turbulence, such as plateaus, fronts, and sheetlike structures.

Investigations of the settling of liquid droplets in another liquid phase have to deal with the potential contamination of the interfaces with residual impurities. It is shown in this Letter that the use of a centrifugal field to generate the drop settling may overcome this issue: the drop terminal velocity and shape are reached at much shorter time scales than that taken by contaminant adsorption from the bulk to the interface, so it is possible to obtain data for clean interfaces. In this study, using a centrifuged cell, drop formation, velocity, and shape have been characterized in the inertial regime. By comparing these quantities to theoretical models and by performing complementary direct numerical simulations with clean interfaces, it is proved that interfacial contamination can be disregarded in the experiments. Such an experiment can therefore be used to establish results of reference for clean interfaces. For instance, a correlation for the drop deformation of settling droplets in clean liquid-liquid systems is obtained for a wide range of parameters, as a function of the sole Weber number. It emphasizes that clean droplets are less distorted than clean bubbles.

The exploration of a two-dimensional wind-driven ocean model with no-slip boundaries reveals the existence of a turbulent asymptotic regime where energy dissipation becomes independent of fluid viscosity. This asymptotic flow represents an out-of-equilibrium state, characterized by a vigorous two-dimensional vortex gas superimposed onto a western-intensified gyre. The properties of the vortex gas are elucidated through scaling analysis for detached Prandtl boundary layers, providing a rationalization for the observed anomalous dissipation. The asymptotic regime demonstrates that boundary instabilities alone can be strong enough to evacuate wind-injected energy from the large-scale oceanic circulation.

A direct numerical simulation of turbulent flow over a backward-facing step is performed at Reynolds number of ${\mathrm{Re}}_{\mathrm{b}}=5600$ based on inflow bulk velocity and channel half-width at the inlet, with an expansion ratio of $\text{ER}=1.2$. To control the flow separation, a wall-normal body force in the form of a wave-machine-like traveling wave, which has streamwise and spanwise periodicity, is applied to the top surface of the step. To clarify the effect of spanwise periodicity on the reattachment length, spanwise-uniform traveling waves (SUTW) and wave-machine-like traveling waves (WMTW) are compared. The maximum reduction rates of the reattachment length in SUTW and WMTW are 51.4% and 58.9%, respectively. SUTW and WMTW exhibit a common flow behavior, in which the recirculation bubble is periodically released in time and in the streamwise direction, contributing significantly to the reduction of the reattachment length. However, spanwise periodicity produces differences in the flow structure. In SUTW, all flow structures become spanwise-uniform. In WMTW, a pair of longitudinal vortices is generated above the step and in the recirculation bubble and the released separation bubble. The pair of longitudinal vortices causes three effects that reduce the reattachment length—a decrease in the streamwise length of the secondary bubble, an enhancement of the negative wall-normal velocity, and an increase in Reynolds shear stress.