By virtue of self-propulsion, active particles impart intricate stresses to the background fluids. We propose that this active stress can be utilized to greatly control evaporation dynamics of active drops. We discover a new phenomenon of puncturing of the active drops, where the air-liquid interface of the drop undergoes spontaneous tearing and there occurs a formation of a new three-phase contact line due to the liquid-air interface hitting the liquid-solid interface through evaporation-driven mass loss. Post puncturing, we see an inside-out evaporation of the drop, where the new contact line sweeps towards the pinned outer contact line of the drops, contrasting regular drops that straightaway shrink to zero volume with self-similar shape. Furthermore, we describe how the activity inside the drops can manipulate the three-phase contact-line dynamics, which for contractile drops can result in an up to 50% enhanced lifetime of the drop and 33% quicker evaporation for extensile drops. By analyzing the flux distribution inside the drop, we gain insights on nonintuitive deposition patterns (e.g., ring galaxy type deposits that demonstrate controllable spatial gradients in the concentrations of the deposited particles) of active particles, which are oftentimes biological substances or bimetallic nanoparticles of interest. Finally, we argue that such unique evaporation and particle deposition dynamics can be leveraged for altering the lifetime of drops for bioapplications and for creating customized thin-film deposits with potential three-dimensional printing applications.

The base of a jet impinging on an ultrapure water bath is studied experimentally. At the impact point, a train of capillary waves develops along the jet. By performing particle tracking velocity measurements, we show that there is a boundary layer separation between the jet and the meniscus. We thus describe the shape of this meniscus with a hydrostatic model. A striking observation is the existence of an effective nonzero water/water contact angle between the jet and the meniscus. The rationalization of this finite contact angle requires a full description of the shape of the interface. By doing an analytical matching between the meniscus and the jet, we show that the capillary waves can be considered as reflected waves present to ensure pressure continuity. It is finally shown that the value of the apparent contact angle is fixed by energy minimization, with an excellent agreement between prediction and experiment for small jets.

In a two-way coupled Euler-Lagrange (EL) simulation, a particle of size comparable to the local grid spacing results in self-induced perturbation, which must be subtracted to obtain the undisturbed velocity of the particle. Several approaches have been advanced to estimate the self-induced velocity in the limit of an isolated particle. The present work addresses the effect of nonzero volume fraction in predicting the self-induced velocity of particles in an EL simulation. In addition to performing EL simulations of flow over a random distribution of stationary particles, we also perform several hundred companion simulations covering a range of Reynolds number and volume fraction. In each companion simulation we have removed one particle from the random distribution whose undisturbed flow and self-induced velocities are thereby precisely computed. By analyzing the self-induced velocity obtained from these simulations, a number of key conclusions are drawn. The most significant of them is the finding that the self-induced correction procedure of an isolated particle can be applied even at a finite volume fraction, with a simple volume fraction dependent modification, in order to accurately capture the average behavior.

In convective fluids, small vortices develop between neighboring convective cells. Familiar in the atmosphere in the form of dust devils and water spouts, these convective vortices have been seen in simulations of oceanic convection where the vortices exhibit an unexplained bias towards cyclonic rotation despite having a large Rossby number. Here we use large eddy simulations (LES) of an idealized oceanic convective mixed layer and vary independently the Coriolis acceleration and the surface buoyancy flux to investigate the development of the cyclonic bias of convective vortices. While large convective vortices are biased for sufficiently large values of the Coriolis parameter, small convective vortices do not exhibit a clear bias. Using Lagrangian particles, we find that the large convective vortices develop through the merger of many small convective vortices. We propose a statistical theory to predict the cyclonic bias of large convective vortices composed of many small unbiased convective vortices and test the theory using LES results. We apply the theory to typical convective conditions and find that convective vortices in upper ocean mixed layers are expected to exhibit a bias, while convective vortices in the terrestrial and Martian atmospheres are expected to be largely unbiased.

Bursting bubbles at the ocean surface can produce liquid drops which transport material into the atmosphere, impacting global climate dynamics through radiative balance and cloud condensation nuclei. Film drops are one of two primary types of spray. We present an extensive experimental study on film drop production, for a wide range of physicochemical liquid conditions, salinity, temperature in saltwater, and small contamination by surfactant. We discuss how thinning and rupture models in the literature are able to describe the film thickness at bursting, bubble lifetime, and number of supermicron film drops emitted. Existing theories for the film drainage rate and number of film drops are shown to be robustly consistent with the experimental results, and we provide prefactors of the scaling equations to enable their implementation into sea spray emission functions. The bubble's lifetime remains poorly described by existing scalings. While significant scatter remains when considering the film thickness at bursting, existing theories describe reasonably well the mean values when varying viscosity, temperature or surfactant contamination. However, we show that varying salinity induces a shift in film thickness which cannot be explained by existing scaling theories.

Suppressing the interfacial instability during fluid displacement, namely, viscous fingering, has been a long-lasting challenge in many applications. Numerous strategies have been proposed to control this phenomenon. Despite the recent advancements in utilizing electric fields to regulate viscous fingering, the absence of a rigorous characterization of this interfacial instability under an electric field hinders its further application. Therefore, in this work, we conduct numerical and theoretical investigations into the impact of an external electric field on viscous fingering in microfluidic channels for perfect dielectric fluids. It is shown that the development of viscous fingering can be delayed in the presence of an electric field and completely suppressed when the electric field strength $E$ exceeds a certain value. Based on the force balance, a nondimensional parameter $\varphi$ is defined to reflect the relative importance of stabilizing and destabilizing stress by taking into account the electrical, capillary, and viscous stress on the fluid interface. Extensive simulations show that $\varphi$ can effectively characterize the transition from an unstable viscous fingering to stable displacement under different fluid properties and flow conditions. The findings of this study are of fundamental importance in elucidating the influence of an external electric field on interfacial instability, thereby contributing to the development of improved strategies for controlling and optimizing displacement efficiency in diverse fluid systems and complex geometries.

This Letter revisits the problem of the existence of a universal Strouhal number in the separated flow past a stationary bluff body. Physical hypotheses based on flow kinematics only are formulated on the phenomenom. They lead to a simple closed-form mathematical formulation. The model thus developped predicts a universal Strouhal number equal to $1/2\pi \approx 0.159$, whichmatches experimental observations. The model has been expanded to predict the Strouhal-Reynolds relationship in the supercritical regime. The formulation has a universal character since said relationship depends on the critical Strouhal and Reynolds numbers only. The circular, square, and triangular cross-section shapes have been used for validation purposes. The case on an accelerating incoming flow has also been considered. The theoretical model thus developed supports the idea, suggested experimentally by other researchers, that time-averaged flow speed during a vortex formation cycle governs vortex dynamics in this accelerating flow case. Lattice Boltzmann simulations were performed to validate the model.

We study the equilibrium solutions of a fluid bridge that connects a horizontal solid substrate with a fluid phase (typically, air) while surrounded by another immiscible liquid. The shape of each interface is considered as a single curve with axial symmetry and constant curvature. The interface between the bridge and the air phase is a spherical cap, while the one between the external liquid and the air has zero curvature. Finally, the liquid-liquid interface corresponds to portions of onduloids or nodoids. The equilibrium solution must satisfy the boundary conditions given by Neumann's at the three fluids junction (triple point) and Young's law at the two fluids-solid contact line (at the substrate). For given fluids, we find that the solution control parameter is the $\gamma$ angle, which is the slope of the surrounding interface respect to the horizontal at the triple point. Using this procedure, we are able to find the $\gamma$ regions where different kinds of solutions are possible. In order to assess which solution is more likely to be found in nature, we compare their surface energies looking for that corresponding to the lowest one. Finally, we find numerical solutions that consider the presence of a vessel wall containing the fluids, by using the analytical results to provide guess values needed to initiate the required iterative process.

The quest for an unambiguous detection of magnetorotational instability (MRI) in experiments is still ongoing despite recent promising results. To conclusively identify MRI in the laboratory, a large cylindrical Taylor-Couette experiment with liquid sodium is under construction within the DRESDYN project. Recently, we have analyzed the nonlinear dynamics and scaling properties of axisymmetric standard MRI with an axial background magnetic field in the context of the DRESDYN-MRI experiment. In this sequel paper, we investigate the linear and nonlinear dynamics of nonaxisymmetric MRI in the same magnetized Taylor-Couette flow of liquid sodium. We show that the achievable highest Lundquist $\text{Lu}=10$ and magnetic Reynolds $\text{Rm}=40$ numbers in this experiment are large enough for the linear instability of nonaxisymmetric modes with azimuthal wave number $\left|m\right|=1$, although the corresponding critical values of these numbers are usually higher than those for the axisymmetric mode. The structure of the ensuing nonlinear saturated state and its scaling properties with respect to Reynolds number Re are analyzed, which are important for the DRESDYN-MRI experiment having very high $\text{Re}\gtrsim {10}^6$. It is shown that for $\text{Re}\lesssim 4\times {10}^4$, the nonaxisymmetric MRI modes eventually decay, since the modified shear profile of the mean azimuthal velocity due to the nonlinear axisymmetric MRI appears to be stable against nonaxisymmetric instabilities. By contrast, for larger $\text{Re}\gtrsim 4\times {10}^4$, a rapid growth and saturation of the nonaxisymmetric modes of nonmagnetic origin occurs, which are radially localized near the inner cylinder wall, forming a turbulent boundary layer. However, for all the parameters considered, the saturation amplitude of these nonaxisymmetric modes is always a few orders smaller than that of the axisymmetric MRI mode. Therefore, the results of our previous axisymmetric study on the scaling properties of nonlinear MRI states also hold when nonaxisymmetric modes are included.

We present a physically motivated low-dimensional model for the dynamics of two interacting large-scale circulations (LSC) in two-layer turbulent convection. Inspired by our experimental results of the flow dynamics and coupling in two-layer turbulent convection [J. Fluid Mech. 728, R1 (2013)], the model extends previous studies of single-LSC dynamics to incorporate four stochastic ordinary differential equations describing the strength $\delta$ and azimuthal orientations $\theta$ of two vertically aligned LSCs. The interaction terms of the two LSCs, i.e., thermal and viscous coupling terms, are predicted based on the influence of the fluid temperature by the other LSC through heat advection and thermal diffusion, and the enhanced (reduced) viscous damping across the interface between the two LSCs. Our model produces two stable LSC rolls and predicts their preferred flow states for the thermal and viscous couplings. The model describes properly the diffusive motion of both $\delta$ and $\theta$ of the two LSCs, and the Poissonian distribution of time interval between LSC cessations. More importantly, our study reveals that flow reversals and cessations in two-layer convection can be achieved when turbulent fluctuations drive the azimuthal diffusion of the two LSCs into a flow state that the two LSC planes are orthogonal to each other, the strength of the LSC in the fluid layer with a relatively larger Rayleigh number reduces to zero deterministically, owing to the unbalanced buoyancy forcing. Our model provides accurate predictions for the enhanced occurrence frequency of flow reversals observed in the experiment, and it suggests a new dynamical process of flow reversals in multilayer turbulent convection.

We report a systematic study of turbulent thermal convection across two vertically stacked layers of immiscible fluids, FC770 and water, with a stable liquid-liquid interface even when each fluid layer is under turbulent convection. The normalized mean temperature profile $\theta \left(z\right)$ and temperature variance profile $\mathrm{\Omega }\left(z\right)$, as a function of distance $z$ away from the interface, are measured along the central vertical axis of the cylindrical convection cell with varying temperature difference $\mathrm{\Delta }$ across the cell. From the measured mean temperature and temperature variance profiles, we find a unique twin-boundary-layer structure across the liquid interface with one of the twin boundary layers (BLs) residing on each side of the interface. The measured $\theta \left(z\right)$ and $\mathrm{\Omega }\left(z\right)$ in each fluid layer are found to have the scaling forms $\theta (z/\lambda )$ and $\mathrm{\Omega }(z/\lambda )$, respectively, with varying BL thickness $\lambda$, and their functional forms are well described by the equations for a BL attaching to a solid conducting plate, so long as a thermal slip length ${\ell }_T$ is introduced to account for the convective heat flux passing through the liquid interface. While the obtained $\theta (z/\lambda )$ and $\mathrm{\Omega }(z/\lambda )$ for the twin BLs share the same scaling forms, they nevertheless have different BL thickness $\lambda$ and slip length ${\ell }_T$ in the two fluid layers. Furthermore, three characteristic temperatures are found as response parameters in the two-layer convection, namely, the mean temperature $T_0$ of the interface, the mean bulk temperature $T_F$ of the FC770 layer, and the mean bulk temperature $T_W$ of the water layer. By combining the scaling result of heat transport across the entire cell and the effects of broken symmetry between the BL near the conducting plate and that near the liquid interface, we obtain three quantitative relations that link the three characteristic temperatures to the normalized slip length ${\xi }_0={(1+\lambda /{\ell }_T)}^{-1}$ and the temperature difference $\mathrm{\Delta }$. The theoretical predictions are found in good agreement with the experimental results.

To design tidal stream turbine arrays, turbine wakes need to be fully characterized to assess the adequate row spacing considering environmental factors such as onset turbulence, velocity shear, and surface waves. The role of waves on wake development varies depending on their characteristics, such as wavelength and amplitude, and needs to be carefully understood. Here large-eddy simulations are performed to analyze the instantaneous and time-averaged wake characteristics developed downstream of a tidal stream turbine for four wave-current conditions ranging from nearly deep to intermediate waves and compared to current-only results. The tip-vortex convection near the free surface is highly influenced by the waves. During the period of increased surface elevation, there is an upwards motion of the vortices which have merged into a single vortical structure during the wave trough period. Downwards vertical transport of tip vortices occurs after the pass of the wave crest, enabling vertical entrainment of momentum into the turbine wake region. Disk-averaged velocity deficit recovery increases for wave-current cases compared to the current-alone condition, with all intermediate wave cases showing a very similar wake recovery rate throughout the wake length. The nearly deep-water waves lead to a slightly slower recovery rate up to 12 turbine diameters ($D$) downstream while, after this distance, the recovery rate is the highest among the simulated wave conditions. The integration of the mean kinetic energy (MKE) budget in the region up to $12D$ shows there is a similar distribution in the balance between terms irrespective of the wave-current case. However, in the far-wake region covering from $12D$ to $20D$, the nearly deep waves have a larger contribution for MKE replenishment from the transverse convection and turbulence transport terms, balanced with their vertical counterparts and the streamwise convection term. Analysis of the wake self-similarity shows that a Gaussian model description holds for the recovery rate and lateral profile of the wake of a tidal turbine operating in coupled wave-current conditions, with a similar rate of velocity recovery after $12D$ irrespective of the wave characteristics. Lateral wake spreading is smaller for the shortest wavelength, which relates to an increased contribution of transverse fluxes in the MKE budget.

While seeking the ultimate statistical invariance of turbulence, classical boundary layer theory is unable to distinguish between the averaged states of wall flows with two-dimensional (2D) and three-dimensional (3D) fluctuations. Here we demonstrate glaring differences between 2D and 3D channel flows and present theoretical explanations for the differences in their Reynolds numbers' $\left({\mathrm{Re}}_{\tau }\right)$ asymptotic behaviors. In particular, due to the peculiar inverse cascade, large-scale wavy structures (LSWSs) are developed in 2D flows, which inject a high-energy flux toward the wall and cause extreme wall dissipation. The latter follows a distinct ${\mathrm{Re}}_{\tau }^{1/3}$ scaling within the range covered by our direct numerical simulation $(130<{\mathrm{Re}}_{\tau }<8100)$. The same trend is also observed for the root mean square of the pressure and velocity fluctuations (as well as for the bulk velocity). Rationale for the scaling is further given through an LSWS-induced dissipative timescale (provided with the 2D friction law), which is unlike the viscous timescale in 3D flows due to the absence of LSWSs. As a counterpart to the classical boundary layer of bounded 3D fluctuations [Chen and Sreenivasan, J. Fluid Mech. 908, R3 (2021); J. Fluid Mech. 933, A20 (2022)], the results here reveal an unprecedented asymptotic state of wall flows in which the inverse cascade induces unbounded 2D fluctuations.

In this paper, we study numerically the temporal evolution of an initially random large-scale velocity field governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution. First, the initial condition development is characterized by a spectrum evolving in a self-similar way with a wave number front $k_{*}\left(t\right)$ propagating toward high values exponentially in time. This evolution corresponds to the formation and shrinking of vortex pancakes exponentially in time, as previously reported in simulations of the incompressible Euler equations. At the second stage, pancakes become unstable, rolling up on the edges and breaking up in the middle, leading to the emergence of vortex ribs—quasiperiodic arrangements of vortex filaments. Those filaments then twist, creating structures akin to ropes. At the last stage, a fully developed turbulent state is observed, characterized by a Kolmogorov energy spectrum and exhibiting a decay law compatible with standard turbulent predictions in the case of an integral scale saturated at the scale of the box.

The study of vortex dynamics using a variational formulation has an extensive history and a rich literature. The standard Hamiltonian function that describes the dynamics of interacting point vortices of constant strength is the Kirchhoff-Routh (KR) function. This function was not obtained from basic definitions of classical mechanics (i.e., in terms of kinetic and potential energies), but it was rather devised to match the already known differential equations of motion for constant-strength point vortices given by the Bio-Savart law. Instead, we develop a variational formulation for vortex dynamics based on the principle of least action. As an application, we consider two-dimensional massive vortices of constant strength. Interestingly, the obtained equations of motion are second-order differential equations defining vortex accelerations, not velocities. The resulting dynamics are more complex than those obtained from the KR formulation. For example, a pair of equal-strength, counter-rotating vortices could be initialized with different velocities, resulting in interesting patterns. Also, the developed model easily admits external body forces. When an electrodynamic force is considered, the interaction between it and the hydrodynamic vortex force leads to a rich, counterintuitive behavior that could not be handled by the KR formulation.

A rotating or stratified fluid supports waves that propagate in fixed directions. If the fluid is uniformly rotating around an axis $Oz$ with a rotation rate $\mathrm{\Omega }$ and/or uniformly stratified along the same axis with a Brunt-Väisälä frequency $N$, then harmonic waves of frequency $\omega$ propagate along characteristic lines that make an angle $\theta$ with respect to the horizontal plane $Oxy$ with $\theta$ satisfying the relation ${\omega }^2=4{\mathrm{\Omega }}^2{cos}^2\theta +N^2{sin}^2\theta .$ Any infinitesimal oscillation of the boundary is a source of waves, but when this boundary is tangent to a direction of propagation of the waves, a singularity generically appears. This critical slope singularity propagates along the critical ray tangent to the boundary. When weak viscous effects are considered, this singular ray forms a concentrated self-similar wave beam with an amplitude that depends on the nature of the singularity and a width of order ${(\nu x_{\parallel }/\omega )}^{1/3}$, where $\nu$ is the kinematic viscosity and $x_{\parallel }$ the distance to the critical point measured along the beam. The goal of the present work is to provide information on the type of singularities that can be generated in an infinite domain and therefore on the amplitude and nature of the concentrated wave beams that can be created from critical points. We analyze in a two-dimensional framework two generic configurations corresponding to oscillations normal and tangent to the boundary, respectively. In the first case (oscillations normal to the boundary), we obtain an amplitude scaling in ${[\omega r_c^3/\left(\nu x_{\parallel }\right)]}^{1/6}$ corresponding to an inviscid singularity in $x_{\perp }^{-1/2}$, where $x_{\perp }$ is the distance to the critical ray and $r_c$ the radius of curvature at the critical point. In the second case (oscillations tangent to the boundary), a weaker beam in ${[\nu r_c^3/\left(\omega x_{\parallel }^5\right)]}^{1/12}$ is obtained corresponding to a stronger singularity in $x_{\perp }^{-5/4}$. In that case, the beam is generated by the particular viscous boundary layer flow obtained close to the critical point and the problem can be completely solved by a local analysis. A general expression for the beam amplitude is derived that depends on the fluid characteristics ($\mathrm{\Omega }$, $N$), the wave frequency $\omega$, the velocity amplitude of imposed tangential oscillations, and the local radius of curvature at the critical point. Finally, the first-order viscous correction to the critical slope beam induced by the no-slip boundary condition on the surface is also calculated.

This paper numerically investigates the wake transition of an unconstrained self-propelled flexible flapping plate, which exhibits the ability to move freely both longitudinally and laterally, at a low Reynolds number of 200. By examining crucial parameters, including pitching amplitude ${\theta }_0$, bending stiffness $K$, and mass ratio of the plate to the fluid $M$, the research identifies three distinct wake patterns: symmetric, deflected, and chaotic. The lateral drift speed of the plate ($V$) is used as a quantitative indicator to differentiate between symmetric and asymmetric wake patterns, where $V$ is approximately zero and nonzero, respectively. The paper indicates that the transition from symmetric to asymmetric wakes occurs when the cruising Reynolds number (${\mathrm{Re}}_c$) reaches the critical value (${\mathrm{Re}}_c^{\mathrm{cr}}$), which follows a simple scaling law vs $M$, i.e., ${\mathrm{Re}}_c^{\mathrm{cr}}\sim M^{-1/2}$. The critical dimensionless translational kinetic energy ${\widehat{E}}_k$ of the plate remains constant for various $M$ when the wake transition occurs. Analyzing translational kinetic energy not only proves the ${\mathrm{Re}}_c^{\mathrm{cr}}$ scaling, but also offers a unique energy perspective on the phenomenon. In addition, the critical flapping Reynolds number (${\mathrm{Re}}_f^{\mathrm{cr}}$) is found to also satisfy a simple scaling similar to ${\mathrm{Re}}_c^{\mathrm{cr}}$, i.e., ${\mathrm{Re}}_f^{\mathrm{cr}}\sim M^{-1/3}$. Finally, it is revealed that passive lateral oscillation and bending deformation of the plate are two key mechanisms affecting wake symmetry properties. This paper provides insights into flapping-based locomotion.

The study presented here addresses the challenging problem of laminar-turbulent flow transition in boundary layers. Directed percolation theory has emerged as a promising approach to understand and describe this transition in different scenarios. This study utilizes differential image thermography (DIT) to investigate the boundary layer transition on the suction side of a heated airfoil, presenting experimental findings. First, the DIT results underline the ability of capturing the near surface transition for the airfoil boundary layer with a high temporal and spatial resolution. Second, the evaluation reveals the effectiveness of directed percolation theory in describing the onset of the transition, showing agreement with all three universal exponents of ($1+1$)-dimensional directed percolation theory. Third, the study shows the applicability of this theory to a wide range of flow situations beyond the parameter space covered in previous examinations. These findings underscore the possible application of directed percolation models in fluid mechanics and suggest that the theory could serve as a high precision tool for describing the transition to turbulence.

Direct numerical simulations of channel turbulence laden with inertial particles were performed to investigate the effects of the Mach number on turbophoresis and the preferential accumulation of particles using the Eulerian-Lagrangian point-particle method. The results show that turbophoresis-induced particle segregation is suppressed at high Mach number. A particle relaxation time weighting transformation is proposed which collapses the concentration profiles not only for particles with small inertia but also for turbulence with various compressibility at the studied low Reynolds number and in the inner region. The conditional sampling reveals that inertial particles in compressible wall turbulence tend to distribute in low-fluid-speed regions near the wall and high-fluid-speed regions in the outer layer, which is similar to that in incompressible turbulence. What is special is that they also tend to distribute in high-fluid-density and negative-fluid-dilatation regions. This is explained by the changes in turbulent structures at varying Mach number, which in turn also account for the varying scales of particle streaks.

Previous results of discrete simulations of steady, unidirectional particle flows, here collected and critically reanalyzed, permit to make the case that the kinetic theory of granular gases, extended to include the correlations in the velocity fluctuations and the role of friction in collisions, provides the long-sought universal framework to predict the flow of realistic particles over the entire range of solid volume fraction from dilute to very dense—the upper limit being the critical value at which rate-independent components of the stresses arise. The case is made even stronger by the explicit derivation of the popular inertial rheology and its nonlocal extension to deal with heterogeneities based on the granular fluidity concept as special limits of the kinetic theory. In the process, common statements about the frictional-collisional duality in the granular stresses and the importance of long-lasting contacts creating a percolating network are shown to be greatly exaggerated for granular flows in practical applications.