A circular jet breaks up into droplets via the Rayleigh-Plateau instability, retaining a circular cross section throughout. If, however, the nozzle from which the jet issues is elongated, the circular symmetry is broken, and the jet forms a chainlike structure with neighboring links separated by ${90}^{\circ }$. The cause of this structure is two-dimensional capillary-inertial oscillation of jet cross sections in their own plane. We perform an experimental study of chain oscillations as a function of flow rate using careful prelaminarization and 12 elliptical nozzles with different areas and eccentricities. The oscillation frequencies inferred from the observed chain-link structure do not agree with those predicted by Rayleigh's infinitesimal theory [L. Rayleigh, Proc. R. Soc. London 29A, 71 (1879)]. However, they do agree with an extended nonlinear theory of Bohr [N. Bohr, Philos. Trans. R. Soc. A 209, 281 (1909)] that accounts for finite-amplitude effects. This agreement shows that our fluid chains are nonlinear oscillations whose frequency decreases with increasing amplitude. We perform direct numerical simulations of chain oscillations using a volume-of-fluid method and find good agreement with the predictions of Bohr's theory. Finally, we generalize Bohr's theory to the case of two interacting modes with quadrupolar and octapolar azimuthal dependencies. The resulting solution explains qualitatively the “dimpled” shape of the jet's surface observed in the experiments.

We study intermittency of circulation moments in turbulent superfluid helium by using experimental grid turbulence and numerical simulations of the Hall-Vinen-Bekarevich-Khalatnikov model. More precisely, we compute the velocity circulation ${\mathrm{\Gamma }}_r$ in loops of size $r$ laying in the inertial range. For both experimental and numerical data, the circulation variance shows a clear Kolmogorov scaling $\langle {\mathrm{\Gamma }}_r^2\rangle \sim r^{8/3}$ in the inertial range, independently of the temperature. Scaling exponents of high-order moments are comparable, within error bars, to previously reported anomalous circulation exponents in classical turbulence and low-temperature quantum turbulence numerical simulations.

The molecular structure of moving contact lines (MCLs) and the emergence of a corresponding macroscopic dissipation have made the MCL a paradigm of fluid dynamics. Through novel averaging techniques that remove capillary waves smearing we achieve an unprecedented resolution in molecular dynamics simulations and find that they match with the continuum description obtained by finite element method down to molecular scales. This allows us to distinguish dissipation at the liquid-solid interface (Navier-slip) and at the contact line, the latter being negligible for the rather smooth substrate considered.

The presence of acoustic waves in models of compressible flows can present complications for analytical and numerical analysis. Therefore, several methods have been developed to filter out these waves, leading to various sound-proof models, including the Boussinesq, anelastic, and pseudoincompressible models. We assess the validity of each of these approximate models for describing magnetic buoyancy in the context of the solar interior. A general sound-proof model is introduced and compared to the fully compressible system in a number of asymptotic regimes, including both nonrotating and rotating cases. We obtain specific constraints that must be satisfied in order for the model to capture the leading-order behavior of the fully compressible system. We then discuss which of the existing sound-proof models satisfy these constraints and in what parameter regimes. We also present a variational derivation of the pseudoincompressible magnetohydrodynamics model, demonstrating its underlying Hamiltonian structure.

While particle inertia is widely known to cause substantial clustering of monodisperse particles in turbulent flows, differential sedimentation of polydisperse particles can rapidly decorrelate their relative positions and attenuate clustering. This paper presents a simple analytical model for the radial distribution function (RDF) of inertial particles settling in homogeneous, isotropic turbulence over a broad range of particle Stokes numbers, settling parameters, size ratios, and interparticle separations. We first draw on previous theories and direct-numerical simulations (DNS) to develop a simple comprehensive fit for the RDF of monodisperse particles without sedimentation. Even in the absence of gravity, the relative positions of polydisperse particles decorrelate as a result of turbulent accelerations, which have been treated as an acceleration-driven relative diffusivity of unequal size particles balancing the radial diffusion and drift resulting from turbulent shearing motions. We develop a similar model to describe the orientational averaged pair distribution function or RDF in the presence of differential sedimentation. The model is validated by comparison with DNS results for polydisperse settling particles. Juxtaposition of the model predictions with a variety of experimental measurements provides a perspective on current empirical knowledge of the RDF of sedimenting particles in turbulence. A sample calculation is then performed to illustrate the effect of preferential concentration in the presence of differential sedimentation on the coalescence rate of cloud droplets.

The probability density function (PDF) of the instantaneous streamwise velocity has consistently been used to extract information on the formation of uniform momentum zones (UMZs) in wall-bounded flows. Its temporal evolution has previously revealed patterns associated with the geometry and amplitude of the underlying velocity fluctuations [Laskari and McKeon, J. Fluid Mech. 913, A6 (2021)]. In this paper, we examine the robustness of these patterns in a variety of data sets including experiments and wall-bounded flow models. Experimental data sets spanning a range of Reynolds numbers, with very long temporal and spatial domains, suggest that the rate of the observed temporal variations scales in inner units. The use of a convection velocity, uniform across heights, to transform space into time has a marginal effect on these features. Similarly, negligible effects are observed between internal and external geometries. Synthetic databases generated following the resolvent framework and the attached eddy model are employed to draw comparisons to the experimental databases. Our findings highlight the distinctive strengths of each: The broadband frequency input of the attached eddy model allows for a better statistical description as opposed to a narrow frequency input in the resolvent data sets; instantaneously, however, representative eddies are seen to lack some structural details leading to the observed temporal behavior, which is better replicated by resolvent modes. Overall, given the considerable variety of the input data tested, the agreement between the data sets highlights the robustness of the spatiotemporal characteristics of the examined UMZs. It also underpins the need for their proper inclusion in UMZ modeling from a statistical as well as an instantaneous viewpoint; the current analysis accentuates important performance indicators for both.

We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential and vortical perturbations in the flow field. The current phase-reduction analysis can also be implemented consistently in the immersed boundary projection method, which facilitates the analysis over arbitrarily shaped bodies. We demonstrate the strength of the phase-based analysis for periodic flows over circular cylinder and symmetric airfoils at high incidence angles. The critical regions for phase modification in the cylinder flow are investigated, and the locations of flow separation are shown to be the most sensitive regions. Further, the results reveal the influence of the angle of attack and airfoil thickness on the phase-sensitivity distribution of flows over various airfoils. The phase for such flows is defined based on the lift coefficient, and hence it is influenced by the vortical structures responsible for lift production. The present framework sheds light on the connection between phase sensitivity and vortex formation dynamics.

Mechanisms of droplet production from bursting bubbles have been extensively studied for single bubbles, but remain sparsely investigated in more complex collective settings. We discuss jet and film drop velocity-size relationships from physics-based mechanisms as a potential means to further differentiate between various mechanisms and correctly determine the drops origin. We report dynamical experiments of drop production by bursting bubbles in single and collective setups. In the collective bubbling experiment, subsurface quasimonodisperse bubbles are rising up to the surface where, depending on the surfactant concentration, they can either merge or assemble in rafts of monodisperse bubbles. Drop trajectories are recorded, analyzed, and shown to exhibit uniquely distinctive features for the different production mechanisms: centrifuge film drops are ejected sideways, and jet drops are ejected vertically. Different single-burst scalings are finally compared to the experimental size-velocity relationships, and reveal that drops coming from collective bubble bursting appear slower and more scattered than when coming from single bursting bubbles.

Experiments have revealed the remarkably long lifetime of surface nanobubbles, but experiments have also demonstrated the diffusive instability of bubbles above micrometers; thus a physical understanding on the transition of bubbles stability is in urgent need. Herein, we develop a model to capture the state transition from stable nanobubbles to unstable microbubbles on homogeneous surfaces. The transition explains the typical long lifetime, limited height, and small contact angle of surface nanobubbles observed in experiments. The phase diagram shows that the bubble size and dissolved gas saturation determine the dynamic behaviors of surface bubbles, namely growth, stability, shrinkage, or dissolution.

Upon coming into contact with a solid surface, a liquid droplet spreads rapidly during the early moments due to inertial/capillary effects before the viscous dissipation slows it down. The temporal evolution of the spreading radius depends on the viscosity of the liquid drop. For low-viscosity liquids, the spreading radius follows a power-law, whereas for higher viscosity liquids it scales linearly with time with additional logarithmic corrections. In this work, the spreading dynamics of molten sand is investigated at isothermal conditions. The molten sand is a mixture of Calcia, Magnesia, Alumina, and Silicate, commonly referred to as CMAS, and is characterized by large viscosity, density, and surface tension. The multiphase many-body dissipative particle dynamics (mDPD) model is carefully parameterized to simulate a highly viscous molten CMAS droplet at ${1260}^{\mathrm{o}}\mathrm{C}$. Three-dimensional (3D) simulations were carried out at different initial drop sizes and equilibrium contact angles. Despite its unique properties, the spreading behavior of molten CMAS is in good agreement with theory and experiments of viscous coalescence of drops. Importantly, the two distinct spreading regimes are observed in the mDPD simulations. Due to the large viscosity, a slower but a nonunique spreading rate is observed in the inertial regime. However, the spreading rate in the viscous regime is in agreement with Tanner's law. The spreading radius remains unaffected by the initial drop size and collapses onto a master curve under viscous time scaling in agreement with theory and experiments. For different equilibrium angles, the spreading rate is observed to be nearly identical in the inertial regime. This indicates a universal spreading behavior during the early stages of spreading unaffected by both the initial drop size and the equilibrium contact angle. The contact line velocity was also computed to assess its relation with the dynamic contact angle. The dynamic contact angle data collapse when plotted as a function of the capillary number, displaying a remarkable agreement with Hoffman's description of dynamic contact angle evolution.

We formulate and analyze a model describing the development and evolution of density staircases in stratified turbulence, using it to investigate the long-term evolution and merger of layers and demonstrating an inverse logarithmic relationship for their decay. Starting from the Boussinesq equations, including viscous stresses and density diffusion, we use spatial averaging and simple closure assumptions to derive a system of equations describing the evolution of the density profile of a turbulent stratified fluid in terms of the horizontally averaged buoyancy and turbulent kinetic energy. Subject to critical conditions on the buoyancy gradient, the model predicts the development of a system of well-mixed layers separated by sharp interfaces. A linear stability analysis determines critical conditions for layer formation and demonstrates both a minimum and maximum initial density gradient necessary for layering. Increasing the viscosity decreases the maximum unstable wave number, thereby increasing the vertical length scale of layers. Increasing the diffusivity has a similar effect, but can also suppress the instability entirely by decreasing the unstable range of gradients. The long-term nonlinear evolution shows that the layers undergo successive mergers, with each merger increasing the magnitude of steps in the density staircase. In particular, by applying boundary conditions of fixed buoyancy, instead of the previously adopted condition of zero buoyancy flux, we reduce the influence of the boundaries at late times, allowing us to investigate the long-term evolution of layer mergers in stratified turbulence in detail. For long times $t$, we infer a general law describing the evolution of the number of layers $N$ as $1/N\sim lnt$, suggesting a self-similar structure to merger dynamics and a link to Cahn-Hilliard models of layering.

We present numerical simulations of radiatively driven convection at temperatures below the temperature of maximum density, as observed in ice-covered lakes in early spring. The purpose of these simulations is to isolate the phenomenon of lateral circulation driven by horizontal variations in surface albedo (e.g., due to partial snow cover) in an idealized and simplified system. The system we consider is one with uniform solar radiation except in a small “shadowed” region at the center of the domain which has damped radiation intensity. By comparing cases with and without a shadowed region, we identify gravity currents at the surface flowing away from the shadowed region. Not only do these gravity currents represent a mechanism for lateral transport at the surface below ice cover, but they also act as a catalyst for inducing earlier vertical mixing that develops at a faster rate than the Rayleigh-Taylor-like instabilities which drive vertical convection away from the shadow. To the authors' knowledge, only bathymetry and wind forcing at the surface have been presented as major mechanisms for lateral circulation in ice-covered lakes, and hence these simulations may provide a hitherto unreported mechanism for inducing lateral circulation.

We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length scales larger than $\ell$ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to Eyink [J. Fluid Mech. 549, 159 (2006)], which exhibits excellent correlation with the exact subscale physics when the partitioning length $\ell$ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, ${\mathbf{v}}_{*}$, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, ${\overline{\mathbf{u}}}_{\ell }$, but by the effective velocity, ${\overline{\mathbf{u}}}_{\ell }+{\mathbf{v}}_{*}$, the physics of which may improve commonly used LES models.

The hawkmoth is able to sustain a steady hover or level flight at lower speeds. However, previous wind tunnel experiments have suggested that long sequences of steady forward flight are less common at higher flying speeds ($>4.0\mathrm{m}/\mathrm{s}$) despite changes to the flight posture. This flying speed is about one-half of the theoretical prediction based on its body mass. It is unclear why hawkmoths have not been observed achieving steady flight at higher speeds. This paper aims to compare the aerodynamics involved in hawkmoth hovering to those in forward flight. High-speed video recordings and three-dimensional surface reconstruction were used to capture a hawkmoth's wing kinematics when hovering and at forward flight speeds of 2 and 4 m/s. Following reconstruction, the insect model was simulated using an in-house immersed-boundary-method based computational fluid dynamics (CFD) solver. The CFD solver provided a quantitative measure of the force generation, power consumption, and vortex structures generated during sustained flight. These results enabled the analysis of certain trends in how a hawkmoth adjusts flapping kinematics and its associated unsteady aerodynamics changes across different flight speeds. The results show that the moth minimizes drag as flying speed increases, but it immediately loses its lift producing upstroke even at the slow forward flight speed (2 m/s). A significant amount of negative lift is generated during upstrokes at the high forward flying speed (4 m/s). This negative lift in the upstroke potentially reduces maximum sustained flight speeds. This paper provides physical insight into the low-speed flights in flying insects.

We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling for the growth of the mixing region, which was observed in recent two-dimensional simulations. To this purpose, we use a Hele-Shaw cell. The flow configuration consists of a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When small perturbations of concentration and velocity fields occur at the interface, convective mixing is eventually produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase of the flow to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. When the gradients become sufficiently small, the system attains a stablystratified state and diffusion is again the dominant mixing mechanisms. We employ an optical method to obtain high-resolution measurements of the density fields, and we perform experiments for values of the Rayleigh-Darcy number (i.e., the ratio between convection and diffusion) sufficiently large to exhibit all the flow phases just described, which we characterize via the mixing length, a measure of the extension of the mixing region. We are able to confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.

The unsteady aerodynamics of a wing in the wake of a periodically plunging upstream airfoil was investigated in water tunnel experiments. By varying the frequency and the amplitude of the plunge oscillations, vortex-street configurations with varying wavelength and circulation were generated. Depending on the angle of attack of the wing, the largest lift force is found when the leading edge of the wing is located at the wake centerline or just above it. Flow separation at the leading edge, formation of a leading-edge vortex, and coupling with incident vortices are observed with increasing angle of attack. The lift time history has higher harmonics up to $n=5$ when the wing is close to the wake centerline. This is due to the cross-stream velocity profile in the undisturbed wake and can be also predicted by a point-vortex model. The peak lift coefficients decrease with increasing deflection angle of the wake if the upstream airfoil is plunged at nonzero mean angle of attack. This occurs as the geometry and circulations of the vortices in the reversed Karman vortex street are modified. For the unloaded wing in the symmetric wakes, the peak lift coefficients increase with increasing frequency and amplitude of the plunging airfoil. These kinematic parameters also determine the amplitude and shape of the cross-stream velocity profiles and the degree of two dimensionality in the undisturbed wake. The amplitude of the lift coefficient of the wing depends on a single wake parameter, which is the Strouhal number based on the amplitude of the upstream airfoil.

Viscoelastic flow through porous media is relevant in many industrial and biological applications including enhanced oil recovery and biofluids' transport inside the body, where the presence of large polymeric stresses in the porous media leads to viscoelastic instability. In the present study, we numerically investigate viscoelastic instability-induced flow states in the channels consisting of (i) a single cylinder and (ii) two streamwise located cylinders. We unravel the presence of a hysteresis for pulsatile viscoelastic flows. For both geometries, the quantitative value of flow asymmetry around the cylinder resulting from the viscoelastic instability forms a closed hysteresis loop. We investigate the effects of fluid rheological properties and periodic inlet flow rates on the hysteresis loop.

Rupture of thin free films of Newtonian fluids is analyzed when the sheets' two free surfaces are covered with insoluble surfactant and surface rheological effects are important. The analysis relies on a long-wavelength model composed of a system of one-dimensional evolution equations for film thickness $h(z,t)$, lateral velocity $v(z,t)$, and surfactant concentration $\mathrm{\Gamma }(z,t)$ ($z$: lateral coordinate, $t$: time). As the dynamics near the space-time singularity in sheet rupture is asymptotically self-similar when surfactants are convected away from the rupture point, the partial differential equations are also reduced to a set of ordinary differential equations in similarity space. For both highly viscous fluids in the Stokes limit and moderately viscous fluids, it is shown that the dominant balance involves van der Waals pressure and bulk viscous as well as surface viscous stresses while surface tension pressure and Marangoni stress are negligible. In the Stokes limit, self-similarity is of the second kind and $h\sim \mathrm{\Gamma }\sim {\tau }^{1/3}, z\sim {\tau }^{{\alpha }_z}$, and $v\sim {\tau }^{{\alpha }_z-1}$ where $\tau$ is time remaining until rupture and ${\alpha }_z$ is the lateral scaling exponent. Although ${\alpha }_z$ cannot be determined by dimensional arguments, it is shown to equal 0.249. For moderately viscous fluids, inertia also enters the picture and self-similarity is of the first kind ($h\sim \mathrm{\Gamma }\sim {\tau }^{1/3}, z\sim {\tau }^{1/2}$, and $v\sim {\tau }^{-1/2}$). Scalings determined from theory are confirmed by numerical solution of the evolution equations. Closed-form expressions for the sheet's thinning rate, which have heretofore been lacking, are also reported.

The dissolution or growth of a droplet in a host liquid is an important part of processes like chemical extraction, chromatography, or emulsification. In this work we look at the dissolution of a pair of vertically aligned droplets immersed in water, both experimentally and numerically. The liquids used for the droplets are long chain alcohols with a low but finite solubility in water and a significantly lower density than that of the host liquid. Therefore, a solutal plume is formed above of the bottom droplet and natural convection dominates the dissolution process. We monitor the volume of the droplets and the velocity field around them over time. When the liquids of the two droplets are the same, our previously found scaling laws for the Sherwood and Reynolds numbers as functions of the Rayleigh number [Dietrich et al., J. Fluid Mech. 794, 45 (2016)] can be applied to the lower droplet. However, remarkably, when the liquid of the top droplet is different than that of the bottom droplet the volume as function of time becomes nonmonotonic, and an oscillatory Marangoni flow at the top droplet is observed. We identify the competition between solutal Marangoni flow and density-driven convection as the origin of the oscillation and numerically model the process.