Motivated by the ablation of vertical ice faces in salt water, we use three-dimensional direct numerical simulations to investigate the heat and salt fluxes in two-scalar vertical convection. For parameters relevant to ice-ocean interfaces in the convection-dominated regime, we observe that the salinity field drives the convection and that heat is essentially transported as a passive scalar. By varying the diffusivity ratio of heat and salt (i.e., the Lewis number Le), we identify how the different molecular diffusivities affect the scalar fluxes through the system. Away from the walls, we find that the heat transport is determined by a turbulent Prandtl number of ${\mathrm{Pr}}_t\approx 1$ and that double-diffusive effects are practically negligible. However, the difference in molecular diffusivities plays an important role close to the boundaries. In the (unrealistic) case where salt diffused faster than heat, the ratio of salt-to-heat fluxes would scale as ${\mathrm{Le}}^{1/3}$, consistent with classical nested scalar boundary layers. However, in the realistic case of faster heat diffusion (relative to salt), we observe a transition towards a ${\mathrm{Le}}^{1/2}$ scaling of the ratio of the fluxes. This coincides with the thermal boundary layer width growing beyond the thickness of the viscous boundary layer. We find that this transition is not determined by a critical Lewis number, but rather by a critical Prandtl number $\mathrm{Pr}\approx 10$, slightly below that for cold seawater where $\mathrm{Pr}=14$. We compare our results to similar studies of sheared and double-diffusive flow under ice shelves, and discuss the implications for fluxes in large-scale ice-ocean models. By coupling our results to ice-ocean interface thermodynamics, we describe how the flux ratio impacts the interfacial salinity, and hence the strength of solutal convection and the ablation rate.

In one-dimensional (1D) evolution models of gas giant planets, an outer convection zone advances into the interior as the surface cools, and multiple convective layers form beneath that convective front. To study layer formation below an outer convection zone in a similar scenario, we investigate the evolution of a stably stratified fluid with a linear composition gradient that is constantly being cooled from above. We use the Boussinesq approximation in a series of two-dimensional simulations at low and high Prandtl numbers ($\mathrm{Pr}=0.5$ and 7), initialized with constant temperature everywhere, and cooled at different rates. We find that multiple convective layers form at $\mathrm{Pr}=7$, as the result of an instability in the diffusive thermal boundary layer below the outer convection zone. At low Pr, layers do not form because the temperature gradient within the boundary layer is much smaller than at large Pr and, consequently, is not large enough to overcome the stabilizing effect of the composition gradient. For the stratification used in this study, on the long-term the composition gradient is an ineffective barrier against the propagation of the outer convection zone and the entire fluid becomes fully mixed, whether layers form or not. Our results challenge 1D evolutionary models of gas giant planets, which predict that layers are long-lived and that the outer convective envelope stops advancing inwards. We discuss what is needed for future work to build more realistic models.

The transitional flow which initiates within the junction (anastomosis) of an arteriovenous fistula (AVF) is known to be a contributing factor in the onset of vascular disease. A novel treatment method involving the implantation of a flexible stent across the anastomosis has enabled the retention of a large proportion of functioning AVFs, despite the propensity for stent malapposition to occur at the sharp inner curve of the anastomosis. Large eddy simulations of a single patient-specific AVF with and without the presence of a stent captured oscillatory flow behavior emanating from the interface of the two inlet flows in the stent-absent case, however, these oscillatory features were subdued in the stented case. The stent-absent case generally had higher turbulent kinetic energy (TKE) in the anastomosis which led to larger cycle-to-cycle variations in wall shear stress (WSS). The significantly lower TKE generated at the heel of the stented AVF was contained within the malapposed stent, thereby resulting in lower WSS fluctuations. However, a slight increase in turbulence downstream of the malapposed stent edge was noted. This detailed study reveals a significant decrease in turbulence within the AVF in the presence of the stent, thereby providing a level of understanding underpinning the success of the treatment strategy (in this patient case) from a fluid dynamic perspective.

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by a small gap. The governing equation of flow within a Hele-Shaw cell is Darcy's law, which also describes flow through a porous medium. In this work, we derive a generalization to Darcy's law starting from a three-dimensional fluid with a parity-broken viscosity tensor with no isotropy. We discuss the observable effects of parity-odd fluids in various physical setups relevant to Hele-Shaw experiments, such as channel flow, flow past an obstacle, bubble dynamics, and the Saffman-Taylor instability. In particular, we show that when such a fluid is pushed through a channel, a transverse force is exerted on the walls, and when a bubble of air expands into a region of such fluid, a circulation develops in the far field, with both effects proportional to the parity-odd viscosity coefficients. The Saffman-Taylor stability condition is also modified, with these terms tending to stabilize the two-fluid interface. Such experiments can in principle facilitate the measurement of parity-odd coefficients in both synthetic and natural active matter systems.

In wall turbulence, meandering behaviors of large-scale structures observed in the logarithmic layer are a crucial spatial feature to understand the spatial organization of these structures and to improve the structure-based turbulence model. These structures extend from the near-wall region to the edge of boundary layers $\left(\delta \right)$. Thus, their meandering motions leave an imprint on the two-point turbulence statistics across the flow, especially in the logarithmic region. Herein, we demonstrate the influence of the meandering motions of wall-attached structures on the two-point correlation and the premultiplied two-dimensional spectra by analyzing the direct numerical simulation data of the turbulent boundary layer at ${\text{Re}}_{\tau }\approx 1000$. The meandering magnitudes of wall-attached structures increase with their height $\left(l_y\right)$ but significantly differ among the identified structures even at a given $l_y$. In addition, the wall-attached structures of streamwise velocity fluctuations $\left(u\right)$ are found to be aligned along with a preferred spanwise offset regardless of the meandering motion. This feature is confirmed through the conditional two-point correlations of $u$ within the meandering structures, which leads to a distinct X pattern in the logarithmic region. We further examine the spectral behavior of the meandering structures across the streamwise and spanwise wavelengths (${\lambda }_x$ and ${\lambda }_z$, respectively) through the premultiplied two-dimensional spectra. With increasing meandering magnitudes, the energy spectra are more inclined to the ${\lambda }_z$ direction. Furthermore, the energy spectra of the strong meandering structures are bounded by a linear relationship ${\lambda }_x\sim {\lambda }_z$ over the large-scale range, reminiscent of self-similar scaling predicted by the attached-eddy hypothesis. In particular, the upper bound is aligned along ${\lambda }_x\approx 2{\lambda }_z$ over ${\lambda }_z>\delta$, which is absent in the energy spectral of the total $u$. This result reveals that the meandering motions allow the large-scale structures to contain wide spanwise scale energy that is self-similar in the logarithmic region. Finally, a discussion on the near-wall parts of the meandering structures is given with an emphasis on Townsend's inactive eddies.

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 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.

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.

The propagation of horizontal dam-break flows induced by the release of a rectangular column of a liquid phase into a negligible ambient fluid is investigated by combining numerical simulations and laboratory experiments. Varying both the geometry of the initial column and liquid properties, the parameter space covered allows the investigation of the transition from inertial to viscous slumping barely considered so far. In light of the Reynolds number $\mathrm{Re}$ based on the initial parameters of the fluid column, we report a newly investigated transient regime following the inertial slumping regime and prior to the viscous-dominated one. The transient intermediate regime is shown (i) to only exist for $\mathrm{Re}\gtrsim 10$ and (ii) to be characterized by an inertial overshoot followed by a strong deceleration of the front position accompanied by an excess and a deficit of fluid at the front and at the origin, respectively, with respect to the expected theoretical prediction of the viscous-dominated regime. Beyond the intuitive idea of an adaptive transition from the inertial to fully viscous slumping, these results highlight and quantify the influence of initial inertia on the spreading of a liquid, which may be particularly useful for modeling industrial and geophysical applications.

Formation of a splash crown and a cavity following the impact of a sphere on a body of liquid is a classical problem. In the related problem of a droplet splashing on a flat surface, it has been established that the properties of the surrounding gas can influence the splashing threshold. At lower impact speeds, this is due mainly to the influence of gas kinetic effects, since the height of the gas lubrication film which is displaced during dynamic wetting is often comparable to the mean free path of the gas. At higher Weber and Reynolds numbers, on the other hand, inertial effects dominate and the density of the gas becomes important in determining whether a splash occurs. In this article, sphere impacts on a liquid body are investigated in a rarefied atmosphere using high-speed photography. It is found that the threshold entry speed for cavity formation is influenced by the density of the surrounding gas, whereas changing the mean free path of the gas has no effect. We attribute this phenomenon to the gas slowing the sealing of the thin crown sheet behind the sphere. This assertion is supported with experimental measurements of the liquid sheet thickness. In the range of parameters considered, the splash crown influences the movement of the contact line.

We present a framework to quantitatively describe energy exchange in high-speed turbulent flows, also including the hypersonic regime. Governing equations are introduced which control the transport of the mean-field kinetic energy ($k_m$), the turbulence kinetic energy ($k_t$), the mean-field internal energy ($e_m$), and the turbulence internal energy ($e_t$). The common terms in the transport equations are found to represent energy exchanges and interactions among $k_m, k_t, e_m$, and $e_t$. The routes of energy exchange are then highlighted and quantified in hypersonic boundary-layer flow, with special attention paid to the effects of wall cooling.

In this article, we present a predictive model for the amplitude of impulse waves generated by the collapse of a granular column into a water layer. The model, which combines the spreading dynamics of the grains and the wave hydrodynamics in shallow water, is successfully compared to a large dataset of laboratory experiments, and captures the influence of the initial parameters while giving an accurate prediction. Furthermore, the role played on the wave generation by two key dimensionless numbers, i.e., the global Froude number and the relative volume of the immersed deposit, is rationalized. These results provide a simplified, yet comprehensive, physical description of the generation of tsunami waves engendered by large-scale subaerial landslides, rockfalls, or cliff collapses in a shallow water.

The motion of a free rising skirt bubble is studied using direct numerical simulation covering the range of Eötvös (Bond) and Morton numbers where they can be observed. We investigate the skirt bubble motion (terminal velocity and drag), the flow field structure (inside the skirt film, around the bubble, and inside the gas film that forms the skirt) as well as the geometrical characteristics of the skirt (both length and thickness). A unified relation for the terminal velocity (and drag force) is provided for all bubble shapes (dimple, skirt, and spherical cap bubbles) when considering Eötvös numbers (based on bubble diameter) larger than 100. The velocity field around and inside the bubble is investigated resulting in the clarification of the wake structure with a major difference with the flow deduced from experimental observations during the 1970s. The numerical simulations reveal that only one recirculation is observed inside the bubble while two vortices are highlighted in the wake. We confirm that a parallel Poiseuille flow develops inside the skirt film resulting in an intense vorticity field. Original modeling is improved with a Reynolds correction that makes possible the prediction of the film thickness in very good agreement with the only experimental value available in the literature. Our simulations combined with experimental observations suggest the existence of a maximum value for the skirt length.

An experimental investigation is conducted to evaluate the effect of polymer injection on the development of a zero-pressure-gradient bypass transitioning boundary layer on a flat plate. Planar particle image velocimetry and planar laser-induced fluorescence measurements conducted at multiple streamwise stations allow for a characterization of the development of the bypass transition process induced by a two-dimensional trip wire in both Newtonian and polymer-injected flow. Two different trip placements with respect to the injection slot are considered to study the effect of polymer injection within the wake of the trip wire and within the laminar boundary layer upstream of the trip. The transition process is initiated in a separated shear layer downstream of the trip wire, where a rapid amplification of the velocity perturbations via an inflectional Kelvin-Helmholtz instability leads to vortex shedding and subsequent breakdown to turbulence. A similar transition process is observed with polymer injection, but a more rapid initial growth of perturbations is observed, leading to earlier transition. Nonetheless, an onset of polymer effect is seen in the late transition stages and leads to significant levels of drag reduction in the developing turbulent boundary layer.

When the interface between a dielectric and a conducting liquid is excited by an oscillatory electric field, electrostatic Faraday waves can be induced. Here, we study the response of the interface to an ac electric field, which is superposed by either a second ac field of different frequency, or by a dc field. An algorithm based on light refraction at the fluidic interface is used to obtain the spatiotemporal response of the Faraday waves, and the critical voltage corresponding to onset of instability, the interfacial oscillation frequency, and the dominant wavelengths are determined. The influence of the mixing ratio, which denotes the relative amplitudes of the different components of the driving signal, is analyzed, and the experimental results are compared with theoretical predictions. For ac/ac driving, gradual variations of the mixing ratio can induce a jump of the pattern wavelength, which is a result of the transition from harmonic to a subharmonic oscillation. For ac/dc driving, the interface oscillates either harmonically or subharmonically, and the response wavelength can be tuned continuously by adjusting the admixture of the dc component. For both driving modes, the experiments show good agreement with theory.

The Arctic Ocean's main thermocline may be characterized by a series of fine-scale thermohaline staircase structures that are present in a wide range of regions, the formation mechanism of which remains unclear. Recent analysis has led to the proposal of a theoretical model which suggested that these staircase structures form spontaneously in the ocean when the turbulent intensity determined by the buoyancy Reynolds number ${\text{Re}}_b$ is sufficiently weak. In the current work, we have designed a series of ${\text{Re}}_b$ controlled direct numerical simulations of turbulence in the Arctic Ocean thermocline to test the effectiveness of this theory. In these simulations, the staircases form naturally when ${\text{Re}}_b$ falls in the range predicted by the instability criterion. The exponential growth rate of the layering mode matches well with the prediction of the theoretical model. The staircases formed in our simulations are further compared with the classical diffusive interface model, which argues that stable staircase structures can only form when the density ratio $R_{\rho }$ is smaller than the critical value of $R_{\rho }^{cr}={\tau }^{-1/2}$. Here $\tau$ is the ratio of haline diffusivity over thermal diffusivity. We show that the staircase structure can stably persist in our model regardless of whether or not $R_{\rho }<R_{\rho }^{cr}$ is satisfied.

We studied homogeneous stably stratified turbulence in a triply periodic domain over a wide range of stratification strengths. We evaluated the statistically stationary, volume-averaged budgets of Reynolds stresses, turbulent potential energy, and turbulent vertical density flux. By separately studying the three components of the turbulent kinetic energy (TKE), we examined the role of pressure-strain correlations and observed connections between changes in the energetics to regime shifts of the mixing coefficient $\left(\mathrm{\Gamma }\right)$ as a function of the turbulent Froude number $\left({\text{Fr}}_k\right)$. As we increase stratification, we find that pressure-strain correlations become more important in producing the vertical component of TKE $\left(k_w\right)$. At the stratification strength where direct production and pressure-strain correlations equally generate $k_w$, we observe the maximum value of $\mathrm{\Gamma }$, and it remains constant as stratification is increased further. However, when we greatly increase stratification from this point, the pressure-strain correlations become the dominant source of $k_w$ with direct production becoming negligible, and this change is accompanied by the mixing coefficient decreasing from its maximum value. Finally, we find that this final transition for the mixing coefficient coincides with a sign change of the pressure scrambling term in the vertical density flux budget.

Objects inserted in a fast-flowing soap film are observed to cause strong disturbances on the film, resembling shock waves. Currently a prevailing opinion is that these shock waves correspond to sudden increases in film thickness caused by elastic symmetric waves, or the propagation of film thickness changes driven by surface tension variations with the film surface area. Here, we show by laser interferometry that these “shock waves” in fact originate from the antisymmetric waves studied by Taylor, which correspond to the bending of the liquid film with no thickness change. This phenomenon thus forms an example of symmetry breaking. These shock waves maintain an antisymmetric structure, but the structure size varies with the size of the intruding object. Our results indicate that these structures could be objects for studying solitary waves, rather than the traditional shocks corresponding to density jumps in compressible flows.

Despite the well-known limitations of linear stability theory in describing nonlinear and turbulent flows, it has been found to accurately capture the transitions between certain nonlinear flow behavior. Specifically, the transition in heat flux scaling in rotating convective flows can be well predicted by applying a linear stability analysis to simple profiles of a convective boundary layer. This fact motivates the present study of the linear mechanisms involved in the stability properties of simple convective setups subject to rotation. We look at an idealized two-layer setup and gradually add complexity by including rotation, a bounded domain, and viscosity. The two-layer setup has the advantage of allowing for the use of wave interaction theory, traditionally applied to understand stratified and homogeneous shear flow instabilities, in order to quantify the various physical mechanisms leading to the growth of convective instabilities. We quantitatively show that the physical mechanisms involved in the stabilization of convection by rotation take two different forms acting within the stratified interfacial region, and in the homogeneous mixed layers. The latter of these we associate with the tendency of a rotating flow to develop Taylor columns (TCs). This TC mechanism can lead to both a stabilization or destabilization of the instability and varies depending on the parameters of the problem. A simple criterion is found for classifying the influence of these physical mechanisms.