Understanding the flows in planetary cores, i.e., the large liquid iron oceans hidden in the central part of terrestrial planets, is a tremendous interdisciplinary challenge, at the frontier of fundamental fluid dynamics and planetary sciences. Beyond buoyancy driven flows that constitute the standard model for core fluid dynamics, an increasing amount of research has focused on the rotational dynamics of these spinning systems, periodically perturbed by tides, precession, and libration. Although of small amplitude, those harmonic forcings are capable of exciting resonant instabilities in planetary cores, providing alternative routes towards turbulence and magnetic field generation. In this paper I provide an overview of some recent works on this field, focusing on the mechanisms of tide and libration driven elliptical instabilities. Combined laboratory experiments and pioneering numerical simulations have allowed a full description of the stability and linear state of these flows, as well as the investigation of some convincing planetary applications. Open questions now remain regarding the nonlinear saturation of the excited flows as well as their dynamo capability. These will undoubtedly be the focus of future research, in the context of intense activity in planetary exploration of our solar system and others, which highlights the need to go beyond the standard convective models.

In this paper we exploit some analogies between flows near capillary interfaces and near elastic interfaces. We first consider the elastohydrodynamics of a ball bearing and the motion of a gas bubble inside a thin channel. It is shown that there is a strong analogy between these two lubrication problems, and the respective scaling laws are derived side by side. Subsequently, the paper focuses on the limit where the involved elastic interfaces become extremely soft. It is shown that soft gels and elastomers, like liquids, can be shaped by their surface tension. We highlight some recent advances on this class of elastocapillary phenomena.

Accurate long-term forecasts of the path and intensity of severe hurricanes are imperative to protect property and save lives. Extensive real-time measurements within hurricanes, especially near their core, are essential for supplementing the limited relevant information accessible by satellites in order to improve such forecasts. Current operational methods for obtaining in situ information, such as dropsondes and repeated manned and unmanned aircraft flights over and within hurricanes, are both expensive and limited in duration. In the present work it is demonstrated by numerical experiments how a swarm of robust, inexpensive, buoyancy-controlled, sensor-laden balloons might be deployed and controlled in an energetically efficient, coordinated fashion, for days at a time, to continuously monitor relevant properties (pressure, humidity, temperature, and wind speed) of a hurricane as it develops. Rather than fighting its gale-force winds, the strong and predictable stratification of these winds is leveraged to efficiently disperse the balloons into a favorable time-evolving distribution. An iterative bootstrap approach is envisioned in which (a) sensor balloons are used to help improve the available computational estimate of the uncertain and underresolved flow field of the hurricane and (b) this (imprecise) estimate of the hurricane flow field is leveraged to improve the distribution of the sensor balloons, which then better facilitates (a), etc. The control approach envisioned in this ambitious effort is a combination of (centrally computed) model predictive control for coordination at the largest scales, which is the focus of the present paper, coupled with a feedback control strategy (decentrally computed, on the balloons themselves), for smaller-scale corrections. Our work indicates that, following such an approach, certain target orbits of interest within the hurricane can be continuously sampled by some balloons, while others make repeated sweeps between the eye and the spiral rain bands.

Diffusive processes exhibit a strong dependence on history effects. For a gas bubble at rest in a liquid, such effects arise when the concentration of dissolved gas at the bubble surface, dictated by Henry's law, depends on time. In this paper we consider several such situations. An oscillating ambient pressure field causes the occurrence of rectified diffusion of gas into or out of the bubble. Unlike previous investigators, who considered the opposite limit, we study this process for conditions when the diffusion length is larger than the bubble radius. It is found that history effects are important in determining the threshold conditions. Under a static ambient pressure, the time dependence of the gas concentration can arise due to the action of surface tension, which increases the gas pressure as the bubble dissolves or, when the bubble contains a mixture of two or more gases, due to the different rates at which they dissolve. In these latter cases history effects prove mostly negligible for bubbles larger than a few hundred nanometers.

The present analysis extends the author's earlier work [Lappa, Phys. Fluids 26, 093301 (2014)] on the properties of patterns formed by the spontaneous accumulation and ordering of solid particles in certain types of flow. It is shown that under certain conditions, when subjected to vibrations to induce natural flow, nonisothermal fluids with dispersed solid particles are characterized by intervals of solid-pattern-forming behavior due to particle rearrangements preceded by intervals in which no recognizable structures of solid matter can be detected. The dynamics of these systems are highly nonlinear in nature. Because this family of particle attractors is known to exhibit strong sensitivity to the symmetry properties of the considered vibrated system and related geometrical constraints, the present study attempts to clarify the related dynamics in a geometry with curved walls (cylindrical enclosure). In particular, by assuming vibrations always directed perpendicularly to the imposed temperature gradient, we show that the morphology, spatial extension (percentage of physical volume occupied), separation (spatial distance), and mechanisms responsible for the formation of the resulting particle structures change significantly according to whether the temperature gradient is parallel or perpendicular to the symmetry axis of the cylinder. This indicates that the physics is not invariant with respect to 90° rotations in space of the specific forcing considered (direction of the imposed temperature gradient and associated perpendicular vibrations). Additional insights into the problem are obtained by assessing separately the influence played by the time-averaged (mean) and oscillatory effects. According to the numerical results, the intriguing diversity of particle agglomerates results from the different role or importance played by (curved or straight) boundaries in constraining particles and from the different structure and topology of the resulting macroscopic (large-scale) thermovibrational flow oscillating in time at the same frequency of the imposed vibrations.

We show that thermocapillary-induced droplet motion is markedly enhanced when using lubricant-impregnated surfaces as compared to solid substrates. These surfaces provide weak pinning, which makes them ideal for droplet transportation and specifically for water transportation. Using a lubricant with viscosity comparable to that of water and temperature gradients as low as 2 K/mm, we observe that drops can propel at 6.5 mm/s, that is, at least 5 times quicker than reported on conventional substrates. Also in contrast with solids, the liquid nature of the different interfaces makes it possible to predict quantitatively the thermocapillary Marangoni force (and velocity) responsible for the propulsion.

Water vapor condensation on superhydrophobic surfaces has received much attention in recent years due to the ability of such surfaces to shed microscale water droplets via coalescence-induced droplet jumping, resulting in heat transfer, anti-icing, and self-cleaning performance enhancement. Here we report the coalescence-induced removal of water nanodroplets ($R\approx 500\mathrm{nm}$) from superhydrophobic carbon nanotube (CNT) surfaces. The two-droplet coalescence time is measured for varying droplet Ohnesorge numbers, confirming that coalescence prior to jumping is governed by capillary-inertial dynamics. By varying the conformal hydrophobic coating thickness on the CNT surface, the minimum jumping droplet radius is shown to increase with increasing solid fraction and decreasing apparent advancing contact angle, allowing us to explore both hydrodynamic limitations stemming from viscous dissipation and surface adhesion limitations. We find that, even for the smallest nanostructure length scale ($\le 100$ nm) and lowest surface adhesions, nonideal surface interactions and the evolved droplet morphology play defining roles in limiting the minimum size for jumping on real surfaces. The outcomes of this work demonstrate the ability to passively shed nanometric water droplets, which has the potential to further increase the efficiency of systems that can harness jumping droplets for a wide range of energy and water applications.

The emergence of turbulence in shear flows is a well-investigated field. Yet, there are some lingering issues that have not been sufficiently resolved. One of them is the apparent contradiction between the results of linear stability analysis showing a flow to be stable and yet experiments and simulations proving it to be otherwise. There is some success, in particular in astrophysical systems, based on magnetorotational instability (MRI), revealing turbulence. However, MRI requires the system to be weakly magnetized. Such instability is neither a feature of general magnetohydrodynamic (MHD) flows nor revealed in purely hydrodynamic flows. Nevertheless, linear perturbations of such flows are non-normal in nature, which argues for a possible origin of nonlinearity therein. The concept behind this is that non-normal perturbations could produce huge transient energy growth (TEG), which may lead to nonlinearity and further turbulence. However, so far, non-normal effects in shear flows have not been explored much in the presence of magnetic fields. In this spirit, here we consider the perturbed viscoresistive MHD shear flows with rotation in general. Basically we recast the magnetized momentum balance and associated equations into the magnetized version of Orr-Sommerfeld and Squire equations and their magnetic analogs. We also assume the flow to be incompressible and in the presence of Coriolis effect solve the equations using a pseudospectral eigenvalue approach. We investigate the possible emergence of instability and large TEG in three different types of flows, namely, the Keplerian flow, the Taylor-Couette (or constant angular momentum) flow, and plane Couette flow. We show that, above a certain value of magnetic field, instability and TEG both stop occurring. We also show that TEG is maximum in the vicinity of regions of instability in the wave number space for a given magnetic field and Reynolds number, leading to nonlinearity and plausible turbulence. Rotating shear flows are ubiquitous in astrophysics, especially accretion disks, where molecular viscosity is too low to account for observed data. The primary accepted cause of energy-momentum transport therein is turbulent viscosity. Hence, these results would have important implications in astrophysics.

The shear-driven drainage of capillary grooves filled with viscous liquid is a dynamic wetting phenomenon relevant to numerous industrial processes and lubricant-infused surfaces for drag reduction and antifouling. Prior work has reported that a finite length $L_{\infty }$ of the capillary groove can remain indefinitely filled with liquid even when large shear stresses are applied. The mechanism preventing full drainage is attributed to a balance between the shear-driven flow and a counterflow driven by capillary pressures caused by deformation of the free surface. In this work, we examine closely the approach to the final equilibrium length $L_{\infty }$ and report a crossover to a slow drainage regime that cannot be described by conventional dynamic models considering solely hydrodynamic and capillary forces. The slow drainage regime observed in experiments can be instead modeled by a kinetic equation describing a sequence of random thermally activated transitions between multiple metastable states caused by surface defects with nanoscale dimensions. Our findings provide insights on the critical role that natural or engineered surface roughness with nanoscale dimensions can play in the imbibition and drainage of capillaries and other dynamic wetting processes in microscale systems.

This study is inspired by the observation and hypothesis that the spreading and decay behaviors of a jet directly depend on the momentum-mixing mechanism between the jet and surrounding fluid. This mixing behavior is dictated by the kinematic viscosity $\nu$ for a laminar jet, which can be dramatically enhanced in a turbulent flow and is represented by the eddy viscosity $\varepsilon$. Similarly, pulsation in a synthetic jet is identified as another mechanism for enhancing mixing, which can be captured by an enhanced eddy viscosity beyond what is observed in a corresponding turbulent continuous jet. To this end, an effective-eddy-viscosity concept is proposed to model any excitation of a jet that could result in enhanced mixing beyond what is predicted by the kinematic viscosity. Our previous study found that $\varepsilon$ is actuator dependent and its relationship with the spreading or decay behavior of a jet is not obvious. To remove the actuator dependence, this study performs a dimensional analysis to relate the spreading and decay behaviors to a scaled effective eddy viscosity $\varepsilon /\sqrt{K}$ ($K$ is the momentum flux). This quantity physically represents a competition between the radial diffusion and the axial convection of the jet axial momentum. The experimental results confirm that $\varepsilon /\sqrt{K}$ governs the spreading and decay rates of the far field for any round jets.

Two particle image velocimetry arrangements are used to make true spatial comparisons between smooth- and rough-wall boundary layers at high Reynolds numbers across a very wide range of streamwise scales. Together, the arrangements resolve scales ranging from motions on the order of the Kolmogorov microscale to those longer than twice the boundary layer thickness. The rough-wall experiments were obtained above a continuous sandpaper sheet, identical to that used by Squire et al. [J. Fluid Mech. 795, 210 (2016)], and cover a range of friction and equivalent sand-grain roughness Reynolds numbers ($12000\lesssim {\delta }^{+}\lesssim$ 18000, $62\lesssim k_s^{+}\lesssim 104$). The smooth-wall experiments comprise new and previously published data spanning $6500\lesssim {\delta }^{+}\lesssim 17000$. Flow statistics from all experiments show similar Reynolds number trends and behaviors to recent, well-resolved hot-wire anemometry measurements above the same rough surface. Comparisons, at matched ${\delta }^{+}$, between smooth- and rough-wall two-point correlation maps and two-point magnitude-squared coherence maps demonstrate that spatially the outer region of the boundary layer is the same between the two flows. This is apparently true even at wall-normal locations where the total (inner-normalized) energy differs between the smooth and rough wall. Generally, the present results provide strong support for Townsend's [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1956), Vol. 1] wall-similarity hypothesis in high Reynolds number fully rough boundary layer flows.

We investigate the effect of particle-size segregation in an upslope propagating granular bore. A bidisperse mixture of particles, initially normally graded, flows down an inclined chute and impacts with a closed end. This impact causes the formation of a shock in flow thickness, known as a granular bore, to travel upslope, leaving behind a thick deposit. This deposit imprints the local segregated state featuring both pure and mixed regions of particles as a function of downstream position. The particle-size distribution through the depth is characterized by a thin purely small-particle layer at the base, a significant linear transition region, and a thick constant mixed-particle layer below the surface, in contrast to previously observed S-shaped steady-state concentration profiles. The experimental observations agree with recent progress that upward and downward segregation of large and small particles respectively is asymmetric. We incorporate the three-layer, experimentally observed, size-distribution profile into a depth-averaged segregation model to modify it accordingly. Numerical solutions of this model are able to match our experimental results and therefore motivate the use of a more general particle-size distribution profile.

We present a scenario for magnetic field amplification where an electrically conducting fluid is confined in a differentially rotating, spherical shell with thin aspect ratio. When the angular momentum sufficiently decreases outwards, a hydrodynamic instability develops in the equatorial region, characterized by pairs of counter-rotating toroidal vortices similar to those observed in cylindrical Couette flow. These spherical Taylor-Couette vortices generate a subcritical dynamo magnetic field dominated by nonaxisymmetric components. We show that the critical magnetic Reynolds number seems to reach a constant value at large Reynolds number and that the global rotation can strongly decrease the dynamo onset. Our numerical results are understood within the framework of a simple dynamical system, and we propose a low-dimensional model for subcritical dynamo bifurcations. Implications for both laboratory dynamos and astrophysical magnetic fields are finally discussed.

Recent experimental measurements have reported that the outer peak of the streamwise wave-number spectra of the streamwise velocity depends on the Reynolds number. Starting from this puzzling observation, here it is proposed that the wall-parallel velocity components of each of the energy-containing motions in the form of Towsnend's attached eddies exhibit an inner-scaling nature in the region close to the wall. Some compelling evidence on this proposition has been presented with a careful inspection of scaling of velocity spectra from direct numerical simulations, a linear analysis with an eddy viscosity, and the recently computed statistical structure of the self-similar energy-containing motions in the logarithmic region. This observation suggests that the viscous wall effect would not be negligible at least below the peak wall-normal location of each of the energy-containing motions in the logarithmic and outer regions, reminiscent of the concept of the mesolayer previously observed in the mean momentum balance. It is shown that this behavior emerges due to a minimal form of scale interaction, modeled by the eddy viscosity in the linear theory, and enables one to explain the Reynolds-number-dependent behavior of the outer peak as well as the near-wall penetration of the large-scale outer structures in a consistent manner. Incorporation of this viscous wall effect to Townsend's attached eddies, which were originally built with an inviscid approximation at the wall, also reveals that the self-similarity of the wall-parallel velocity components of the energy-containing motions would be theoretically broken in the region close to the wall.

Large-scale hydrodynamic instabilities of periodic helical flows of a given wave number $K$ are investigated using three-dimensional Floquet numerical computations. In the Floquet formalism the unstable field is expanded in modes of different spacial periodicity. This allows us (i) to clearly distinguish large from small scale instabilities and (ii) to study modes of wave number $q$ of arbitrarily large-scale separation $q\ll K$. Different flows are examined including flows that exhibit small-scale turbulence. The growth rate $\sigma$ of the most unstable mode is measured as a function of the scale separation $q/K\ll 1$ and the Reynolds number $\text{Re}$. It is shown that the growth rate follows the scaling $\sigma \propto q$ if an AKA effect [Frisch et al., Physica D: Nonlinear Phenomena 28, 382 (1987)] is present or a negative eddy viscosity scaling $\sigma \propto q^2$ in its absence. This holds both for the $\text{Re}\ll 1$ regime where previously derived asymptotic results are verified but also for $\text{Re}=O\left(1\right)$ that is beyond their range of validity. Furthermore, for values of $\text{Re}$ above a critical value ${\text{Re}}_S^c$ beyond which small-scale instabilities are present, the growth rate becomes independent of $q$ and the energy of the perturbation at large scales decreases with scale separation. The nonlinear behavior of these large-scale instabilities is also examined in the nonlinear regime where the largest scales of the system are found to be the most dominant energetically. These results are interpreted by low-order models.

We consider thin fluid films placed on thermally conductive substrates and exposed to a time-dependent spatially uniform heat source. The evolution of the films is considered within the long-wave framework in the regime such that both fluid-substrate interaction, modeled via disjoining pressure, and Marangoni forces are relevant. We analyze the problem by the means of linear stability analysis as well as time-dependent nonlinear simulations. The main finding is that when self-consistent computation of the temperature field is performed, a complex interplay of different instability mechanisms results. This includes either monotonous or oscillatory dynamics of the free surface. This oscillatory behavior is absent if the film temperature is assumed to be slaved to the current value of the film thickness. The results are discussed within the context of liquid metal films but are of relevance to dynamics of any thin film involving variable temperature of the free surface, such that the temperature and the film interface itself evolve on comparable time scales.

In this paper we present three-dimensional fully resolved numerical simulations of shock propagation in air over a face centered cubic (fcc) array of particles. It is well know that shock interaction with a single particle results in nonmonotonic drag on the particle and that the peak force is an order of magnitude greater than the steady-state force. However, there is currently a substantial lack of numerical results for shock propagation over multiple particles. We therefore compute the unsteady inviscid drag coefficient as a function of time for the fcc array of particles and investigate the effect of varying the shock Mach number and the volume fraction. We compare the unsteady drag for the fcc array against the unsteady drag for a single spherical particle and against the unsteady drag for a structured one-dimensional array of spherical particles and make relevant observations. We also plot the local Mach number contours to explain the various observed complex physical mechanisms occurring during shock-particle interaction. Finally, since shock interaction with particles lead to transmitted and reflected waves, we compute the average pressure in the computational domain to characterize the strength of the transmitted shock wave to study pressure attenuation behind the particle barrier. By analyzing the pressure field we can determine the effect of particles on the flow.

We study the transition in dimensionality of a three-dimensional magnetohydrodynamic flow forced only mechanically when the strength of a magnetic guide field is gradually increased. We use numerical simulations to consider cases in which the mechanical forcing injects (or not) helicity in the flow. As the guide field is increased, the strength of the magnetic field fluctuations decreases as a power law of the guide field intensity. We show that for strong enough guide fields the helical magnetohydrodynamic flow can become almost two-dimensional. In this case, the mechanical energy can undergo a process compatible with an inverse cascade, being transferred preferentially towards scales larger than the forcing scale. The presence of helicity changes the spectral scaling of the small magnetic field fluctuations, and affects the statistics of the velocity field and of the velocity gradients. Moreover, at small scales the dynamics of the flow becomes dominated by a direct cascade of helicity, which can be used to derive scaling laws for the velocity field.

We carry out direct numerical simulations of the fluctuating Navier-Stokes equation together with the particle equations governing the motion of a nanosized particle or nanoparticle (NP) in a cylindrical tube. The effects of the confining boundary, its curvature, particle size, and particle density variations are investigated. To reveal how the nature of the temporal correlations (hydrodynamic memory) in the inertial regime is altered by the full hydrodynamic interaction due to the confining boundaries, we employ the arbitrary Lagrangian-Eulerian method to determine the dynamical relaxation of a spherical NP located at various positions in the medium over a wide span of time scales compared to the fluid viscous relaxation time ${\tau }_{\nu }=a^2/\nu$, where $a$ is the spherical particle radius and $\nu$ is the kinematic viscosity. The results show that, as compared to the behavior of a particle in regions away from the confining boundary, the velocity autocorrelation function for a particle in the lubrication layer initially decays exponentially with a Stokes drag enhanced by a factor that is proportional to the ratio of the particle radius to the gap thickness between the particle and the wall. Independent of the particle location, beyond time scales greater than $a^2/\nu$, the decay is always algebraic followed by a second exponential decay (attributed to the wall curvature) that is associated with a second time scale $D^2/\nu$, where $D$ is the vessel diameter.

We report on a series of results provided by three-dimensional numerical simulations of nearly spheroidal bubbles freely rising and deforming in a still liquid in the regime close to the transition to path instability. These results improve upon those of recent computational studies [Cano-Lozano et al., Int. J. Multiphase Flow 51, 11 (2013); Phys. Fluids 28, 014102 (2016)] in which the neutral curve associated with this transition was obtained by considering realistic but frozen bubble shapes. Depending on the dimensionless parameters that characterize the system, various paths geometries are observed by letting an initially spherical bubble starting from rest rise under the effect of buoyancy and adjust its shape to the surrounding flow. These include the well-documented rectilinear axisymmetric, planar zigzagging, and spiraling (or helical) regimes. A flattened spiraling regime that most often eventually turns into either a planar zigzagging or a helical regime is also frequently observed. Finally, a chaotic regime in which the bubble experiences small horizontal displacements (typically one order of magnitude smaller than in the other regimes) is found to take place in a region of the parameter space where no standing eddy exists at the back of the bubble. The discovery of this regime provides evidence that path instability does not always result from a wake instability as previously believed. In each regime, we examine the characteristics of the path, bubble shape, and vortical structure in the wake, as well as their couplings. In particular, we observe that, depending on the fluctuations of the rise velocity, two different vortex shedding modes exist in the zigzagging regime, confirming earlier findings with falling spheres. The simulations also reveal that significant bubble deformations may take place along zigzagging or spiraling paths and that, under certain circumstances, they dramatically alter the wake structure. The instability thresholds that can be inferred from the computations compare favorably with experimental data provided by various sets of recent experiments guaranteeing that the bubble surface is free of surfactants.