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.

The Leidenfrost state is typically studied by placing droplets on flat or slightly curved surfaces. Here this phenomenon is investigated by depositing water in hot conical bowls. We found that this phase exists even for large amounts of liquid in very narrow cones without considerable effect of the confinement on the Leidenfrost transition temperature $T_L$. At a fixed temperature, $T>T_L$, the total evaporation time $\tau$ has a nonmonotonic dependence on the angle of confinement $\theta$: for large volumes $(\sim 20$ ml) on flat surfaces $\left(\theta \sim 0^{\circ }\right)$, vapor chimneys appear and accelerate the evaporation rate, their frequency diminishes as $\theta$ augments and becomes zero at a certain angle ${\theta }_c$, at which $\tau$ reaches its maximum value; then, $\tau$ decreases again at larger angles because the vapor layer holding up the water becomes thinner due to the increase of hydrostatic pressure and because the geometry facilitates the vapor expulsion along the conical wall. For small volumes $(\sim 1$ ml), surface tension mainly determines the drop curvature and the lifetime is practically independent of $\theta$. Different chimney regimes and oscillation patterns were observed and summarized in a phase diagram. Finally, we developed a simple model to decipher the shape adopted by the liquid volume and its evolution as a function of time, and the predictions are in good agreement with the experimental results.

Reynolds averaged Navier-Stokes models represent the workhorse for studying turbulent flows in academia and in industry. Such single-point turbulence models have limitations in accounting for the influence of the nonlocal physics and flow history on turbulence evolution. In this context, we investigate the sensitivity inherent in such single-point models due to their characterization of the internal structure of homogeneous turbulent flows solely by the means of the Reynolds stresses. For a wide variety of mean flows under diverse conditions, we study the prediction intervals engendered due to this coarse-grained description. The nature of this variability and its dependence on parameters such as the mean flow topology, the initial Reynolds stress tensor, and the relative influence of linear contra nonlinear physics is identified, analyzed, and explicated.

Hypersonic boundary layer flows over a circular cone at moderate incidence angle can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to more efficient excitation of stationary crossflow vortices by surface roughness, such boundary layer flows may transition to turbulence via rapid amplification of the high-frequency secondary instabilities of finite-amplitude stationary crossflow vortices. The amplification characteristics of these secondary instabilities are investigated for crossflow vortices generated by an azimuthally periodic array of roughness elements over a 7° half-angle circular cone in a Mach 6 free stream. The analysis is based on both quasiparallel stability theory in the form of a partial-differential-equation-based eigenvalue analysis and plane marching parabolized stability equations that account for the effects of the nonparallel basic state on the growth of secondary disturbances. Depending on the local amplitude of the stationary crossflow mode, the most unstable high-frequency disturbances either originate from the second (i.e., Mack) mode instabilities of the unperturbed boundary layer or correspond to genuine secondary instabilities that reduce to stable disturbances at sufficiently small amplitudes of the stationary crossflow vortex. The predicted frequencies of the dominant secondary disturbances of either type are similar to those measured during wind tunnel experiments at Purdue University and the Technical University of Braunschweig, Germany. Including transverse surface curvature within the quasiparallel predictions does not alter the topology of the unstable modes; however, the resulting changes in both mode shape and disturbance growth rate are rather significant and curvature can be either stabilizing or destabilizing depending on the disturbance frequency and mode type. Nonparallel effects are shown to be strongly destabilizing for secondary instabilities originating from both Mack modes and instabilities of the inclined shear layer bounding the crossflow vortex. Consequently, the two types of instabilities are found to achieve logarithmic amplification factors of up to $N=10$ and $N=7$, respectively. Results also reveal possible phase synchronization between a pair of modes that may have a significant influence on their overall amplification.

For wall-bounded flows, the model of Marusic et al. [Science 329, 193 (2010)] allows one to predict the statistics of the streamwise fluctuating velocity in the inner region, from a measured input signal in the logarithmic region. Normally, a user-defined large-scale portion of the input forms the large-scale content in the prediction by scaling its amplitude, as well as temporally shifting the signal to account for the physical inclination of these scales. Incoherent smaller scales are then fused to the prediction via universally expressed fluctuations that are subject to an amplitude modulation. Here we present a refined version of the model using spectral linear stochastic estimation, which eliminates a user-defined scale separation of the input. Now, an empirically derived transfer kernel comprises an implicit filtering via a scale-dependent gain and phase; this kernel captures the coherent portion in the prediction. An additional refinement of the model embodies a relative shift between the stochastically estimated scales in the prediction and the modulation envelope of the universal small scales. Predictions over a three-decade span of Reynolds numbers, ${\text{Re}}_{\tau }\sim O\left({10}^3\right)$ to $O\left({10}^6\right)$, highlight promising applications of the refined model to high-Reynolds-number flows, in which coherent scales become the primary contributor to the fluctuating energy.

Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.

Active matter is a new class of intrinsically out-of equilibrium material with intriguing properties. The recent upsurge of studies in this field has mostly focused on the spontaneous behavior of these systems. Yet, many systems evolve under external constraints and driving forces, being subjected to both flow and various taxis. We present a new experimental system based on the directional control of magnetotactic bacteria which enables quantitative investigations to complement the challenging theoretical description of such systems. We explore the behavior of self-propelled magnetotactic bacteria as a particularly rich and versatile class of driven matter, whose behavior can be studied under a range of hydrodynamic and magnetic field stimuli. In particular we demonstrate that the competition between cell orientation toward a magnetic field and hydrodynamic flow lead not only to jetting, but to a new pearling instability. This model system illustrates new structuring capabilities of driven active matter.

Oscillatory flows are commonly experienced by swimming micro-organisms in the environment, industrial applications, and rheological investigations. We characterize experimentally the response of the alga Dunaliella salina to oscillatory shear flows and report the surprising discovery that algal swimming trajectories orient perpendicular to the flow-shear plane. The ordering has the characteristics of a resonance in the driving parameter space. The behavior is qualitatively reproduced by a simple model and simulations accounting for helical swimming, suggesting a mechanism for ordering and criteria for the resonant amplitude and frequency. The implications of this work for active oscillatory rheology and industrial algal processing are discussed.

Understanding the conformational dynamics of polymers in time-dependent flows is of key importance for controlling materials properties during processing. Despite this importance, however, it has been challenging to study polymer dynamics in controlled time-dependent or oscillatory extensional flows. In this work, we study the dynamics of single polymers in large-amplitude oscillatory extension (LAOE) using a combination of experiments and Brownian dynamics (BD) simulations. Two-dimensional LAOE flow is generated using a feedback-controlled stagnation point device known as the Stokes trap, thereby generating an oscillatory planar extensional flow with alternating principal axes of extension and compression. Our results show that polymers experience periodic cycles of compression, reorientation, and extension in LAOE, and dynamics are generally governed by a dimensionless flow strength (Weissenberg number $\text{Wi})$ and dimensionless frequency (Deborah number $\text{De})$. Single molecule experiments are compared to BD simulations with and without intramolecular hydrodynamic interactions (HI) and excluded volume (EV) interactions, and good agreement is obtained across a range of parameters. Moreover, transient bulk stress in LAOE is determined from simulations using the Kramers relation, which reveals interesting and unique rheological signatures for this time-dependent flow. We further construct a series of single polymer stretch-flow rate curves (defined as single molecule Lissajous curves) as a function of $\text{Wi}$ and $\text{De}$, and we observe qualitatively different dynamic signatures (butterfly, bow tie, arch, and line shapes) across the two-dimensional Pipkin space defined by $\text{Wi}$ and $\text{De}$. Finally, polymer dynamics spanning from the linear to nonlinear response regimes are interpreted in the context of accumulated fluid strain in LAOE.

The turbulent Rayleigh-Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh-Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in the presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective, and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry.

We show that a volatile liquid drop placed at the surface of a nonvolatile liquid pool warmer than the boiling point of the drop can be held in a Leidenfrost state even for vanishingly small superheats. Such an observation points to the importance of the substrate roughness, negligible in the case considered here, in determining the threshold Leidenfrost temperature. A theoretical model based on the one proposed by Sobac et al. [Phys. Rev. E 90, 053011 (2014)] is developed in order to rationalize the experimental data. The shapes of the drop and of the liquid substrate are analyzed. The model notably provides scalings for the vapor film thickness profile. For small drops, these scalings appear to be identical to the case of a Leidenfrost drop on a solid substrate. For large drops, in contrast, they are different, and no evidence of chimney formation has been observed either experimentally or theoretically in the range of drop sizes considered in this study. Concerning the evaporation dynamics, the radius is shown to decrease linearly with time whatever the drop size, which differs from the case of a Leidenfrost drop on a solid substrate. For high superheats, the characteristic lifetime of the drops versus the superheat follows a scaling law that is derived from the model, but, at low superheats, it deviates from this scaling by rather saturating.

The nearly frictionless flow of water in narrow carbon nanotubes is a genuine nanofluidic phenomenon with many prospects of applications in membrane technology. When inner dissipation is vanishing, the limiting factor to high flux lies in the viscous dissipation occurring at the tube mouth. As shown by Gravelle et al. [Gravelle, Joly, Detcheverry, Ybert, Cottin-Bizonne, and Bocquet, Proc. Natl. Acad. Sci. USA 110, 16367 (2013)], these so-called end effects can be reduced by adding a conical entrance. In this work, we take a step further and search for the optimal entrance shape. We use finite element calculations to compute the hydrodynamic resistance of a frictionless tube with superellipse-shaped entrances and propose an approximate analytical model. If perfect slip applies on its wall, an optimal entrance which is only 10 tube radii in length is sufficient to reduce end effects by an order of magnitude, a performance almost three times better than the optimal cone. In the case of partial slip, the resistance decreases with the entrance length before reaching a plateau at an optimal length controlled by liquid-solid slip. Our results are discussed in connection with biological and artificial systems.

Intense recurring bursts of turbulence on a long time scale are observed in direct numerical simulations (DNSs) of channel flow subject to rapid spanwise rotation for a range of Reynolds numbers and rotation speeds. A necessary condition for manifestation of cyclic turbulent bursts is that the Reynolds number and rotation speed are sufficiently high. The principal cause of turbulent bursts is a linearly unstable Tollmien-Schlichting-like wave with a wave vector normal to the rotation axis. This exponentially growing wave breaks down through a secondary instability when its amplitude is large causing a burst of turbulence. A new instability develops once turbulence has subsided leading to a continuous and self-sustained cycle of bursts. In several DNSs a recurring instability happens despite the flow being strongly and continuously turbulent in a part of the channel while in other DNSs turbulence is mostly weak between bursts. DNS observations have been compared to linear stability theory using the spatially averaged velocity of the DNS as base flow. Analysis shows that Tollmien-Schlichting waves are linearly unstable if Reynolds number and rotation speed are sufficiently high and bursts are observed. In several cases a good agreement between predicted and observed growth rate and eigenfunction of the instability is found, but in other cases the growth rate is overpredicted by linear stability theory and in some cases a Tollmien-Schlichting instability is predicted but not observed. Further study indicates that when observations and predictions differ turbulence or other modes alter the unstable wave, thereby reducing its ability to extract energy from the mean flow. In none of the analyzed DNSs was a significant nonlinear energy transfer from the unstable mode to other modes noted. Inclusion of an eddy viscosity in linear stability theory did not notably improve correspondence with DNSs.