Circular systems are advantageous for interfacial studies since they do not suffer from end effects, but their hydrodynamics is more complicated because their flows are not unidirectional. Here, we analyze the shear rheology of a harmonically driven knife-edge viscometer through experiments and computations based on the Navier-Stokes equations with a Newtonian interface. The measured distribution of phase lag in the surface velocity relative to the knife-edge speed is found to have a good signal-to-noise ratio and provides robust comparisons to the computations. For monomolecular films of stearic acid, the surface shear viscosity deduced from the model was found to be the same whether the film is driven steady or oscillatory, for an order of magnitude range in driving frequencies and amplitudes. Results show that increasing either the amplitude or forcing frequency steepens the phase lag next to the knife edge. In all cases, the phase lag is linearly proportional to the radial distance from the knife edge and scales with surface shear viscosity to the power $-1/2$.

Insight into vortex reconnections in superfluids is presented, making use of analytical results and numerical simulations of the Gross-Pitaevskii model. Universal aspects of the reconnection process are investigated by considering different initial vortex configurations and making use of a recently developed tracking algorithm to reconstruct the vortex filaments. We show that during a reconnection event the vortex lines approach and separate always according to the time scaling $\delta \sim t^{1/2}$ with prefactors that depend on the vortex configuration. We also investigate the behavior of curvature and torsion close to the reconnection point, demonstrating analytically that the curvature can exhibit a self-similar behavior that might be broken by the development of shocklike structures in the torsion.

We introduce a regime of the coalescence cascade of a liquid drop—the damped coalescence cascade (DCC)—where the rebound of daughter drops is suppressed. DCC typically occurs when the surface tension difference between the bath and the drop is larger than a critical value. A local Marangoni flow generated in the bath at every pinch-off is expected to accelerate air drainage in the gap between the daughter drop and the bath, and thus leads to suppression of the rebound of the daughter drop. Both scaling arguments and lubrication calculations demonstrate faster air drainage in the presence of local Marangoni flow.

We experimentally investigate the self-sustained, star-shaped oscillations of Leidenfrost drops. The drops levitate on a cushion of evaporated vapor over a heated, curved surface. We observe modes with $n=2\text{–}13$ lobes around the drop periphery. We find that the wavelength of the oscillations depends only on the capillary length of the liquid and is independent of the drop radius and substrate temperature. However, the number of observed modes depends sensitively on the liquid viscosity. The dominant frequency of pressure variations in the vapor layer is approximately twice the drop oscillation frequency, consistent with a parametric forcing mechanism. Our results show that the star-shaped oscillations are driven by capillary waves of a characteristic wavelength beneath the drop and that the waves are generated by a large shear stress at the liquid-vapor interface.

We investigate the influence of buoyancy on electroconvection at an ion-exchange membrane in an aqueous electrolyte solution. Electrokinetic instabilities (EKIs) and Rayleigh-Bénard (RB) convection are both known to mix the appearing concentration gradient layer and overcome the limiting current arising from diffusional limitations. The different physics, as well as the interplay between them, are investigated by electrical, flow, and concentration characterization. In the buoyancy stable orientation, an EKI mixing layer, having a low concentration, grows till saturated size. In the buoyancy unstable orientation, RB occurs and dominates the advective transport due to the large system size. When current density $i<5i_{\text{lim}}$, RB mixes the system and EKI does not arise. If $i>5i_{\text{lim}}$ EKI starts before RB and hastens the onset of RB. Upon onset of RB, EKI is suppressed while the overall resistance is still decreased. The onset times of EKI and RB could be predicted using a simple diffusion-migration model based on Fick's second law.

Sediment transport occurs when the nondimensional fluid shear stress $\mathrm{\Theta }$ at the bed surface exceeds a minimum value ${\mathrm{\Theta }}_c$. A large collection of data, known as the Shields curve, shows that ${\mathrm{\Theta }}_c$ is primarily a function of the shear Reynolds number ${\mathrm{Re}}_{*}$. It is commonly assumed that $\mathrm{\Theta }>{\mathrm{\Theta }}_c\left({\mathrm{Re}}_{*}\right)$ occurs when the ${\mathrm{Re}}_{*}$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify ${\mathrm{\Theta }}_c\left({\mathrm{Re}}_{*}\right)$ as the applied shear stress at which grains cannot stop moving. With respect to grain dynamics, ${\mathrm{Re}}_{*}$ can be viewed as the viscous time scale for a grain to equilibrate to the fluid flow divided by the typical time for the fluid force to accelerate a grain over the characteristic bed roughness. We performed simulations of granular beds sheared by a model fluid, varying only these two time scales. We find that the critical Shields number ${\mathrm{\Theta }}_c\left({\mathrm{Re}}_{*}\right)$ obtained from the model mimics the Shields curve and is insensitive to the grain properties, the model fluid flow, and the form of the drag law. Quantitative discrepancies between the model results and the Shields curve are consistent with previous calculations of lift forces at varying ${\mathrm{Re}}_{*}$. Grains at low ${\mathrm{Re}}_{*}$ find more stable configurations than those at high ${\mathrm{Re}}_{*}$ due to differences in the grain reorganization dynamics. Thus, instead of focusing on mechanical equilibrium of a typical grain at the bed surface, ${\mathrm{\Theta }}_c\left({\mathrm{Re}}_{*}\right)$ may be better described by the stress at which mobile grains cannot find a stable configuration and stop moving.

The features of turbulence modulation produced by a heavy-loaded suspension of small solid particles or liquid droplets are discussed by using a physically based regularization of particle-fluid interactions. The approach allows a robust description of the small-scale properties of the system exploiting the convergence of the statistics with respect to the regularization parameter. It is shown that sub-Kolmogorov particles or droplets modify the energy spectrum, leading to a scaling law, $E\left(k\right)\propto k^{-4}$, that emerges at small scales where the particle forcing balances the viscous dissipation. This regime is confirmed by direct numerical simulation data of a particle-laden statistically steady homogeneous shear flow, demonstrating the ability of the regularized model to capture the relevant small-scale physics. The energy budget in spectral space, extended to account for the interphase momentum exchange, highlights how the particle provides an energy sink in the production range that turns into a source at small scales. Overall, the dissipative fluid-particle interaction is found to stall the energy cascade processes typical of Newtonian turbulent flows. In terms of particle statistics, clustering at small scale is depleted, with potential consequences for collision models.

Eddi et al. [Phys. Rev Lett. 102, 240401 (2009)] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928)], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet's position.

An inverse cascade, energy transfer to progressively larger scales, is a salient feature of two-dimensional turbulence. If the cascade reaches the system scale, it creates a coherent flow expected to have the largest available scale and conform with the symmetries of the domain. In a doubly periodic rectangle, the mean flow with zero total momentum was therefore believed to be unidirectional, with two jets along the short side; while for an aspect ratio close to unity, a vortex dipole is expected. Using direct numerical simulations, we show that in fact neither is the box symmetry respected nor the largest scale realized: the flow is never purely unidirectional since the inverse cascade produces coherent vortices, whose number and relative motion are determined by the aspect ratio. This spontaneous symmetry breaking is closely related to the hierarchy of averaging times. Long-time averaging restores translational invariance due to vortex wandering along one direction, and gives jets whose profile, however, can neither be deduced from the largest-available-scale argument, nor from the often employed maximum-entropy principle or quasilinear approximation.

Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures traveling coherently through the inertial range. These solutions might influence the energy transfer and the anomalous scaling properties empirically observed for the forced and viscous models. In this paper we present a study of the instantonic solutions for a set of four shell models of turbulence based on the exact decomposition of the Navier-Stokes equations in helical eigenstates. We find that depending on the helical structure of each model, instantons are chaotic or regular. Some instantonic solutions tend to recover mirror symmetry for scales small enough. Models that have anomalous scaling develop regular nonchaotic instantons. Conversely, models that have nonanomalous scaling in the stationary regime are those that have chaotic instantons. The direction of the energy carried by each single instanton tends to coincide with the direction of the energy cascade in the stationary regime. Finally, we find that whenever the small-scale stationary statistics is intermittent, the instanton is less steep than the dimensional Kolmogorov scaling, independently of whether or not it is chaotic. Our findings further support the idea that instantons might be crucial to describe some aspects of the multiscale anomalous statistics of shell models.

Although the roll-streak structure is ubiquitous in both observations and simulations of pretransitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the roll-streak structure has been invoked to explain its appearance as resulting from chance occurrence in the background turbulence of perturbations configured to optimally excite it. However, there is an alternative interpretation for the role of free-stream turbulence in the genesis of the roll-streak structure, which is that the background turbulence interacts with the roll-streak structure to destabilize it. Statistical state dynamics (SSD) provides analysis methods for studying instabilities of this type that arise from interaction between the coherent and incoherent components of turbulence. SSD in the form of a closure at second order is used in this work to analyze the cooperative eigenmodes arising from interaction between the coherent streamwise invariant component and the incoherent background component of turbulence. In pretransitional Couette flow a manifold of stable modes with roll-streak form is found to exist in the presence of low-intensity background turbulence. The least stable mode of this manifold is destabilized at a critical value of a parameter controlling the background turbulence intensity and a finite-amplitude roll-streak structure arises from this instability through a bifurcation in this parameter. Although this bifurcation has analytical expression only in the infinite ensemble formulation of second order SSD, referred in this work as the S3T system, it is closely reflected in numerical simulations of both the dynamically similar quasilinear system, referred to as the restricted nonlinear (RNL) system, as well as in the full Navier-Stokes equations. This correspondence is verified using ensemble implementations of the RNL system and the Navier-Stokes equations. The S3T system also predicts a second bifurcation at a higher value of the turbulent excitation parameter that results in destabilization of the finite-amplitude roll-streak equilibria. This second bifurcation is shown to lead first to time dependence of the roll-streak structure in the S3T system and then to chaotic fluctuation corresponding to minimal channel turbulence. This transition scenario is also verified in simulations of the RNL system and of the Navier-Stokes equations. This bifurcation from a finite-amplitude roll-streak equilibrium provides a direct route to the turbulent state through the S3T roll-streak instability.

A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics, we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius ${\beta }_{\max }$. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter ${\mu }_f$. Moreover, our analysis shows that dissipation at the contact line can limit the dynamics and we describe ${\beta }_{\max }$ by the scaling law ${\beta }_{\max }\sim {(\text{Re}{\mu }_{\mathrm{l}}/{\mu }_f)}^{1/2}$ that is a function of the droplet viscosity $\left({\mu }_{\mathrm{l}}\right)$ and its Reynolds number $\left(\text{Re}\right)$.

A numerical model for direct phase-resolved simulation of nonlinear ocean waves propagating through fragmented sea ice is proposed. In view are applications to wave propagation and attenuation across the marginal ice zone. This model solves the full equations for nonlinear potential flow coupled with a nonlinear thin-plate formulation for the ice cover. A key contribution is to modeling fragmented sea ice, which is accomplished by allowing the coefficient of flexural rigidity to vary spatially so that distributions of ice floes can be directly specified in the physical domain. Two-dimensional simulations are performed to examine the attenuation of solitary waves by scattering through an irregular array of ice floes. Two different measures based on the wave profile are used to quantify its attenuation over time for various floe configurations. Slow (near linear) or fast (exponential-like) decay is observed depending on such parameters as incident wave height, ice concentration, and ice fragmentation.

We present a similarity transformation for the mean velocity profiles in sink flow turbulent boundary layers, including effects of blowing and suction. It is based on symmetry analysis which transforms the governing partial differential equations (for mean mass and momentum) into an ordinary differential equation and yields a new result including an exact, linear relation between the mean normal ($V$) and streamwise ($U$) velocities. A characteristic length function is further introduced which, under a first order expansion (whose coefficient is $\eta$) in wall blowing and suction velocity, leads to the similarity transformation for $U$ with the value of $\eta \approx -1/9$. This transformation is shown to be a group invariant and maps different $U$ profiles under different blowing and suction conditions into a (universal) profile for no blowing or suction. Its inverse transformation enables predictions of all mean quantities in the mean mass and momentum equations, in good agreement with DNS data.

Two vortices of opposite sign in two dimensions merely move along parallel lines. We show that even a small buoyancy completely changes this dynamics. When the vortices are of different density from their surroundings, buoyancy produces a lateral drift by Kutta lift. This causes the density patches to merge, and the vortex dipole to collapse. This is followed by a rapid upward (for light vortices) ejection and creation of small-scale structures by baroclinic torque. Our simple analytical equation explains the trajectory of the vortices. We show that these events occur in viscous simulations of many buoyant vortices.

Inertial waves are known to exist in the Earth's rapidly rotating outer core and could be important for the dynamo generation. It is well known that a monochromatic inertial plane wave traveling parallel to the rotation axis (along positive $z$) has negative helicity while the wave traveling antiparallel (negative $z$) has positive helicity. Such a helicity segregation, north and south of the equator, is necessary for the ${\alpha }^2$-dynamo model based on inertial waves [Davidson, Geophys. J. Int. 198, 1832 (2014)] to work. The core is likely to contain a myriad of inertial waves of different wave numbers and frequencies. In this study, we investigate whether this characteristic of helicity segregation also holds for an inertial wave packet comprising waves with the same sign of $C_{g,z}$, the $z$ component of group velocity. We first derive the polarization relations for inertial waves and subsequently derive the resultant helicity in wave packets forming as a result of superposition of two or more waves. We find that the helicity segregation does hold for an inertial wave packet unless the wave numbers of the constituent waves are widely separated. In the latter case, regions of opposite color helicity do appear, but the mean helicity retains the expected sign. An illustration of this observation is provided by (a) calculating the resultant helicity for a wave packet formed by superposition of four upward-propagating inertial waves with different wave vectors and (b) conducting the direct numerical simulation of a Gaussian eddy under rapid rotation. Last, the possible effects of other forces such as the viscous dissipation, the Lorentz force, buoyancy stratification, and nonlinearity on helicity are investigated and discussed. The helical structure of the wave packet is likely to remain unaffected by dissipation or the magnetic field, but can be modified by the presence of linearly stable stratification and nonlinearity.

A liquid droplet on a hot solid can generate enough vapor to prevent its contact on the surface and reduce the rate of heat transfer, the so-called Leidenfrost effect. We show theoretically and experimentally that for a sufficiently high electrostatic potential on the droplet, the formation of the vapor layer is suppressed. The interplay of the destabilizing electrostatic force and stabilizing capillary force and evaporation determines the minimum or threshold voltage to suppress the Leidenfrost effect. Linear stability theory accurately predicts threshold voltages for different size droplets and varying temperatures.

We study the effect of a no-slip rigid boundary on the dynamics of a flexible helical filament rotating in a viscous fluid, at low Reynolds number conditions (Stokes limit). This system is taken as a reduced model for the propulsion of uniflagellar bacteria, whose locomotion is known to be modified near solid boundaries. Specifically, we focus on how the propulsive force generated by the filament, as well as its buckling onset, are modified by the presence of a wall. We tackle this problem through numerical simulations that couple the elasticity of the filament, the hydrodynamic loading, and the wall effect. Each of these three ingredients is respectively modeled by the discrete elastic rods method (for a geometrically nonlinear description of the filament), Lighthill's slender body theory (for a nonlocal fluid force model), and the method of images (to emulate the boundary). The simulations are systematically validated by precision experiments on a rescaled macroscopic apparatus. We find that the propulsive force increases near the wall, while the critical rotation frequency for the onset of buckling usually decreases. A systematic parametric study is performed to quantify the dependence of the wall effects on the geometric parameters of the helical filament.

The mechanism of the collapse of the superhydrophobic state is elucidated for submerged nanoscale textures forming a three-dimensional interconnected vapor domain. This key issue for the design of nanotextures poses significant simulation challenges as it is characterized by diverse time and length scales. State-of-the-art atomistic rare events simulations are applied for overcoming the long time scales connected with the large free energy barriers. In such interconnected surface cavities wetting starts with the formation of a liquid finger between two pillars. This break of symmetry induces a more gentle bend in the rest of the liquid-vapor interface, which triggers the wetting of the neighboring pillars. This collective mechanism, involving the wetting of several pillars at the same time, could not be captured by previous atomistic simulations using surface models comprising a small number of pillars (often just one). Atomistic results are interpreted in terms of a sharp-interface continuum model which suggests that line tension, condensation, and other nanoscale phenomena play a minor role in the simulated conditions.