The merging of a single row of plumes in a quiescent environment has been studied using irrotational flow theory [G. Rooney, J. Fluid Mech. 771, R1 (2015)]. The present study extends this theory by considering (i) two parallel rows of plumes in a quiescent environment, and (ii) a single row of plumes in a crosswind, with and without a pressure drag term. For plumes in two rows with and without offset, the effect of varying the spacing ratio on the plume dynamics is investigated. Two definitions of the contact height are suggested according to the shape of the velocity potential contours. For a single row of plumes in a crosswind, the governing equations are closed using an entrainment flux evaluated by the irrotational flow theory. This theory predicts the correct near- and far-field similarity solutions in both modest and strong crosswinds. A comparison of the theory in question to previous towing tank experiments yields satisfactory agreement in terms of plume trajectory. The present theory of single and dual rows of plumes is applied to long rows of cooling tower plumes.

We consider the bypass transition in a flat-plate boundary layer subject to free-stream turbulence and compute the evolution of the second-order structure function of the streamwise velocity, $\langle d{u}^2\rangle (\vec{x},\vec{r})$, from the laminar to the fully turbulent region using DNS. In order to separate the contributions from laminar and turbulent events at the two points used to define $du(\vec{x},\vec{r})$, we apply conditional sampling based on the local instantaneous intermittency, $\tau$ (1 for turbulent and 0 for laminar events). Using $\tau (\vec{x},t)$, we define two-point intermittencies, ${\gamma }^{\left(TT\right)}, {\gamma }^{\left(LL\right)}$, and ${\gamma }^{\left(TL\right)}$, which physically represent the probabilities that both points are in turbulent patches, both are in laminar patches, or one is in a turbulent and the other in a laminar patch, respectively. Similarly, we also define the conditionally averaged structure functions, ${\langle d{u}^2\rangle }^{\left(TT\right)}, {\langle d{u}^2\rangle }^{\left(LL\right)}$, and ${\langle d{u}^2\rangle }^{\left(TL\right)}$, and decompose $\langle d{u}^2\rangle (\vec{x},\vec{r})$ in terms of these conditional averages. The derived expressions generalize existing decompositions of single-point statistics to two-point statistics. It is found that in the transition region, laminar streaky structures maintain their geometrical characteristics in the physical and scale space well inside the transition region, even after the initial breakdown to form turbulent spots. Analysis of the ${\langle d{u}^2\rangle }^{\left(TT\right)}$ fields reveals that the outer mode is the dominant secondary instability mechanism. Further analysis reveals how turbulent spots penetrate the boundary layer and approach the wall. The peaks of ${\langle d{u}^2\rangle }^{\left(TT\right)}$ in scale space appear in larger streamwise separations as the transition progresses and this is explained by the strong growth of turbulent spots in this direction. On the other hand, the spanwise separation where the peak occurs remains relatively constant and is determined by the initial inception process. We also analyze the evolution of the two-point intermittency field, ${\gamma }^{\left(TT\right)}$, at different locations. In particular, we study the growth of the volume enclosed within an isosurface of ${\gamma }^{\left(TT\right)}$ and note that it increases in both directions, with growth in the streamwise direction being especially large. The evolution of these conditional two-point statistics sheds light on the transition process from a different perspective and complements existing analyses using single-point statistics.

Rapid magnetic resonance imaging is used to study the interaction between two gas jets injected into a 3D incipiently fluidized bed. At large separation distances and in cases with larger particles, bubbles pinch off from the two jets simultaneously with one another. At small separation distances with smaller particles, a jet grows at one orifice while a jet pinches off to form a bubble at the other orifice, resulting in bubbles pinching off the two jets nearly completely out-of-phase from one another. Discrete particle simulations coupled with computational fluid dynamics reproduce these two patterns. Simulations demonstrate that the asynchronous pattern emerges due to drag forces on the particles causing particle inertia dominate dissipation, causing motion of particles between the jets to become unstable. Specifically, when one jet is growing, it forces particles to move toward the neighboring jet, causing a bubble to break off from the neighboring jet.

The late stage of the free fall of homogeneous and heterogeneous cones in a quiescent water medium and the induced flow are experimentally inspected using three-dimensional particle tracking velocimetry and volumetric particle image velocimetry. The structures shared the same geometry but had different combined specific gravity $\mathrm{SG}\in [1.2,8]$. Results showed four distinct free-fall patterns, which were modulated by the degree of heterogeneity and $\mathrm{SG}$. They included (i) straight fall, (ii) regular sinusoidal-like trajectories with a maximum angle of oscillation with respect to the vertical, ${\theta }_{\max }<\pi /2$, (iii) motions characterized by inclined translations and large rotations with ${\theta }_{\max }>\pi /2$, and (iv) tumbling followed by an irregular motion. The straight fall occurred in cones with $\mathrm{SG}\gtrsim 6$ regardless of the mass distribution. The sinusoidal motions arose in the homogeneous cones with $\mathrm{SG}<3$. The large rotations occurred with heterogeneous cones of $\mathrm{SG}<3$, whereas the tumbling with irregular motions occurred in the heterogeneous cone with the highest ratio between the center of mass and geometrical centroid. Inspection of the linear and angular components of the velocities and accelerations reveal the distinct patterns and the linkage with the surrounding flow.

We study the planar two-dimensional relative induced-charge electrophoretic (ICEP) motion of a pair of identical, ideally polarizable circular cylindrical microparticles carrying no net charge and freely suspended in an unbounded electrolyte solution under a uniform steady (DC) external electric field acting in an arbitrary direction relative to the instantaneous orientation of their line-of-centers (LOC). Within the framework of the thin electric-double-layer (EDL) limit and sufficiently weak fields description of particle paths is obtained via integration of the quasisteady kinematic equations of motion based on the instantaneous geometric configuration. Owing to the inherent nonlinearity of the ICEP mechanism, interaction of the effects of external-field components parallel and perpendicular, respectively, to the LOC results in its rotation which, in turn, determines that particles undergo transient pairing eventually moving apart in the general direction perpendicular to the external field. Dielectrophoresis is demonstrated to only have a secondary effect on the resulting motion.

A small spherical bubble of high internal pressure is inserted into water at constant ambient pressure as a model of a laser-induced bubble. Its subsequent dynamics near a flat solid boundary is studied in dependence on the distance of the bubble to the boundary by numerically solving the Navier-Stokes equations with the help of the open source software environment OpenFOAM. Implemented is the finite-volume method for discretization of the equations of motion and the volume-of-fluid method for capturing the interface between the bubble interior and exterior. The bubble contains a small amount of noncondensable gas that is treated as an ideal gas. The liquid is water obeying the Tait equation. Surface tension is included where necessary. The evolution of the bubble shape and a selection of pressure and velocity fields are given for normalized distances $D^{*}=D/R_{\max }$ between 0 and 3 ($D$ is the initial distance of the bubble center to the boundary and $R_{\max }$ is the maximum radius the bubble would attain without any boundary). The value $R_{\max }=$ 500 $\mu \mathrm{m}$ is chosen for the study. Normal axial-jet formation ($\sim 100$ m/s) by axial flow focusing is found for $0.24\le D^{*}\le 3$ and the change to a different type of axial-jet formation ($\sim 1000$ m/s) by annular-liquid-flow collision for bubbles very close to the solid boundary ($0\le D^{*}\le 0.2$). The transition region ($0.2<D^{*}<0.24$) is characterized by additional inbound and outbound annular jets. Remarkably, the inclusion of the viscosity of the water is decisive to get the fast jets.

The effect of surfactants on the tail and film dynamics of elongated gas bubbles propagating through circular capillary tubes is investigated by means of an extensive three-dimensional numerical study using a hybrid front-tracking/level-set method. The focus is on the visco-inertial regime, which occurs when the Reynolds number of the flow is much larger than unity. Under these conditions, “clean” bubbles exhibit interface undulations in the proximity of the tail, with an amplitude that increases with the Reynolds number. We perform a systematic analysis of the impact of a wide range of surfactant properties, including elasticity, bulk surfactant concentration, solubility, and diffusivity, on the bubble and flow dynamics in the presence of inertial effects. The results show that the introduction of surfactants is effective in suppressing the tail undulations as they tend to accumulate near the bubble tail. Here large Marangoni stresses are generated, which lead to a local “rigidification” of the bubble. This effect becomes more pronounced for larger surfactant elasticities and adsorption depths. At reduced surfactant solubility, a thicker rigid film region forms at the bubble rear, where a Couette film flow is established, while undulations still appear at the trailing edge of the downstream “clean” film region. In such conditions, the bubble length becomes an influential parameter, with short bubbles becoming completely rigid.

Rotating fluids frequently show nonlinear wave interactions and turbulence. This is true in particular for nonuniformly rotating systems. One example of such a nonuniform rotating object is the Earth. Due to its fast rotation it is not exactly spherical. As a result of the interaction with the Sun and Moon, the nonspherical Earth cannot rotate uniformly but shows precession and libration. This has consequences for the fluid enclosed in the outer Earth core. Due to the forcing it might become turbulent, one of the key factors in the present theories explaining the generation of the geomagnetic field. In the present paper we show experimental results from a system that is simpler than classical precession experiments but still shows very similar wave interactions and a collapse to turbulence. This system consists of a partly filled rotating annulus that rotates about its symmetry axis slightly tilted with respect to the gravity vector and allows us to explore Ekman numbers ranging from $7.9\times {10}^{-6}$ to $3.2\times {10}^{-5}$. In analogy to the more classical precession experiments, we also find a resonant collapse when the forcing frequency corresponds with a resonant frequency of the rotating tank. The forced mode and two free Kelvin modes give rise to triadic resonance. Besides the parametric triadic resonance we further observed a shear-type instability of the nonlinearly excited geostrophic flow. This instability gives rise to a barotropic mode that interacts with the forced mode and generates secondary modes. We also observed a dependency of the mode frequencies on the Ekman number, which can, at least partly, be explained by a Doppler shift due to the mean flow. Finally, we try to connect our data to a low-order dynamical system that describes the main features of single triad interaction in precession experiments. Although this model is originally not designed for the multiple triads we observe, it is still useful for a qualitative understanding of mode interactions, e.g., for the mechanism of geostrophic mode excitation.

The formation and destabilization of viscoelastic filaments are of importance in many industrial and biological processes. Filament instabilities have been observed for viscoelastic fluids but recently also for soft elastic solids. In this work, we address the central question of how to connect the dynamical behavior of viscoelastic liquids to that of soft elastic solids. We take advantage of a biopolymer material whose viscoelastic properties can be tuned over a very large range by its pH, and study the destabilization and ensuing instabilities in uniaxial extensional deformation. In agreement with very recent theory, we find that the interface shapes dictated by the instabilities converge to an identical similarity solution for low-viscosity viscoelastic fluids and highly elastic gels. We thereby bridge the gap between very fluid and strongly elastic materials. In addition, we provide direct evidence that at late times an additional filament instability occurs due to a dynamical phase separation.

We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to $R_{\lambda }=650$, with excellent small-scale resolution of $k_{\text{max}}\eta \approx 6$, and additionally at $R_{\lambda }=1300$ with $k_{\text{max}}\eta \approx 3$, where $k_{\text{max}}$ is the maximum resolved wave number and $\eta$ is the Kolmogorov length scale. We find that for a limited range of wave numbers $k$ past the bottleneck, in the range $0.15\lesssim k\eta \lesssim 0.5$, the spectra for all $R_{\lambda }$ display a universal stretched exponential behavior of the form $exp(-k^{2/3})$, in rough accordance with recent theoretical predictions. In contrast, the stretched exponential fit does not possess a unique exponent in the near dissipation range $1\lesssim k\eta \lesssim 4$, but one that persistently decreases with increasing $R_{\lambda }$. This region serves as the intermediate dissipation range between the $exp(-k^{2/3})$ region and the far dissipation range $k\eta \gg 1$ where analytical arguments as well as DNS data with superfine resolution [S. Khurshid et al., Phys. Rev. Fluids 3, 082601 (2018)] suggest a simple $exp(-k\eta )$ dependence. We briefly discuss our results in connection to the multifractal model.

We show how phasing between tandem bioinspired fins flapping at high-stroke amplitudes modulates rear fin thrust production and wake characteristics. Load cell thrust measurements show that the rear fin generates 25% more thrust than the front fin when it lags the latter by a quarter cycle, and performs 8% worse when it leads the front fin by the same amount. The flow interactions between the fins responsible for these observations are analyzed using two-dimensional particle image velocimetry measurements and three-dimensional computational fluid dynamics simulations. Distributions of velocity elucidate variations in the effective flow induced on the rear fin for different phase offsets. Vortex structure interactions and particle rakes reveal the contributions of the leading- and trailing-edge vortices shed by the front fin in modulating the suction at the rear fin leading edge. Furthermore, the wake structure far downstream of the fins changes in its coherence, axial and radial extents for the different phase offsets. These findings are relevant for the design and performance optimization of various unmanned underwater vehicles that utilize such tandem systems.

Drop motion on a dry solid substrate is determined by the lateral adhesion force associated with the contact angle hysteresis and by any applied external forces. In this experimental and computational study the lateral adhesion force is measured directly, through dragging of a drop along a surface by a cantilever. These force measurements are compared with the estimated value of the aerodynamic force needed to displace a wall-bound drop in a channel flow. The scaled lateral adhesion and aerodynamic forces are functions of the capillary number. Their values agree for capillary numbers higher than ${10}^{-4}$. For smaller capillary numbers, $\mathrm{Ca}<{10}^{-4}$, the value of the required aerodynamic force can be smaller than the lateral adhesion force. This unexpected result is explained by the complex three-dimensional periodic motion of the drop, similar to a shuffling gait. During the shuffling gait propagation, at any instant only a part of the drop contact line propagates, which requires a smaller force to displace the drop. Alternating motion of different parts of the contact line forms a continuous shuffling gait propagation. As soon as the aerodynamic force exceeds a threshold value $F^{*}$ the drop slides nearly steadily.

Recent experiments have shown that liquid Leidenfrost drops levitated by their vapor above a flat hot surface can exhibit symmetry-breaking spontaneous dynamics [A. Bouillant et al., Nat. Phys. 14, 1188 (2018)]. Motivated by these observations, we theoretically investigate the translational and rotational dynamics of Leidenfrost drops on the basis of a simplified two-dimensional model, focusing on near-circular drops small relative to the capillary length. The model couples the equations of motion of the drop, which flows as a rigid wheel, and thin-film equations governing the vapor flow, the profile of the deformable vapor-liquid interface, and thus the hydrodynamic forces and torques on the drop. In contrast to previous analytical models of Leidenfrost drops levitating above a flat surface which predict only symmetric solutions, we find that the symmetric Leidenfrost state is unstable above a critical drop radius: $R_1$ for a free drop and $R_2>R_1$ for an immobilized drop. In these respective cases, symmetry breaking is manifested in supercritical pitchfork bifurcations into steady states of pure rolling and constant angular velocity. In further qualitative agreement with the experiments, when a symmetry-broken immobilized drop is suddenly released it initially moves at an acceleration $\alpha g$, where $\alpha$ is an angle characterizing the slope of the liquid-vapor profile and $g$ is the gravitational acceleration; moreover, $\alpha$ exhibits a maximum with respect to the drop radius at a radius increasing with the temperature difference between the surface and the drop.

We study the effect of inhomogeneous environments on the swimming direction of the microalgae Chlamydomonas reinhardtii (CR) in the presence of a light stimulus. Positive or negative phototaxis describe the ability of microorganisms to bias their swimming toward or away from a light source. Here we consider microswimmers with negative phototaxis in a microfluidic device with a microfabricated square lattice of pillars as obstacles. We measured a mean deflection of microswimmers that shows an interesting nonlinear dependence on the direction of the guiding light beam with respect to the symmetry axes of the pillar lattice. By simulating a model swimmer in a pillar lattice and analyzing its scattering behavior, we identified the width of the reorientation distribution of swimmers to be also crucial for the nonlinear behavior of the swimmer deflection. On the basis of these results we suggest in addition an analytical model for microswimmers, where the pillar lattice is replaced by an anisotropic scattering medium, that depends only on a scattering rate and the width of the reorientation distribution of swimmers. This flexible and handy model fits the experimental results as well. The presented analysis of the deflection of light guided swimmers through pillar lattice may be used for separating swimmers having different reorientation distributions.

We study the retraction of a viscous liquid sheet of finite length with negligible effect of the ambient medium. Using the long-wavelength model we derive the scaling laws and similarity solution for the interface profile of the retracting sheet. Far from the tip, the similarity solution for the interface profiles converges to an asymptotic value of 1/4. Direct numerical simulations are performed to compare the theoretical results with the simulations. When the inertia is negligible, the interface profiles remain flat during the retraction process which is in agreement with the self-similar solution. Using this similarity solution we derive the expression for the temporal variation of the tip speed for finite liquid sheets. We demonstrate that unlike an infinite sheet where the sheet retracts with a steady speed (known as Taylor-Culick speed), the tip speed decreases as a function of time for a finite liquid sheet. This is true when the viscous effects are larger than or of the same order with the inertia effects. Otherwise, the sheet retracts with the formation of a bulbous tip whose speed reaches a value closer to the Taylor-Culick speed.

We present a new mesoscale model for ionic liquids based on a low Mach number fluctuating hydrodynamics formulation for multicomponent charged species. The low Mach number approach eliminates sound waves from the fully compressible equations leading to a computationally efficient incompressible formulation. The model uses a Gibbs free-energy functional that includes enthalpy of mixing, interfacial energy, and electrostatic contributions. These lead to a new fourth-order term in the mass equations and a reversible stress in the momentum equations. We calibrate our model using parameters for [$\mathrm{DMPI}+$][F6P-], an extensively studied room temperature ionic liquid (RTIL), and numerically demonstrate the formation of mesoscopic structuring at equilibrium in two and three dimensions. In simulations with electrode boundaries the measured double-layer capacitance decreases with voltage, in agreement with theoretical predictions and experimental measurements for RTILs. Finally, we present a shear electroosmosis example to demonstrate that the methodology can be used to model electrokinetic flows.

Stability analysis of gravity-driven flow of a thermoviscous liquid on the exterior surface of a uniformly heated or cooled vertical cylinder is presented. The film evolution model derived using lubrication approximation consists of four dimensionless groups, namely, Marangoni number, Biot number, Bond number, and thermoviscosity number. The viscosity of the liquid is modeled as an exponentially varying function of temperature. The thermocapillary stress significantly affects the Rayleigh-Plateau instability for flow over a nonisothermal cylinder with intricate dependence on various parameters involved. For the temporally unstable system, spatiotemporal stability analysis is performed to delineate the parameter regions for convectively and absolutely unstable systems. Brigg's criterion is employed and the critical value of a composite parameter $\beta$ is evaluated to study the transition from convective to absolute instability. A proper rescaling of the dispersion relation shows that the condition on the composite parameter is $\beta <1.507$ for the existence of absolute instability, which is consistent with an earlier work on isothermal flows. Further, an expression is found for the critical composite Marangoni number beyond which the film is always absolutely unstable independent of the Bond number. This critical value is shown to be an increasing function of thermoviscosity number. Results from the nonlinear simulations are in agreement with the predictions of the linear temporal and spatiotemporal analyses.

We investigate two distinct scenarios of spatial modulation that are candidate mechanisms for streamwise localization of waves in two-dimensional plane Poiseuille flow. The first one stems from a symmetry-breaking bifurcation that disrupts the half-shift and reflect equivariance of Tollmien-Schlichting waves (TSW). A new state, an asymmetric TSW (ATSW), emerges from unstable lower-branch TSWs at subcritical Reynolds number and undergoes subharmonic Hopf bifurcations that lead to branches of asymmetric time-periodic space-modulated waves (MATSW). Streamwise modulation does not evolve into localization within the range of parameters explored. In breaking the last standing remnants of the reflectional symmetry about the channel midplane, ATSW and MATSW admit a bias toward either one of the channel walls, thus bearing a potential for explaining near-wall structures that are typical of developed turbulence. The second scenario follows the fate of a branch of time-periodic space-modulated TSWs (MTSW) initially discovered by Mellibovsky and Meseguer [J. Fluid Mech. 779, R1 (2015)]. We find that these waves can lead to localization but the mechanism is not new, as they do so through their connection, by means of a codimension-2 bifurcation point, with other known localizing MTSWs. The codimension-2 point is, however, responsible for the appearance of MTSWs that exclusively bridge upper-branch TSW-trains of different number of replicas. In this respect, these MTSWs possess all required properties that single them out as possible constituents of the strange saddle that governs domain-filling turbulent dynamics at high Reynolds numbers.

We investigate the local energy flux rate ${\mathrm{\Pi }}_{\ell }\left(\mathbf{x}\right)$ towards small scales in isotropic turbulent flows using direct numerical simulations and applying different low-pass filters. Two different filters are examined: A sharp Fourier filter and a Gaussian filter. The probability density function (PDF) of the local energy flux is calculated for the different filters and for different filtering scales. It is shown that the local energy flux is a largely fluctuating quantity taking both negative and positive values and this is more pronounced for the sharp filter. The variance, skewness, and kurtosis of these fluctuations are shown to increase as the filtering scale is decreased. Furthermore, we calculate the joint PDF of ${\mathrm{\Pi }}_{\ell }\left(\mathbf{x}\right)$ with the local filtered strain rate $S_{\ell }$ and the enstrophy ${\mathrm{\Omega }}_{\ell }$. The flux shows a good correlation with the strain, but not with the enstrophy. It is shown that its conditional mean value scales like ${\langle {\mathrm{\Pi }}_{\ell }\rangle }_S\propto {\ell }^2{S}_{\ell }^3$ in support of the Smagorinsky eddy viscosity model. Nonetheless, strong fluctuations exist around this value that also need to be modeled. We discuss the implications of our results for subgrid scale models and propose new modeling directions.

Steady and oscillatory instabilities of buoyancy convection in a laterally heated cube with perfectly thermally insulated horizontal boundaries and perfectly thermally conducting spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from ${100}^3$ to ${256}^3$ finite volumes. It is revealed that en route to unsteadiness the flow undergoes a steady symmetry-breaking pitchfork bifurcation, which breaks its reflection and two-dimensional rotational symmetries. With a further increase of the Grashof number, the nonsymmetric flow bifurcates into an oscillatory state via a Hopf bifurcation. It is argued that the steady symmetry-breaking bifurcation takes place owing to the instability of counter-rotating vortical motions. The oscillatory instability develops as a result of the interaction between the unstable boundary layer flow and the stabilizing effect of the stable temperature stratification.