Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of the large-scale magnetic field is dependent only weakly on changes in flow behavior. In contrast, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field. However, our results are limited to the linear, kinematic dynamo regime; future simulations that include the Lorentz force are therefore necessary to assess the robustness of these results.

The scaling properties of the mean wall-normal velocity $V(x,y)$ in zero-pressure-gradient laminar and turbulent boundary-layer flows are investigated using numerical simulation data, physical experiment data, and integral analyses of the governing equations. The maximum mean wall-normal velocity $V_{\infty }$ and the boundary-layer thickness $\delta$ are evidenced to be the proper scaling for $V$ over most if not all of the boundary layer. This is different from the behavior of the mean streamwise velocity $U$ or the turbulent shear stress $T=-\rho \langle uv\rangle$, which depend on different characteristic length scales in the regions near and away from the surface, respectively. The reason for this apparent difference in scaling behaviors is described physically relative to the downstream development of the $U$ velocity profile and the mechanisms of boundary-layer growth. Insights pertaining to this are further surmised from an analytical relationship for the ratio of the displacement to momentum thickness, i.e., shape factor $H$. Integral analyses using the continuity and mean momentum equation show that $U_{\infty }{V}_{\infty }/u_{\tau }^2=H$, where $u_{\tau }$ is the friction velocity. Both the laminar similarity solution and direct numerical simulation data in post-transitional flows convincingly support this relation. Over the transitional regime, data of sufficiently high quality are lacking to check if this relation remains valid.

We investigate the stability of thin viscous films coated on the inside of a horizontal cylindrical substrate. In such a case, gravity acts both as a stabilizing force through the progressive drainage of the film and as a destabilizing force prone to form droplets via the Rayleigh-Taylor instability. The drainage solution, derived from lubrication equations, is found asymptotically stable with respect to infinitesimally small perturbations, although in reality, droplets often form. To resolve this paradox, we perform an optimal transient growth analysis for the first-order perturbations of the liquid's interface, generalizing the results of Trinh et al. [Phys. Fluids 26, 051704 (2014)]. We find that the system displays a linear transient growth potential that gives rise to two different scenarios depending on the value of the Bond number (prescribing the relative importance of gravity and surface tension forces). At low Bond numbers, the optimal perturbation of the interface does not generate droplets. In contrast, for higher Bond numbers, perturbations on the upper hemicircle yield gains large enough to potentially form droplets. The gain increases exponentially with the Bond number. In particular, depending on the amplitude of the initial perturbation, we find a critical Bond number above which the short-time linear growth is sufficient to trigger the nonlinear effects required to form dripping droplets. We conclude that the transition to droplets detaching from the substrate is noise and perturbation dependent.

Transition induced by stationary streaks undergoing transient growth in a supersonic flat plate boundary layer flow is studied using numerical computations. While the possibility of strong transient growth of small-amplitude stationary perturbations in supersonic boundary layer flows has been demonstrated in previous works, its relation to laminar-turbulent transition cannot be established within the framework of linear disturbances. Therefore, this paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite amplitude streaks in the downstream region, and then studies the modal instability of those streaks as a likely cause for the onset of bypass transition. The nonmodal evolution of linearly optimal stationary perturbations in a supersonic, Mach 3 flat plate boundary layer is computed via the nonlinear plane-marching parabolized stability equations (PSE) for stationary perturbations, or equivalently, the perturbation form of parabolized Navier-Stokes equations. To assess the effect of the nonlinear finite-amplitude streaks on transition, the linear form of plane-marching PSE is used to investigate the instability of the boundary layer flow modified by the spanwise periodic streaks. The onset of transition is estimated using an $N$-factor criterion based on modal amplification of the secondary instabilities of the streaks. In the absence of transient growth disturbances, first mode instabilities in a Mach 3, zero pressure gradient boundary layer reach $N=10$ at ${\text{Re}}_x\approx {10}^7$. However, secondary instability modes of the stationary streaks undergoing transient growth are able to achieve the same $N$-factor at ${\text{Re}}_x<2\times {10}^6$ when the initial streak amplitude is sufficiently large. In contrast to the streak instabilities in incompressible flows, subharmonic instability modes with twice the fundamental spanwise wavelength of the streaks are found to have higher amplification ratios than the streak instabilities at fundamental wavelength. This behavior is shown to be related to the destabilizing influence of the streaks on oblique first mode disturbances, which tend to have longer spanwise wavelengths than those of the optimal stationary disturbances.

Two vortex rings can form a localized configuration whereby they continually pass through one another in an alternating fashion. This phenomenon is called leapfrogging. Using parameters suitable for superfluid helium-4, we describe a recurrence phenomenon that is similar to leapfrogging, which occurs for two coaxial straight vortex filaments with the same Kelvin wave mode. For small-amplitude Kelvin waves we demonstrate that our full Biot-Savart simulations closely follow predictions obtained from a simplified model that provides an analytical approximation developed for nearly parallel vortices. Our results are also relevant to thin-cored helical vortices in classical fluids.

The distributions of flow topologies within the flames representing the corrugated flamelets, thin reaction zones, and broken reaction zone regimes of premixed turbulent combustion are investigated using direct numerical simulation data of statistically planar turbulent ${\mathrm{H}}_2$-air flames with an equivalence ratio $\varphi =0.7$. It was found that the diminishing influence of dilatation rate with increasing Karlovitz number has significant influences on the statistical behaviors of the first, second, and third invariants (i.e., $P,Q$, and $R$) of the velocity gradient tensor. These differences are reflected in the distributions of the flow topologies within the flames considered in this analysis. This has important consequences for those topologies that make dominant contributions to the scalar-turbulence interaction and vortex-stretching terms in the scalar dissipation rate and enstrophy transport equations, respectively. Detailed physical explanations are provided for the observed regime dependences of the flow topologies and their implications on the scalar dissipation rate and enstrophy transport.

We investigate experimentally the influence of the liquid viscosity on the problem of the generation of waves by a turbulent wind at the surface of a liquid, extending the results of Paquier et al. [A. Paquier et al., Phys. Fluids 27, 122103 (2015)] over nearly three decades of viscosity. The surface deformations are measured with micrometer accuracy using the free-surface synthetic schlieren method. We recover the two regimes of surface deformations previously identified: the wrinkle regime at small wind velocity, resulting from the viscous imprint on the liquid surface of the turbulent fluctuations in the boundary layer, and the regular wave regime at large wind velocity. Below the wave threshold, we find that the characteristic amplitude of the wrinkles scales as ${\nu }^{-1/2}{u}^{*3/2}$ over nearly the whole range of viscosities, whereas their size is essentially unchanged. We propose a simple model for this scaling, which compares well with the data. We show that the critical friction velocity $u^{*}$ for the onset of regular waves slowly increases with viscosity as ${\nu }^{0.2}$. Whereas the transition between wrinkles and waves is smooth at low viscosity, including for water, it becomes rather abrupt at high viscosity. A third wave regime is found at $\nu >(100–200)\times {10}^{-6}{\mathrm{m}}^2{\mathrm{s}}^{-1}$, characterized by a slow, nearly periodic emission of large-amplitude isolated fluid bumps.

We investigate the hydrodynamics of spherical Janus particles at the interface between two immiscible fluids using a multicomponent lattice-Boltzmann method. The Cahn-Hilliard model is used to evolve the composition for this binary system of incompressible fluids, while the particle-fluid interactions are taken into account by adding a supplemental force to recover the appropriate wettability at solid boundaries. We evaluate the capillary-induced interactions between multiple Janus particles at a sheared interface and demonstrate the possibility of directing their assembly. In response to the flow, all particles approach a steady orientation resulting from the balance between shear-induced torque and the resistance due to preferred wetting. At sufficiently large shear rates leading to strong capillary dipoles, the particles rearrange and form chains normal to the shear direction. For the particle sizes considered, an intermediate window of surface coverage between 32% and 65% is found to give effective alignment with order parameters in the range of 0.7–1.0. An interesting feature of this directed assembly method is that the structure is preserved after removing the flow field: Janus particles only rotate to upright orientation without disintegrating the chains. This approach can enable directing a randomly oriented or distributed cluster of Janus particles into an ordered structure with controllable rheological properties.

We characterize the two-dimensionalization process in the turbulent flow produced by an impeller rotating at a rate $\omega$ in a fluid rotating at a rate $\mathrm{\Omega }$ around the same axis for Rossby number $\text{Ro}=\omega /\mathrm{\Omega }$ down to ${10}^{-2}$. The flow can be described as the superposition of a large-scale vertically invariant global rotation and small-scale shear layers detached from the impeller blades. As $\text{Ro}$ decreases, the large-scale flow is subjected to azimuthal modulations. In this regime, the shear layers can be described in terms of wakes of inertial waves traveling with the blades, originating from the velocity difference between the nonaxisymmetric large-scale flow and the blade rotation. The wakes are well defined and stable at low Rossby number, but they become disordered at $\text{Ro}$ of order of 1. This experiment provides insight into the route towards pure two-dimensionalization induced by a background rotation for flows driven by a nonaxisymmetric rotating forcing.

Most superhydrophobic surfaces undergo a wetting transition from the Cassie to the Wenzel state, either spontaneously or under the action of external perturbations. The reverse dewetting transition is hampered by a large energy barrier and in order to achieve it, external fields are usually applied. Here we perform experiments, theoretical analysis, and lattice Boltzmann simulations of droplet condensation on a patterned superhydrophobic surface and demonstrate that the dewetting energy barrier can be reduced by manipulating the adhesion forces. Moreover, the kinetics of dewetting is a result of a subtle interplay of wetting and adhesion and in certain geometries, such as cone-shaped texture, the dewetting transition from Wenzel to Cassie state becomes spontaneous.

Consider the dynamics of a thin film flowing down a heated substrate. The substrate heating generates a temperature distribution on the free surface, which in turn induces surface-tension gradients and corresponding thermocapillary stresses that affect the free surface and therefore the fluid flow. We study here the effect of finite substrate thermal diffusivity on the film dynamics. Linear stability analysis of the full Navier-Stokes and heat transport equations indicates if the substrate diffusivity is sufficiently small, the film becomes unstable at a finite wavelength and at a Reynolds number smaller than that predicted in the long-wavelength limit. This property is captured in a reduced-order system of equations derived using a weighted-residual integral-boundary-layer method. This reduced-order model is also used to compute the bifurcation diagrams of solution branches connecting the trivial flat film to traveling waves including solitary pulses. The effect of finite diffusivity is to separate a simultaneous Hopf-transcritical bifurcation into its individual component bifurcations. The appropriate Hopf bifurcation then connects only to the solution branch of negative-hump pulses, with wave speed less than the linear wave speed, while the branch of positive-single-hump pulses merges with the branch of positive-two-hump pulses at a supercritical Reynolds number. In the regime where finite-wavelength instability occurs, there exists a Hopf-bifurcation pair connected by a branch of periodic solutions, whose period cannot be increased indefinitely. Numerical simulation of the reduced-order system shows the development of a train of coherent structures, each of which resembles a stationary positive-hump pulse, and, in the regime of finite-wavelength instability, wavelength selection and saturation to periodic traveling waves.

We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes the persistence of velocities over a characteristic spatial scale, unlike classical random walk methods, which model the persistence over a characteristic time scale. We first establish the relation between Eulerian and Lagrangian velocities for both equidistant and isochrone sampling along streamlines, under transient and stationary conditions. Based on this, we develop a space-continuous CTRW approach for the spatial and temporal dynamics of Lagrangian velocities. While classical CTRW formulations have nonstationary Lagrangian velocity statistics, the proposed approach quantifies the evolution of the Lagrangian velocity statistics under both stationary and nonstationary conditions. We provide explicit expressions for the Lagrangian velocity statistics and determine the behaviors of the mean particle velocity, velocity covariance, and particle dispersion. We find strong Lagrangian correlation and anomalous dispersion for velocity distributions that are tailed toward low velocities as well as marked differences depending on the initial conditions. The developed CTRW approach predicts the Lagrangian particle dynamics from an arbitrary initial condition based on the Eulerian velocity distribution and a characteristic correlation scale.

A combined numerical and experimental investigation of airfoil leading edge flow separation control with a nanosecond dielectric barrier discharge (DBD) plasma actuator is presented. Our study concentrates on describing dynamics of detailed flow actuation process and elucidating the nanosecond DBD actuation mechanism. A loose coupling methodology is employed to perform simulation, which consists of a self-similar plasma model for the description of pulsed discharge and two-dimensional Reynolds averaged Navier-Stokes (RANS) equations for the calculation of external airflow. A series of simulations of poststall flows around a NACA0015 airfoil is conducted with a Reynolds number range covering both low and high Re at $\text{Re}=(0.05,0.15,1.2)\times {10}^6$. Meanwhile, wind-tunnel experiment is performed for two low Re flows to measure aerodynamic force on airfoil model and transient flow field with time-resolved particle image velocimetry (PIV). The PIV measurement provides possibly the clearest view of flow reattachment process under the actuation of a nanosecond plasma actuator ever observed in experiments, which is highly comparable to that predicted by simulation. It is found from the detailed simulation that the discharge-induced residual heat rather than shock wave plays a dominant role in flow control. For any leading edge separations, the preliminary flow reattachment is realized by residual heat-induced spanwise vortices. After that, the nanosecond actuator functions by continuing exciting flow instability at poststall attack angles or acting as an active trip near stall angle. As a result, the controlled flow is characterized by a train of repetitive, downstream moving vortices over suction surface or an attached turbulent boundary layer, which depends on both angle of attack and Reynolds number. The advection of residual temperature with external flow offers a nanosecond plasma actuator a lot of flexibility to extend its influence region. Animations are provided for baseline flow and that subjected to plasma control at two typical Reynolds numbers.

In an effort to understand the locomotion dynamics of a simple vertebrate, the lamprey, both physical and computational models have been developed. A key feature of these models is the ability to vary the passive stiffness of portions of the swimmer, focusing on highly flexible models similar in material properties to lampreys and other anguilliform fishes. The physical model is a robotic lampreylike swimmer that is actuated along most of its length but has passively flexible tails of different stiffnesses. The computational model is a two-dimensional model that captures fluid-structure interactions using an immersed boundary framework. This simulated lamprey is passively flexible throughout its length and is also actuated along most of its length by the activation of muscle forces. Although the three-dimensional robot and the two-dimensional computational swimmer are such different constructs, we demonstrate that the wake structures generated by these models share many features and we examine how flexibility affects these features. Both models produce wakes with two or more same-sign vortices shed each time the tail changes direction (a “2P” or higher-order wake). In general, wakes become less coherent as tail flexibility increases. We examine the pressure distribution near the tail tip and the timing of vortex formation in both cases and find good agreement. Because we include flexibility, we are able to estimate resonant frequencies for several of the robotic and computational swimmers. We find that actuation at the resonant frequency dramatically increases the distance traveled per tail-beat cycle with only a small increase in the lost kinetic energy in the wake, suggesting that the resonant swimmers are more efficient.

We formulate and study computationally the low Mach number fluctuating hydrodynamic equations for electrolyte solutions. We are interested in studying transport in mixtures of charged species at the mesoscale, down to scales below the Debye length, where thermal fluctuations have a significant impact on the dynamics. Continuing our previous work on fluctuating hydrodynamics of multicomponent mixtures of incompressible isothermal miscible liquids [A. Donev et al., Phys. Fluids 27, 037103 (2015)], we now include the effect of charged species using a quasielectrostatic approximation. Localized charges create an electric field, which in turn provides additional forcing in the mass and momentum equations. Our low Mach number formulation eliminates sound waves from the fully compressible formulation and leads to a more computationally efficient quasi-incompressible formulation. We demonstrate our ability to model saltwater (NaCl) solutions in both equilibrium and nonequilibrium settings. We show that our algorithm is second order in the deterministic setting and for length scales much greater than the Debye length gives results consistent with an electroneutral approximation. In the stochastic setting, our model captures the predicted dynamics of equilibrium and nonequilibrium fluctuations. We also identify and model an instability that appears when diffusive mixing occurs in the presence of an applied electric field.

Laboratory experiments are performed to examine the sedimentation of particles that initially rise in a plume, then spread radially and settle in uniformly stratified fluid. Using light attenuation, the depth of the sediment bed is measured nonintrusively as a function of radius from the center of the plume. To gain some insight into these dynamics, an idealized model is developed by adapting well-established plume theory and a theory that accounts for sedimentation from surface gravity currents emanating from a plume impacting a rigid lid. We also account for recycling of falling particles that are re-entrained into the plume. With a suitable choice of parameters determining the intrusion height, entrainment during fountain collapse, and the radius at which settling from the intrusion begins, in most cases for which particles are predicted to be drawn back into the plume and recycled. The predictions for intrusion height, particle mound height, and spread agree within 20% of observations.

Liquid-infused surfaces display great advantages such as omniphobicity, anti-icing, antifouling, and self-cleaning. They can also reduce the drag of an object moving through an immiscible fluid since there is slip along the fluid-fluid interface. However, the trapped liquids are susceptible to the shear of the external flow, which will drain the lubricants from the surfaces and hinder their practical use. In this study, we investigate the shear-driven failure of liquid-infused surfaces under a broad range of ratios of the viscosity of the external fluid to that of the lubricant. The effect of viscosity ratio on the steady-state lubricant retention is characterized experimentally and analyzed analytically. The model offers a possible way to estimate the shear-driven failure of surfaces filled with different lubricants. In particular, it is shown that for a given external flow a lower lubricant viscosity results in more infused fluid being retained.

Molecular dynamics simulations are used to investigate the effective slip boundary condition for a simple fluid flowing over surfaces with one-dimensional sinusoidal roughness in the Wenzel state. The effective slip length is calculated as a function of the corrugation amplitude for flows along two principal orientations: transverse and longitudinal to the corrugation. Different atomic configurations, bent and stepped, are examined for strong and weak wall-fluid interactions and high and low wall densities. Molecular dynamics results for sparse bent surfaces quantitatively agree with continuum hydrodynamic predictions with a constant local slip length. Increasing the roughness amplitude reduces the effective slip length and the reduction is larger for transverse flow than longitudinal flow. Atomic effects become important for dense surfaces, because the local slip length varies with the local curvature and atomic spacing along the wall. These effects can be captured by applying a spatially varying boundary condition to the Navier-Stokes equations. Results for stepped surfaces are qualitatively different than continuum predictions, with the effect of corrugation rising linearly with corrugation amplitude rather than quadratically. There is an increased drag for transverse flow that is proportional to the density of step edges and lowers the slip length. Edges tend to increase the slip length for longitudinal flow because of order induced along the edges.

Transient growth of optimal disturbances with a turbulent mean velocity profile in a channel is investigated for Reynolds numbers, based on the wall-shear velocity and channel half height, of ${\mathrm{Re}}_{\tau }=180\sim 10000$. We consider optimal disturbances within near-wall regions ($0<y^{+}\le y_c^{+}$) by suppressing disturbances at $y^{+}>y_c^{+}$. The most amplified disturbances are streamwise velocity streaks induced by streamwise rolls. The wavelength and the growth time of these constrained optimal disturbances normalized in viscous wall units are nearly independent of ${\mathrm{Re}}_{\tau }$ but depend on the cutoff location $y_c^{+}$. The optimal disturbance corresponding to the cutoff location $y_c^{+}=40$, which is roughly the edge of the buffer layer, shows very similar characteristics to those of near-wall turbulence structures observed in turbulent channel flows, thus suggesting that the commonly observed turbulence structures are indeed the optimal disturbance within the buffer layer. The choice of this particular cutoff location, $y_c^{+}=40$, is justified from consideration of the shear rate parameter, $S^{*}=S{q}^2/\epsilon$, which is a measure of whether nonlinearity of turbulence can be neglected.

We study the origins of anomalous dispersion in heterogeneous porous media in terms of the medium and flow properties. To identify and quantify the heterogeneity controls, we focus on porous media which are organized in assemblies of equally sized conductive inclusions embedded in a constant conductivity matrix. We study the behavior of particle arrival times for different conductivity distributions and link the statistical medium characteristics to large-scale transport using a continuous time random walk (CTRW) approach. The CTRW models particle motion as a sequence of transitions in space and time. We derive an explicit map of the conductivity onto the transition time distribution. The derived CTRW model predicts solute transport based on the conductivity distribution and the characteristic heterogeneity length. In this way, heavy tails in solute arrival times and anomalous particle dispersion as measured by the centered mean square displacement are directly related to the medium properties. These findings shed light on the mechanisms of anomalous dispersion in heterogeneous porous media, and provide a basis for the predictive modeling of large-scale transport.