We study the stability of density stratified flow between corotating vertical cylinders with rotation rates ${\mathrm{\Omega }}_o<{\mathrm{\Omega }}_i$ and radius ratio $r_i/r_o=0.877$, where subscripts $o$ and $i$ refer to the outer and inner cylinders. Just as in stellar and planetary accretion disks, the flow has rotation, anticyclonic shear, and a stabilizing density gradient parallel to the rotation axis. The primary instability of the laminar state leads not to axisymmetric Taylor vortex flow but to a nonaxisymmetric stratorotational instability (SRI). The present work extends the range of Reynolds numbers and buoyancy frequencies $[N=\sqrt{(-g/\rho )(\partial \rho /\partial z)}]$ examined in previous experiments. We present the first experimental results for the axial wavelength $\lambda$ of the instability as a function of the internal Froude number, $\text{Fr}={\mathrm{\Omega }}_i/N$; $\lambda$ increases by nearly an order of magnitude over the range of $\text{Fr}$ examined. For small outer cylinder Reynolds number, the SRI occurs for inner inner Reynolds number larger than for the axisymmetric Taylor vortex flow (i.e., the SRI is more stable). For somewhat larger outer Reynolds numbers the SRI occurs for smaller inner Reynolds numbers than Taylor vortex flow and even below the Rayleigh stability line for an inviscid fluid. Shalybkov and Rüdiger [Astron. Astrophys. 438, 411 (2005)] proposed that the laminar state of a stably stratified rotating shear flow should be stable for ${\mathrm{\Omega }}_o/{\mathrm{\Omega }}_i>r_i/r_o$, but we find that this stability criterion is violated for $N$ sufficiently large. At large Reynolds number the primary instability is not the SRI but a previously unreported nonperiodic state that mixes the fluid.

The Rayleigh-Taylor instability (RTI) is investigated using the direct simulation Monte Carlo (DSMC) method of molecular gas dynamics. Here, fully resolved two-dimensional DSMC RTI simulations are performed to quantify the growth of flat and single-mode perturbed interfaces between two atmospheric-pressure monatomic gases as a function of the Atwood number and the gravitational acceleration. The DSMC simulations reproduce many qualitative features of the growth of the mixing layer and are in reasonable quantitative agreement with theoretical and empirical models in the linear, nonlinear, and self-similar regimes. In some of the simulations at late times, the instability enters the self-similar regime, in agreement with experimental observations. For the conditions simulated, diffusion can influence the initial instability growth significantly.

Linear control applied to fluid systems near an equilibrium point has important applications for many flows of industrial or fundamental interest. In this article we give an exposition of tools and approaches for the design of control strategies for globally stable or unstable flows. For unstable oscillator flows a feedback configuration and a model-based approach is proposed, while for stable noise-amplifier flows a feedforward setup and an approach based on system identification is advocated. Model reduction and robustness issues are addressed for the oscillator case; statistical learning techniques are emphasized for the amplifier case. Effective suppression of global and convective instabilities could be demonstrated for either case, even though the system-identification approach results in a superior robustness to off-design conditions.

We investigate shear-induced clustering and its impact on fluid rheology in polymer-colloid mixtures at moderate colloid volume fraction. By employing a thermoresponsive system that forms associative polymer-colloid networks, we present experiments of rheology and flow-induced microstructure on colloid-polymer mixtures in which the relative magnitudes of the time scales associated with relaxation of viscoelasticity and suspension microstructure are widely and controllably varied. In doing so, we explore several limits of relative magnitude of the relevant dimensionless shear rates, the Weissenberg number Wi and the Péclet number Pe. In all of these limits, we find that the fluid exhibits two distinct regimes of shear thinning at relatively low and high shear rates, in which the rheology collapses by scaling with Wi and Pe, respectively. Using three-dimensionally-resolved flow small-angle neutron scattering measurements, we observe clustering of the suspension above a critical shear rate corresponding to $\mathrm{Pe}\sim 0.1$ over a wide range of fluid conditions, having anisotropy with projected orientation along both the vorticity and compressional axes of shear. The degree of anisotropy is shown to scale with Pe. From this we formulate an empirical model for the shear stress and viscosity, in which the viscoelastic network stress is augmented by an asymptotic shear thickening contribution due to hydrodynamic clustering. Overall, our results elucidate the significant role of hydrodynamic interactions in contributing to shear-induced clustering of Brownian suspensions in viscoelastic liquids.

Plateau borders (PBs) are liquid microchannels located at the contact between three bubbles in liquid foams. They are stable, deformable, and can be thought of as quasi-one-dimensional model systems to study surface waves in fluid dynamics. We show that the burst of a bubble trapped in a PB produces local constrictions which travel along the liquid channel at constant velocity, without significant change in shape. These patterns are reminiscent of the depression solitary waves encountered in nonlinear systems. By coupling flow inertia to capillary stresses, we derive a simple model that admits solitonic solutions, which we characterized numerically and analytically in the limit of small deformation. These solutions capture most of the features observed experimentally.

Minimum-dissipation models are a simple alternative to the Smagorinsky-type approaches to parametrize the subfilter turbulent fluxes in large-eddy simulation. A recently derived model of this type for subfilter stress tensor is the anisotropic minimum-dissipation (AMD) model [Rozema et al., Phys. Fluids 27, 085107 (2015)], which has many desirable properties. It is more cost effective than the dynamic Smagorinsky model, it appropriately switches off in laminar and transitional flows, and it is consistent with the exact subfilter stress tensor on both isotropic and anisotropic grids. In this study, an extension of this approach to modeling the subfilter scalar flux is proposed. The performance of the AMD model is tested in the simulation of a high-Reynolds-number rough-wall boundary-layer flow with a constant and uniform surface scalar flux. The simulation results obtained from the AMD model show good agreement with well-established empirical correlations and theoretical predictions of the resolved flow statistics. In particular, the AMD model is capable of accurately predicting the expected surface-layer similarity profiles and power spectra for both velocity and scalar concentration.

We study the intrinsic dynamics of cusps, or indentations, moving along a liquid sheet border, and characterize their ensemble statistics. Gordillo and collaborators [J. Fluid Mech. 754, R1 (2014)] have shown that the symmetrical stationary cusp is the only structure accommodating for both mass and momentum conservation at a steadily receding liquid sheet rim. Cusps are also known to typically move along a sheet border, to present an asymmetry, and to be distributed in size around a mean. We show here why a heterogeneous assembly of cusps traveling along the sheet rim occurs spontaneously, why big and small cusps coexist at the same time, and, more precisely, we establish a specific link between the microscopic dynamics directing their motion, and the ensemble averaged distribution of their sizes.

The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999)], which are the rigorous asymptotic limit of the Navier-Stokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental performance limit), based only on the system matrices and the initial and free-stream boundary conditions. The adjoint equations admit a self-similar solution for large spanwise wave numbers with a scaling which is different from that of the LUBR equations. The controlled flow field also has a self-similar solution if the weighting matrices of the objective function are chosen appropriately. The code developed to implement this algorithm is efficient and has modest memory requirements. Computations show the significant reduction of energy for each wave number. The control of the full spectrum streaks, for conditions corresponding to a realistic experimental case, shows that the root-mean-square of the streamwise velocity is strongly suppressed in the whole domain and for all the frequency ranges examined.

We present a molecular-level investigation of nitrogen dissociation at high temperature. The computational technique, called direct molecular simulation (DMS), solely relies on an ab initio potential energy surface and both ${\mathrm{N}}_2+{\mathrm{N}}_2$ and $\mathrm{N}+{\mathrm{N}}_2$ processes are simulated as they concurrently take place in an evolving nonequilibrium gas system. Quasiclassical trajectory calculations (QCT) reveal that dissociation rate coefficients calculated at thermal equilibrium, i.e., assuming Boltzmann energy distributions, are approximately equal (within less than 15%) for both ${\mathrm{N}}_2+{\mathrm{N}}_2$ and $\mathrm{N}+{\mathrm{N}}_2$ collisions for the range of temperatures considered. The DMS (nonequilibrium) results indicate, however, that the presence of atomic nitrogen significantly affects the dissociation rate of molecular nitrogen, but indirectly. In fact, the presence of atomic nitrogen causes an important reduction of the vibrational relaxation time of ${\mathrm{N}}_2$, by almost one order of magnitude. This, in turn, speeds up the replenishment of high-$v$ states that are otherwise significantly depleted if only ${\mathrm{N}}_2+{\mathrm{N}}_2$ collisions are considered. Because of the strong favoring of dissociation from high-$v$ states, this results in dissociation rates that are 2–3 times higher when significant atomic nitrogen is present compared to systems composed of mainly diatomic nitrogen, such as during the initial onset of dissociation. Specifically, we find that exchange events occur frequently during $\mathrm{N}+{\mathrm{N}}_2$ collisions and that such exchange collisions constitute an effective mechanism of scrambling the internal energy states, resulting in multiquantum jumps in vibrational energy levels that effectively promote energy transfers. The resulting vibrational relaxation time constant we calculate for $\mathrm{N}+{\mathrm{N}}_2$ collisions is significantly lower than the widely used Millikan-White model. Significant discrepancies are found between predictions of the Park two-temperature model (using the Millikan-White vibrational relaxation model) and the DMS results for dissociating nitrogen systems involving both atomic and molecular nitrogen. Such direct comparisons also illustrate how the DMS method is able to reveal all relevant nonequilibrium physics without the need to compute large numbers of state-transition probabilities. In this manner, DMS presents an accurate and tractable approach to construct models for direct-simulation Monte Carlo and computational fluid dynamics simulations from first principles.

We study the rheology of a sheared two-dimensional (2D) suspension of non-Brownian disks in the presence of walls. Although it is of course possible today with modern computers and powerful algorithms to perform direct numerical simulations that fully account for multiparticle 3D interactions in the presence of walls, the analysis of the simple case of a 2D suspension provides valuable insights and helps in the understanding of 3D results. Due to the direct visualization of the whole 2D flow (the shear plane), we are able to give a clear interpretation of the full hydrodynamics of semidilute confined suspensions. For instance, we examine the role of disk-wall and disk-disk interactions to determine the dissipation of confined sheared suspensions whose effective viscosity depends on the area fraction $\varphi$ of the disks as ${\eta }_{\text{eff}}={\eta }_0[1+\left[\eta \right]\varphi +\beta {\varphi }^2+O\left({\varphi }^3\right)]$. We provide numerical estimates of $\left[\eta \right]$ and $\beta$ for a wide range of confinements. As a benchmark for our simulations, we compare the numerical results obtained for $\left[\eta \right]$ and $\beta$ for very weak confinements with analytical values ${\left[\eta \right]}_{\infty }$ and ${\beta }_{\infty }$ obtained for an infinite fluid. If the value ${\left[\eta \right]}_{\infty }=2$ is well known in the literature, much less is published on the value of $\beta$. Here we analytically calculate with very high precision ${\beta }_{\infty }=3.6$. We also reexamine the 3D case in the light of our 2D results.

We report the results of an experimental study of the fully developed flow of a viscoelastic, shear-thinning aqueous polymer solution through two large-scale parallel shear flows: a pipe and channel-flow facility. We show that, at low flow rates, the velocity profile in both geometries is steady and is in good agreement with expected analytical solutions. However, in both geometries at higher flow rates the flow becomes weakly time dependent and the mean velocity profile is radically altered, exhibiting an overshoot near the duct center, a reduced shear rate at the wall, and an inflection point (i.e., a nonmonotonic gradient). Although inertia is not completely negligible at instability onset, we speculate that the origin of these unstable flows lies in the combination of elasticity and strong shear thinning.

The concept of electromagnetic energy enhancement and nanofocusing phenomena near the tip of a metaconical conducting tip by means of a surface plasmon-polaritons mechanism is discussed theoretically. In particular, we consider conical metallic structures with small apex angles and derive the corresponding dispersion relation under optimal (maximal field enhancement) operating conditions. It is demonstrated analytically that the aforementioned conditions can induce large dielectrophoretic forces near the conical tip, which can be harnessed for sorting and controlling nanoparticles in a manner similar to optical tweezers. Similarly, by considering Joule heating effects in the metal and heat conduction in the surrounding solute, it is shown that a considerable (dc) flow convection and mixing can be generated in the aqueous phase near the tip by such ac incited optical means (including common low-input lasers operating in the visible and near-infrared spectrum ranges). Analytic near-field expressions are also obtained for the opto-electro-thermo-induced flow and vorticity distributions in the electrolyte exhibiting a singular behavior near the rounded tip. Using a coax conical metastructure composed of two noble metals, surface-plasmon field enhancement is a technique for the optimal manipulation of dielectric and polarizable nanoparticles as well as for inducing indirect mixing in the liquid around the tip by generating microvortices.

Induced charge electrophoresis of a conducting cylinder suspended in a nonconducting cylindrical pore is theoretically analyzed and a micromotor is proposed that utilizes the cylinder rotation. The cylinder velocities are analytically obtained in the Dirichlet and the Neumann boundary conditions of the electric field on the cylindrical pore. The results show that the cylinder not only translates but also rotates when it is eccentric with respect to the cylindrical pore. The influences of a number of parameters on the cylinder velocities are characterized in detail. The cylinder trajectories show that the cylinder approaches and becomes stationary at certain positions within the cylindrical pore. The proposed micromotor is capable of working under a heavy load with a high rotational velocity when the eccentricity is large and the applied electric field is strong.

The description of hydrodynamic interactions between a particle and the surrounding liquid, down to the nanometer scale, is of primary importance since confined liquids are ubiquitous in many natural and technological situations. In this paper we combine three nonconventional atomic force microscopes to study hydrodynamics around micro- and nanocylinders. These complementary methods allow the independent measurement of the added mass and friction terms over a large range of probe sizes, fluid viscosities, and solicitation conditions. A theoretical model based on an analytical description of the velocity field around the probe shows that the friction force depends on a unique parameter, the ratio of the probe radius to the thickness of the viscous boundary layer. We demonstrate that the whole range of experimental data can be gathered in a master curve, which is well reproduced by the model. This validates the use of these atomic force microscopy modes for a quantitative study of hydrodynamics and opens the way to the investigation of other sources of dissipation in simple and complex fluids down to the submicron scale.

We present a complete theoretical framework for the axial dispersion of a Brownian colloidal suspension confined in a parallel plate channel, extending the Taylor-Aris treatment to particles with diameters comparable to the channel width. The theoretical model incorporates the effects of confinement on the colloid distribution, corrections to the velocity profile due to the effects of colloid concentration on the suspension viscosity, and position-dependent diffusivities. We test the theoretical model using explicit-solvent molecular dynamics simulations that fully incorporate hydrodynamic correlations and thermal fluctuations and obtain good quantitative agreement between theory and simulations. We find that the nonuniform colloid distributions that arise in confinement due to excluded volume between the colloids and channel walls significantly impact the axial dispersion.

In rarefied gases, mass and heat transport processes interfere with each other, leading to the mechano-caloric effect and thermo-osmotic effect, which are of interest to both theoretical study and practical applications. We employ the unified gas-kinetic scheme to investigate these cross coupling effects in gas flows in micro-channels. Our numerical simulations cover channels of planar surfaces and also channels of ratchet surfaces, with Onsager's reciprocal relation verified for both cases. For channels of planar surfaces, simulations are performed in a wide range of Knudsen number, and our numerical results show good agreement with the literature results. For channels of ratchet surfaces, simulations are performed for both the slip and transition regimes, and our numerical results not only confirm the theoretical prediction [Phys. Rev. Lett. 107, 164502 (2011)] for the Knudsen number in the slip regime but also show that the off-diagonal kinetic coefficients for cross coupling effects are maximized at a Knudsen number in the transition regime. Finally, a preliminary optimization study is carried out for the geometry of Knudsen pump based on channels of ratchet surfaces.

This study presents a direct numerical simulation analysis of the force distribution within a cluster of monodisperse spherical particles. A direct forcing immersed boundary method is used to calculate the forces on individual particles for a volume fraction range of $0.11\le \varphi \le 0.44$ and a Reynolds number range of $1.47\le \mathrm{Re}\le 636$. The hydrodynamic streamwise force is shown to have a normal distribution with a standard deviation ratio to the mean drag that decreases with increasing volume fraction and ranges between 17% and 26%. The lift forces also follow a normal distribution that has a significant standard deviation to mean drag ratio of around 14.5%, which does not vary significantly with the Reynolds number and volume fraction. A model is introduced that adds the identified normal distribution of the forces to the quasisteady force used in point-particle models. A nonisotropic method of defining spatial parameters is presented. It highlights the contribution of each parameter to the variation of the forces on each particle. The results show that the drag is influenced by the closest four to eight neighboring spheres. The drag force is highly dependent on the streamwise distances of the spheres located upstream. For low volume fractions and Reynolds number, the lateral distances of the spheres located downstream also have a significant contribution to those variations. The results also show that the lateral force variation is mostly dictated by the lateral distance of one to two spheres located upstream of each sphere.

We study the dynamics of evaporating ethanol films deposited by a receding liquid meniscus. The films are surrounded by pure vapor in a capillary heated above the saturation temperature. We observe the substrate dewetting with the dewetting ridge in spite of the complete wetting at equilibrium. The dewetting is caused by a high contact angle ($\sim {30}^{\circ }$) induced by evaporation. The obtained values agree with a theory proposed earlier. The film shape is measured with both grid deflection technique and interferometry. The phenomenon is convenient to observe inside a capillary with an axial thermal gradient. When the capillary is closed at one end and open at another to a constant pressure reservoir, the meniscus oscillations are known to appear spontaneously. Such a system is the simplest version of an industrial device called a pulsating heat pipe. The effect is general and can be used in any system to control the wetting properties.

A simplified model is developed for intrusive gravity currents propagating along the interface of a two-layer stratified ambient. The model is based on the conservation of mass and vorticity and it does not require any empirical closure assumptions. A parametric study conducted with this model reproduces the correct behavior in various limits and is consistent with previously reported experimental observations. Specifically, it predicts the formation of equilibrium intrusions when the intrusion density equals the depth-weighted mean density of the two ambient layers. It furthermore demonstrates the existence of nonsmooth limits under certain conditions. An energy analysis shows that under nonequilibrium conditions the intrusion gains energy. The predictions by the parametric study are furthermore compared to two-dimensional direct numerical simulation results and very good agreement is observed with regard to all flow properties.

Wind tunnel measurements in the wake of an axial flow miniature wind turbine provide evidence of large-scale motions characteristic of wake meandering [Howard et al., Phys. Fluids 27, 075103 (2015)]. A numerical investigation of the wake, using immersed boundary large eddy simulations able to account for all geometrical details of the model wind turbine, is presented here to elucidate the three-dimensional structure of the wake and the mechanisms controlling near and far wake instabilities. Similar to the findings of Kang et al. [Kang et al., J. Fluid Mech. 744, 376 (2014)], an energetic coherent helical hub vortex is found to form behind the turbine nacelle, which expands radially outward downstream of the turbine and ultimately interacts with the turbine tip shear layer. Starting from the wake meandering filtering used by Howard et al., a three-dimensional spatiotemporal filtering process is developed to reconstruct a three-dimensional meandering profile in the wake of the turbine. The counterwinding hub vortex undergoes a spiral vortex breakdown and the rotational component of the hub vortex persists downstream, contributing to the rotational direction of the wake meandering. Statistical characteristics of the wake meandering profile, along with triple decomposition of the flow field separating the coherent and incoherent turbulent fluctuations, are used to delineate the near and far wake flow structures and their interactions. In the near wake, the nacelle leads to mostly incoherent turbulence, while in the far wake, turbulent coherent structures, especially the azimuthal velocity component, dominate the flow field.