The numerical investigation of a circular Couette flow with a radial temperature gradient is performed to elucidate the influence of the radial buoyancy on flow and heat transfer for different values of the Prandtl number when the gravitational acceleration is neglected. We consider an infinite-length cylindrical annulus of radius ratio 0.8 with the inner rotating cylinder and the outer stationary cylinder. The flow is stabilized with the outward heating while it is destabilized with the inward heating. A weakly nonlinear analysis shows that the transition to stationary axisymmetric modes is supercritical while the oscillatory axisymmetric modes occur via a subcritical bifurcation. The effect of the centrifugal buoyancy on the transfer of angular momentum (i.e., torque) is quite weak while the effect on the heat transfer is significant.

In this work, we investigate the behavior of dilute and semidilute polymer solutions flowing in a microfluidic flow focusing device, in which an inlet stream is stretched by two balanced lateral streams. By varying the flow rates in the inlet and lateral channels and their ratio, several types of flow transitions are observed and the resulting velocity fields are analyzed both upstream and downstream of the intersection. At high flow rates, the flow becomes chaotic and the path to this state depends on both the Weissenberg number and the imposed Hencky strain. The thresholds of successive elastic instabilities leading to the chaotic state are also investigated using time-resolved microparticle imaging velocimetry.

An artificial neural network (ANN) is tested as a tool for finding a new subgrid model of the subgrid-scale (SGS) stress in large-eddy simulation. An ANN is used to establish a functional relation between the grid-scale flow field and the SGS stress without any assumption of the form of function. Data required for training and test of the ANN are provided by direct numerical simulation of a turbulent channel flow. It is shown that an ANN can establish a model similar to the gradient model. The correlation coefficients between the real SGS stress and the output of the ANN are comparable to or larger than similarity models, but smaller than a two-parameter dynamic mixed model. Large-eddy simulations using the trained ANN are also performed. Although ANN models show no advantage over the Smagorinsky model, the results confirm that the ANN is a promising tool for establishing a new subgrid model with further improvement.

It is demonstrated that micron-sized particles suspended in fluid near oscillating interfaces experience strong inertial displacements above and beyond the fluid streaming. Experiments with oscillating bubbles show rectified particle lift over extraordinarily short (millisecond) times. A quantitative model on both the oscillatory and the steady time scales describes the particle displacement relative to the fluid motion. The formalism yields analytical predictions confirming the observed scaling behavior with particle size and experimental control parameters. It applies to a large class of oscillatory flows with applications from particle trapping to size sorting.

Recently Schumacher et al. [Phys. Rev. Fluids 1, 084402 (2016)] used direct numerical simulation to calculate the shear stress exerted on the top and bottom viscous boundary layers (BLs) of Rayleigh-Bénard convection with a Prandtl number $\mathrm{Pr}=0.021$ and aspect ration $\mathrm{\Gamma }=1$ for Rayleigh numbers $\mathrm{Ra}$ up to $4\times {10}^8$. By extrapolating their results to larger $\mathrm{Ra}$, they concluded that the sample would undergo a transition to turbulent BLs and enter the “ultimate state” at ${\mathrm{Ra}}^{*}\simeq {10}^{11}$ for $\mathrm{Pr}=0.021$. Here we show that their result is consistent with the experimentally determined ${\mathrm{Ra}}^{*}=2\times {10}^{13}$ for $\mathrm{Pr}=0.82$ by He et al. [Phys. Rev. Lett. 108, 024502 (2012); He et al., New J. Phys. 17, 063028 (2015)] and the $\mathrm{Pr}$ dependence of ${\mathrm{Ra}}^{*}$ predicted by Grossmann and Lohse [Phys. Rev. E 66, 016305 (2002)]. Thus the numerical results of Schumacher et al. support the interpretation of the experimentally observed transition at ${\mathrm{Ra}}^{*}=2\times {10}^{13}$ for $\mathrm{Pr}=0.82$ as the ultimate-state transition.

Lagrangian acceleration statistics in a fully developed turbulent channel flow at ${\text{Re}}_{\tau }=1440$ are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced Lagrangian stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.

The efficiency of fluid flow for mixing passive tracers is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here we address the natural corollary question: Given a fluid flow, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small length-scale threshold ${\ell }_{\nu }$ under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of two-dimensional turbulence. Evaluating the optimal initial condition through this framework requires only the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data are available through numerical simulations or experimental measurements.

Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the hydrodynamic or kinetic equations. By incorporating stochastic fluxes into the mean field kinetic equation, we quantify the dynamics of a suspension of microswimmers in the parameter regime where the deterministic equation is stable. We can thereby compute nontrivial collective phenomena concerning spatial correlations of orientation and stress as well as the enhanced diffusion of tracer particles. Our analysis here focuses primarily on two-dimensional systems, though we also show how superdiffusion of tracers in three dimensions can occur by our framework.

The sensitivity of porous energetic materials depends on mesostructural heterogeneities such as voids, defects, cracks, and grain boundaries. The mesostructure of pressed explosives contains voids of arbitrary shapes including elongated voids of various orientations and aspect ratios. Mesoscale simulations to date have analyzed the effect of void morphology on the sensitivity of energetic materials for idealized shapes such as cylindrical, conical, and elliptical. This work analyzes the sensitivity behavior of elongated voids in an HMX matrix subject to shock loading. Simulations show that sensitivity of elongated voids depends strongly on orientation as well as aspect ratio. Ranges of orientations and aspects ratios are identified that enhance or inhibit initiation. Insights obtained from single elongated void analyses are used to identify sensitive locations in an imaged mesostructure of a pressed explosive sample.

Void collapse in energetic materials leads to hot spot formation and enhanced sensitivity. Much recent work has been directed towards simulation of collapse-generated reactive hot spots. The resolution of voids in calculations to date has varied as have the resulting predictions of hot spot intensity. Here we determine the required resolution for reliable cylindrical void collapse calculations leading to initiation of chemical reactions. High-resolution simulations of collapse provide new insights into the mechanism of hot spot generation. It is found that initiation can occur in two different modes depending on the loading intensity: Either the initiation occurs due to jet impact at the first collapse instant or it can occur at secondary lobes at the periphery of the collapsed void. A key observation is that secondary lobe collapse leads to large local temperatures that initiate reactions. This is due to a combination of a strong blast wave from the site of primary void collapse and strong colliding jets and vortical flows generated during the collapse of the secondary lobes. The secondary lobe collapse results in a significant lowering of the predicted threshold for ignition of the energetic material. The results suggest that mesoscale simulations of void fields may suffer from significant uncertainty in threshold predictions because unresolved calculations cannot capture the secondary lobe collapse phenomenon. The implications of this uncertainty for mesoscale simulations are discussed in this paper.

The secondary instability of nonlinear streaks and transition to turbulence in viscoelastic Couette flow are studied using direct numerical simulations. Viscoelasticity is modeled using the FENE-P constitutive equations. Both the polymer concentration $\beta$ and Weissenberg number Wi are varied in order to assess their effects on transition at moderate Reynolds number. The base streaks are obtained from nonlinear simulations of the Couette flow response to a streamwise vortex. We select the initial amplitude of the vortex which yields a desired maximum amplitude of the nonlinear streaks during their temporal evolution. The development of streaks in both Newtonian and non-Newtonian flows is primarily due to the action of streamwise vorticity onto the mean shear. In the viscoelastic case, it is also affected by the polymer torque, which opposes the vorticity and becomes more pronounced at large Weissenberg number. Streaks with the same maximum streamwise velocity perturbation can therefore have different total kinetic energy at higher Weissenberg number. At every streak amplitude of interest, harmonic forcing is introduced along the transverse direction to trigger the secondary instability and breakdown to turbulence. We demonstrate that the critical amplitude of the forcing, $A_d$, increases at large Weissenberg number. The degree of stabilization due to elasticity depends on the initial streak intensity, $A_{s,\text{in}}$. For weak streaks the critical amplitude for secondary instability is more sensitive to Wi than for strong ones. This is explained by the existence of two different mechanisms that can trigger transition to turbulence. The perturbation to weak streaks is initially stabilized by the polymer torque which acts to oppose the amplification of wall-normal vorticity and, as a result, delays breakdown to turbulence. The secondary instability of strong streaks, on the other hand, is more immune to this stabilizing influence of the polymer.

The effect on the base pressure of a thin slit located at the base edge of a blunt axisymmetric body, communicating an internal cavity with the external flow, is investigated. A parametric study is performed of the effect on base pressure of changes in slit size and cavity depth. The base pressure increases initially with increasing cavity depth, but saturates at a depth which depends on the slit size. The base pressure increases monotonically up to $5\%$ with increasing slit size for the geometries tested. An upper limit of base pressure recovery of $20\%$ is extrapolated from the data. It is observed that the main effect of the slit is to reduce the instantaneous pressure asymmetry, which is linked to the total base pressure in a similar fashion for all the slit sizes. As a second-order effect, for highly asymmetric pressure distributions, the slit produces a base pressure increase not associated with the base pressure asymmetry. The results suggest a global effect of the slit on the wake due to a diametrical flow within the cavity driven by the pressure differences across the slit and regulated by the largest of the pressure drops between the slit and cavity. The slit also reduces the periodic base pressure fluctuations, corresponding mainly to the vortex shedding, and increases the rotational speed of the wake.

Lubricated transport of heavy viscous oils is a popular technology in the pipelining industry, where pumping pressures can be reduced significantly by concentrating the strain rate in a lubricating layer. However, the interface between the lubricating layer and heavy oil is vulnerable to any perturbations in the system as well as transients due to start up, shut down, temperature change, etc. We present a method in which we purposefully position an unyielded skin of a viscoplastic fluid between the oil and the lubricating fluid. The objective is to reduce the frictional pressure gradient while avoiding interfacial instability. We study this methodology in both concentric and eccentric configurations and show its feasibility for a wide range of geometric and flow parameters found in oil pipelining. The eccentric configuration benefits the transport process via generating lift forces to balance the density differences among the layers. We use classical lubrication theory to estimate the leading order pressure distribution in the lubricating layer and calculate the net force on the skin. We explore the effects of skin shape, viscosity ratio, and geometry on the pressure drop, the flow rates of skin and lubricant fluids, and the net force on the skin. We show that the viscosity ratio and the radius of the core fluid are the main parameters that control the pressure drop and consumptions of outer fluids, respectively. The shape of the skin and the eccentricity mainly affect the lubrication pressure. These predictions are essential in designing a stable transport process. Finally, we estimate the yield stress required in order that the skin remain unyielded and ensure interfacial stability.

Controlling interactions out of thermodynamic equilibrium is crucial for designing addressable and functional self-organizing structures. These active interactions also underpin collective behavior in biological systems. Here we study a general setting of active particles in a bath of passive particles and demonstrate a mechanism for long-range attraction between active particles. The mechanism operates when the translational persistence length of the active particle motion is smaller than the particle diameter. In this limit, the system reduces to particles of higher diffusivity (“hot” particles) in a bath of particles with lower diffusivity (“cold” particles). This attractive interaction arises as a hot particle pushes cold particles away to create a large hole around itself, and the holes interact via a depletion-like attraction. Strikingly, the interaction range is more than an order of magnitude larger than the particle radius, well beyond the range of the conventional depletion force. Although the mechanism occurs outside the parameter regime of typical biological swimmers, the mechanism could be realized in the laboratory.

We examine the flow and instabilities of three viscoelastic fluids—a semidilute aqueous solution of polyethylene oxide (PEO) and two wormlike micellar solutions of cetylpyridinium chloride and sodium salicylate—around a microfluidic ${90}^{\circ }$ bend, in which shear deformation and streamline curvature dominate. Similar to results reported by Gulati et al. [S. Gulati et al., Phys. Rev. E 78, 036314 (2008); S. Gulati et al., J. Rheol. 54, 375 (2010)] for PEO solutions, we report a critical Weissenberg number (Wi) for the onset of lip vortex formation upstream of the corner. However, the decreased aspect ratio (channel depth to width) results in a slightly higher critical Wi and a vortex that grows more slowly. We consider wormlike micellar solutions of two salt to surfactant concentration ratios $R=0.55$ and $R=0.79$. At $R=0.55$, the wormlike micelles are linear and exhibit strong viscoelastic behavior, but at $R=0.79$, the wormlike micelles become branched and exhibit shear-banding behavior. Microfluidic experiments on the $R=0.55$ solution reveal two flow transitions. The first transition, at $\mathrm{Wi}=6$, is characterized by the formation of a stationary lip vortex upstream of the bend; at the second transition, at $\mathrm{Wi}=20$, the vortex fluctuates in time and changes size. The $R=0.79$ solution also exhibits two transitions. The first transition at $\mathrm{Wi}=4$ is characterized by the appearance of two intermittent vortices, one at the lip and one at the far outside corner. Increasing the flow rate to $\mathrm{Wi}>160$ results in a transition to a second unstable regime, where there is only a lip vortex that fluctuates in size. The difference in flow transitions in PEO and wormlike micellar solutions presumably arises from the additional contribution of wormlike micellar breakage and reformation under shear. The flow transitions in wormlike micellar solutions are also significantly affected by chain branching.

We present an experimental setup that creates a shear flow with zero mean advection velocity achieved by counterbalancing the nonzero streamwise pressure gradient by moving boundaries, which generates plane Couette-Poiseuille flow. We obtain experimental results in the transitional regime for this flow. Using flow visualization, we characterize the subcritical transition to turbulence in Couette-Poiseuille flow and show the existence of turbulent spots generated by a permanent perturbation. Due to the zero mean advection velocity of the base profile, these turbulent structures are nearly stationary. We distinguish two regions of the turbulent spot: the active turbulent core, which is characterized by waviness of the streaks similar to traveling waves, and the surrounding region, which includes in addition the weak undisturbed streaks and oblique waves at the laminar-turbulent interface. We also study the dependence of the size of these two regions on Reynolds number. Finally, we show that the traveling waves move in the downstream (Poiseuille) direction.

We address a problem of fundamental importance in the physics of interfaces, which is central to the description of multiphase fluid dynamics. This work is important to study interfaces in systems such as polymer melts and solutions, where velocity jumps have been observed and interpreted as a manifestation of slip. This is in violation of classical interfacial conditions that require continuity of velocity and has been remedied in the literature via use of ad hoc models, such as the so-called Navier slip condition. This paper suggests that it is possible to obviate completely the need for such an approach. Instead, we show that one simply requires knowledge of the density field and the molar fraction of the fluid components and the dependence of the viscosity on the density. This information can be obtained easily through molecular dynamics simulations.

The manipulation of particles using inertial lift forces has broad implications in the separation, concentration and sorting of particles. In this work, we show that in the presence of a secondary flow, equilibrium locations of particles subject to inertial lift can be spatially varying. Using a well-defined microfabricated straight microfluidic channel with perpendicular permeate channels, we perform experiments over a range of particle sizes and inlet and outlet flow rates to highlight different focusing regimes. We show that a permeate flow can control the equilibrium location of particles and can be used to interrogate the balance between inertial and permeate forces.

The effect of long-wavelength sinusoidal surface waviness on the development of Tollmien-Schlichting (TS) wave instabilities is investigated. The analysis is based on the compressible flow that forms over an unswept infinite wavy wing with surface variations of variable amplitude, wavelength, and phase. Boundary layer profiles are extracted directly from solutions of a Navier-Stokes solver, which allows a thorough parametric analysis to be undertaken. Many wavy surface configurations are examined that can be sufficient to establish localized pockets of separated flow. Linear stability analysis is undertaken using parabolized stability equations (PSE) and linearized Navier-Stokes (LNS) methods, and surface waviness is generally found to enhance unstable behavior. Results of the two schemes are compared and criteria for PSE to establish accurate solutions in separated flows are determined, which are based on the number of TS waves per wavelength of the surface deformation. Relationships are formulated, relating the instability variations to the surface parameters, which are consistent with previous observations regarding the growth of TS waves on a flat plate. Additionally, some long-wavelength surface deformations are found to stabilize TS disturbances.

We report particle image velocimetry of the large-scale circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-Bénard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one, so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow us to consider a bidimensional mean flow. Many previous heat flux measurements have shown a Nusselt-Rayleigh regime transition corresponding to an increase of the heat flux in the presence of roughness that is higher than the surface increase. Our velocity measurements show that if the mean velocity field is not clearly affected by the roughness, the velocity fluctuations rise dramatically, which is accompanied by a change of the longitudinal velocity structure functions scaling. Moreover, we show that the boundary layer becomes turbulent close to roughness, as it was observed recently in air [O. Liot et al., J. Fluid Mech. 786, 275 (2016)]. Finally, we discuss the link between the change of the boundary layer structure and the changes observed in the velocity fluctuations.