An active inline mixer suitable for flows at low Reynolds number and high Péclet number is studied. An alternated oscillatory forcing protocol is imposed by three rotating circular arc-walls in a straight channel. In the two-dimensional case, simple phenomenological arguments are used to estimate heuristically the mixing efficiency with two nondimensional control parameters: the Strouhal number based on the bulk flow velocity and the strength of the cross flow relative to the transport flow. The validity and limitations of the proposed mixing conditions are explained by the transport mechanisms in the mixer. The beneficial role of the elliptic flow regions for stretching and folding the passive scalar interfaces is highlighted as well as a correlation between good mixing ability and the chaotic advection of tracers in the mixing zone.

We analyze the vector nulls of velocity, Lagrangian acceleration, and vorticity, coming from direct numerical simulations of forced homogeneous isotropic turbulence at ${\text{Re}}_{\lambda }\in O\left(\left[40\text{–}600\right]\right)$. We show that the clustering of velocity nulls is much stronger than those of acceleration and vorticity nulls. These acceleration and vorticity nulls, however, are denser than the velocity nulls. We study the scaling of clusters of these null points with ${\text{Re}}_{\lambda }$ and with characteristic turbulence lengthscales. We also analyze datasets of point inertial particles with Stokes numbers $\text{St}=0.5$, 3, and 6, at ${\text{Re}}_{\lambda }=240$. Inertial particles display preferential concentration with a degree of clustering that resembles some properties of the clustering of the Lagrangian acceleration nulls, in agreement with the proposed sweep-stick mechanism of clustering formation.

Conventional shock-wave–turbulent boundary-layer interactions are often treated as quasi-two dimensional for a tractable analysis. In practical applications such as high-speed engine inlets and combustors, the additional presence of sidewalls leads to dramatic changes in the baseline flow structure by enhancing the inherent three dimensionality of the interaction, in addition to modifying its unsteadiness. This study investigates the flow field generated by a ${24}^{\circ }$ compression ramp in presence of sidewalls, with a confinement ratio $\delta /w=0.12$. The free-stream unit Reynolds number and Mach number are $2.5\times {10}^7{\mathrm{m}}^{-1}$ and 2.25, respectively. Statistical analysis of results obtained from high-fidelity simulations carried out by Poggie and Porter [Phys. Rev. Fluids 4, 024602 (2019)] is performed to explore the large-scale unsteadiness of this flow field. The mean and instantaneous flow fields displayed strong three dimensionality due to influence of sidewalls. Fourier analysis of wall-pressure data revealed frequency bands typically associated with low-frequency shock oscillations, $\text{St}\approx O\left(0.01\right)$, as well as vortex shedding occurring at mid frequencies, $\text{St}\approx O\left(0.1\right)$. The spectra of shock oscillations and separation bubble breathing indicated a dominant low- and mid-frequency component, respectively, akin to a quasi-two-dimensional shock-induced separation. The centerline shock oscillations were well correlated with the breathing motion of the centerline separation bubble, as well as turbulence in the upstream boundary layer. Effects of sidewalls on the overall unsteadiness were investigated by estimating coherence and correlations between various quantities. Plots of coherence between shock motion and pressure fluctuations in the domain indicated asymmetric motion of the interaction, possibly caused by alternating breathing motion of the separated zones on the sidewalls. Space-time correlations on the floor suggested a strong influence of centerline separation on the corner separations and vice versa. Similar correlations with left and right sidewalls confirmed the asymmetric motion of the interaction with a frequency of $\text{St}\approx 0.026$.

Lagrangian analysis of materially conserved scalars is applied to the problem of turbulent transport in variable-density flows. The consequences of an additional material conserved quantity, the density, is generally not acknowledged and leads to significant and meaningfully different expressions for turbulent transport in the moment equations. The formal Lagrangian analysis produces gradient transport expressions substantially different from those obtained by the physically intuitive “argument by analogy” method used in computational models. Various intuitive arguments, in Favre and Reynolds averaged settings, are contrasted to the formal Lagrangian results. Using expressions from the formal analysis, we derive consistent gradient transport closures for the turbulent transport terms that appear in the first- and second-order Favre moment equations. Results for coupled multispecies turbulent transport are given. The analysis is limited to variable-density turbulence in which the dilatation of the fluctuating velocity is small. The results are applicable to turbulent combustion and to stellar convection problems in which the density fluctuations are on the order of the mean density.

Hydrodynamic modes in the turbulent mixing layer over a cavity can constructively interact with the acoustic modes of that cavity and lead to aeroacoustic instabilities. The resulting limit cycles can cause undesired structural vibrations or noise pollution in many industrial applications. To further the predictive understanding of this phenomenon, we propose two physics-based models which describe the nonlinear aeroacoustic response of a side branch aperture under harmonic forcing with variable acoustic pressure forcing amplitude $p_a$. One model is based on Howe's classic formulation that describes the shear layer as a thin vortex sheet, and the other is based on an assumed vertical velocity profile in the side branch aperture. These models are validated against experimental data. Particle image velocimetry (PIV) was performed to quantify the turbulent and coherent fluctuations of the shear layer under increasing $p_a$. The specific acoustic impedance $Z$ of the aperture was acquired over a range of frequencies for different bulk flow velocities $U$ and acoustic pressure forcing amplitudes $p_a$. In this work, we show that once the handful of parameters in the two models for $Z$ have been calibrated using experimental data at a given condition, it is possible to make robust analytical predictions of this impedance over a broad range of the frequency, bulk flow velocity, and forcing amplitude. In particular, the models allow prediction of a necessary condition for instability, implied by negative values of the acoustic resistance $\mathrm{Re}\left(Z\right)$, which corresponds to a reflection coefficient $R$ of the aperture with magnitude larger than 1. Furthermore, we demonstrate that the models are able to describe the nonlinear saturation of the aeroacoustic response caused by alteration of the mean flow at large forcing amplitudes, which was recently reported in literature. This effect stabilizes the coupling between the side branch opening and the acoustic field in the cavity, and its quantitative description may be of value for control of aeroacoustic instabilities. We visualize and compare the models' representations of the hydrodynamic response in the side branch aperture and of the saturation effect under increasing $p_a$.

Many natural flyers and swimmers routinely flex their lifting or propulsive surfaces to control the leading-edge vortex (LEV) that forms on the suction side during maneuvering at a high angle of attack. In this paper, we studied the effect of a similar bending on the vortex dynamics of a flat-plate airfoil of aspect ratio 3 (chord $5\text{cm}$) and held at an angle of attack of ${30}^{\circ }$. This flat plate is accelerated from rest to a Reynolds number of 2400, while being dynamically bent along the span in a controlled manner with a bending ratio of 0.65 and a maximum bending angle of ${30}^{\circ }$. We investigated the effect of such spanwise bending on the resultant vorticity transfer via both experiments and numerical simulation. It shows that a dynamic spanwise bending induces a change in the effective shear layer velocity along the span's bent part and creates spanwise vorticity convection. As a result, the growth of circulation in the LEV gets delayed along the bent part, and the final circulation is smaller than the no-bending case.

We experimentally investigate internal coastal Kelvin waves in a two-layer fluid system on a rotating table. Waves in our system propagate in the prograde direction and are exponentially localized near the boundary. Our experiments verify the theoretical dispersion relation of the wave and show that the wave amplitude decays exponentially along the propagation direction. We further demonstrate that the waves can robustly propagate along boundaries of complex geometries without being scattered and that adding obstacles to the wave propagation path does not cause additional attenuation.

Modification of flow characteristics by wall roughness has been intensively analyzed in the field of fluid mechanics. However, few studies have considered wall roughness in boundary layer flame flashback. In the present study, laminar boundary layer flashback in channels with roughness at the walls is studied using two-dimensional simulations. The laminar premixed flame interacts with a linear shear flow along a wall with triangle-shaped fine roughness. The simulation results show that wall roughness in this configuration can attenuate flashback tendency due to enhanced heat loss to the boundary. By comparing results for isothermal and adiabatic boundary conditions at the walls, it is shown that the heat loss enhancement due to wall roughness may be a dominant effect in determining flame propagation characteristics for the walls with low thermal resistance. The critical velocity gradient is shown to decrease with wall roughness level and increase with thermal gas expansion ratio.

The simplified model by W. R. Dean, based on a low-curvature assumption, provided an early understanding of the laminar flow in curved ducts. However, most of the following studies relied on computer simulations of the complete curvilinear Navier-Stokes equations controlled by two nondimensional parameters, the curvature ratio and the Reynolds number. In the present article an extended version of Dean's model is used and compared to existing results. The set of equations is unsteady, parabolic in a streamwise direction, expressed in Cartesian coordinates, and contains a single control parameter, namely, the Dean number. The equations are identical to those used for the Görtler instability in boundary layer flows. Nonetheless, their extension to duct flows remains to be validated, which is the main purpose of the present article. The model satisfactorily reproduces benchmark results in the literature. In particular we retrieve the successive bifurcations between steady, unsteady, and chaotic regimes for 2D flows. The model also reproduces the development of three-dimensional flow in an elbow with a curvature radius equal to 15.1 times the square duct width. In addition, the present results confirm the Dean number as the single control parameter for laminar flows in a weakly curved ducts.

The effect of a small density difference, i.e., lower than $12\%$, between the two miscible liquid streams fed to a T-shaped junction is investigated experimentally and through numerical simulations. Micron-resolution particle image velocimetry (micro-PIV) experiments provided detailed support to the numerical analysis of how stratification influences flow features in different flow regimes. From dimensional analysis, we find that gravitational and inertial fluxes balance each other at a distance $L=d/\sqrt{\text{Ri}}$ from the confluence along the mixing channel, where $d$ is the hydraulic diameter and Ri is the Richardson number. In general, at distances $\left|y\right|\ll L$, the influence of gravity can be neglected, while at $\left|y\right|\gg L$ the two fluids are fully segregated; in particular, at the confluence, the flow field is the same as the one that we obtain assuming that the two inlet fluids are identical. Thus, in the segregated regime, the contact region separating the two fluids of the inlet streams remains vertical at distances $\left|y\right|\ll L$ along the mixing channel while it becomes progressively horizontal at $\left|y\right|\approx L$. In the vortex regime as well, near the confluence the flow field presents a mirror symmetry, with a very small resulting degree of mixing; however, as we move down the mixing channel, when $\left|y\right|>L$, gravity becomes relevant, leading to a symmetry breaking that promotes convection and enhances mixing. When we further increase the Reynolds number, in the engulfment regime, the degree of mixing becomes much larger due to the mixing induced by the flow instability at the confluence and thus the successive stratification appears to have a small effect on the flow topology, with a degree of mixing that continues to grow very slowly in the mixing channel, similar to what happens in the case of identical inlet fluids. As expected, the onsets of the vortex and engulfment regimes occur at values of the Reynolds number Re that hardly depend on the density difference between the two inlet fluids, provided that Re is defined in terms of the fluid properties of a homogeneous fluid mixture. Finally, the reaction yield along the mixing channel is computed both from numerical and experimental data. In agreement with theoretical predictions, we found that the reaction yield depends on the Damköhler number and the kinetic constant, while it is independent of the density ratio, at least within the range of the investigated conditions.

While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general nonequilibrium flows. In this paper, a method is developed based on a local reconstruction of the inviscid velocity profile $U_I\left[y\right]$ resulting from the application of the Bernoulli equation in the wall-normal direction. The boundary-layer thickness ${\delta }_{99}$ is then defined as the location where $U/U_I=0.99$, which is consistent with its classical definition for the zero-pressure-gradient boundary layers. The proposed local-reconstruction method is parameter-free and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the local-reconstruction method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the local-reconstruction method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.

Holmboe waves are long-lived traveling waves commonly found in environmental stratified shear flows in which a relatively sharp, stable density interface is embedded within a more diffuse shear layer. Although previous research has focused on their linear properties (the Holmboe instability), and on their turbulent properties (Holmboe wave turbulence), little is known about their finite-amplitude properties in the nonlinear but nonturbulent regime. In this paper we tackle this problem with a weakly nonlinear temporal stability analysis of Holmboe waves. We employ the rigorous and versatile amplitude expansion method recently proposed by Pham and Suslov [R. Soc. Open Sci. 5, 180746 (2018)], which remains well posed a finite distance away from the critical point of linear instability. Starting with the most amplified linear Fourier mode (order 1 in amplitude), we systematically derive the hierarchy of nonlinear modes (orders 2 and 3) required to obtain Landau coefficients that allow the instability to eventually saturate to a stable equilibrium amplitude. We introduce the algorithm step by step, first on a single-mode instability (suited to the weakly stratified Kelvin-Helmholtz instability), before extending it to the more subtle case of a double-mode instability (suited to the more strongly stratified Holmboe instability of interest). We present numerical solutions for the canonical stratified shear layer with hyperbolic-tangent symmetric profiles, shear-to-density thickness ratio $R=5$, and Prandtl (or Schmidt) number $\text{Pr}=700$. We select four locations on the linear stability boundary: three qualitatively distinct Holmboe cases (having widely different Reynolds numbers Re, Richardson numbers $J$, streamwise wave numbers $k$, and phase speeds), and one Kelvin-Helmholtz case to serve as a comparison. We produce supercritical bifurcation diagrams for each case, both in Re and $J$, and we find great differences in the scaling and magnitude of stable equilibrium branches, be it between Holmboe cases, between the Holmboe and Kelvin-Helmholtz cases, and between bifurcations in supercritical Re or $J$. We also study phase portraits to delve into the transient dynamics of the two counterpropagating Holmboe modes, and we find a special case in which specific initial conditions can lead to the nonmonotonic growth or decay of individual modes. Next, we deconstruct the perturbation expansions to investigate in detail the spatial structures of all the component modes (linear and nonlinear), and highlight the underlying saturation mechanisms. We again find differences between Holmboe cases, and Re or $J$ (such as the dominance of order-2 vs order-3 terms, and of various wave-number harmonics $0,k,2k,3k$). Finally, we discuss the potential relevance of our analysis to recent experimental measurements of supercritical Holmboe waves, and its possible extension to asymmetric Holmboe waves to tackle the question of mode selection. We believe these results provide a basis for a future fully nonlinear analysis of the Holmboe dynamical system.

One of the most distinctive hallmarks of many-body systems far from equilibrium is the spontaneous emergence of order under conditions where disorder would be plausibly expected. Here, we report on the self-transition between ordered and disordered emulsions in divergent microfluidic channels, i.e., from monodisperse assemblies to heterogeneous polydisperse foamlike structures, and back again to ordered ones. The transition is driven by the nonlinear competition between viscous dissipation and surface tension forces as controlled by the device geometry, particularly the aperture angle of the divergent microfluidic channel. An unexpected route back to order is observed in the regime of large opening angles, where a trend towards increasing disorder would be intuitively expected.

In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data, state-of-the-art neural networks, such as convolutional neural networks, may not preserve well-known physical priors, which may in turn question their application to real case-studies. To address this issue, we investigate hard and soft constraints into the model based on classical transformation invariances and symmetries derived from physical laws. From simulation-based experiments, we show that the proposed transformation-invariant NN model outperforms both purely data-driven ones as well as parametric state-of-the-art subgrid-scale models. The considered invariances are regarded as regularizers on physical metrics during the a priori evaluation and constrain the distribution tails of the predicted subgrid-scale term to be closer to the DNS. They also increase the stability and performance of the model when used as a surrogate during a large-eddy simulation. Moreover, the transformation-invariant NN is shown to generalize to regimes that have not been seen during the training phase.

In a linearly stratified fluid, two sets of resonant triads with one member in common, hence coupled, can arise for a wide range of wave numbers where all five waves travel in the same direction. The nonlinear dynamics is investigated by deriving the evolution equations of slowly varying wave packets. The dependence of the interaction coefficients on the channel depth and the buoyancy frequency are explicitly demonstrated. Coupling may produce instabilities with growth rates bigger than those displayed by either triad in isolation. Similar properties are expected for layered fluids with shear currents. By drawing on a recent link between modulation instability and the occurrence of rogue waves, surprisingly large displacements in the interior of the fluid are thus more likely. For applications to oceanography, the interaction coefficients of the evolution equations will affect the magnitude of the actual amplitude of an internal rogue wave. Computations indicate that displacements much larger than those of surface rogue waves are possible. From a more theoretical perspective of wave resonance through the Madelung representation, special ranges of dynamical phase angles are identified for the existence of time invariants. Finally, numerical simulations of a simplified system are performed to highlight the spontaneous generation of modes due to coupling.

Marginal regeneration is the process at the origin of the thinner patches produced at the bottom of vertical soap films and slowly rising to the top. It controls the film drainage, and thus its lifetime, and ultimately the life span of the whole foam sample. Despite its importance, the dynamical properties of this original hydrodynamical instability remains to be elucidated. Using a deformable frame, we identify a way to trigger the instability in a horizontal film; as the gravity-induced rising motion of the patches is suppressed in this case, we are able to study its long time dynamics for the first time, in a well-controlled situation. The predictions made by Mysels et al. [Soap Films: Study of Their Thinning and a Bibliography (Pergamon, New York, 1959)] are successfully tested on our data and are extended by an original coarsening model we develop. This model quantitatively reproduces the patch growth in the horizontal geometry and, when adapted to the vertical situation, is consistent with the known properties of the instability.

We study the subgrid-scale characteristics of a vorticity-transport-based approach for large-eddy simulations. In particular, we consider a multidimensional upwind scheme for the vorticity transport equations and establish its properties in the under-resolved regime. The asymptotic behavior of key turbulence statistics of velocity gradients, vorticity, and invariants is studied in detail. Modified equation analysis indicates that dissipation can be controlled locally via nonlinear limiting of the gradient employed for the vorticity reconstruction on the cell face such that low numerical diffusion is obtained in well-resolved regimes and high numerical diffusion is realized in under-resolved regions. The enstrophy budget highlights the remarkable ability of the truncation terms to mimic the true subgrid-scale dissipation and diffusion. The modified equation also reveals diffusive terms that are similar to several commonly employed subgride-scale models including tensor-gradient and hyperviscosity models. Investigations on several canonical turbulence flow cases show that large-scale features are adequately represented and remain consistent in terms of spectral energy over a range of grid resolutions. Numerical dissipation in under-resolved simulations is consistent and can be characterized by diffusion terms discovered in the modified equation analysis. A minimum state of scale separation necessary to obtain asymptotic behavior is characterized using metrics such as effective Reynolds number and effective grid spacing. Temporally -evolving jet simulations, characterized by large-scale vortical structures, demonstrate that high Reynolds number vortex-dominated flows are captured when criteria is met and necessitate diffusive nonlinear limiting of vorticity reconstruction be employed to realize accuracy in under-resolved simulations.

We investigate energy transfer mechanisms for vortex shedding in the two-dimensional cylinder wake at a Reynolds number of $\text{Re}=100$. In particular, we focus on a comparison of the energy transfer in the true flow field to that predicted by resolvent analysis. The energy balances achieved by the true cylinder flow are first characterized—both for the flow as a whole and for each of its most energetic harmonic frequencies. It is found that viscous dissipation balances production when each is considered over the entire flow field and therefore that linear mechanisms achieve an energy balance on their own, thus respecting the Reynolds–Orr equation. Suitable energy conservation laws reveal that while nonlinear mechanisms neither produce nor consume energy overall, they nevertheless account for an important transfer of energy to higher frequencies. The energy balance for DNS is compared to that predicted by resolvent analysis. Although a suitable energy balance is achieved for each harmonic, resolvent analysis does not correctly model nonlinear energy transfer between temporal frequencies since it only models interactions between the mean flow and fluctuations. The impact of the neglected nonlinear energy transfer on the resolvent mode shapes is also made clear by analyzing the spatial distribution of the energy transfer mechanisms. We then investigate the detailed roles of energy transfer from the viewpoint of nonlinear triadic interactions by considering a finite number of harmonic frequencies. It is shown that interfluctuation interactions play a critical role in the redistribution of energy to higher harmonic frequencies. We observe not only an energy cascade from low frequencies to high frequencies, but also a considerable inverse cascade from high frequencies to low frequencies. The true energy pathways observed among harmonic modes provide additional constraints that could help to improve the modeling of nonlinear energy transfer in the cylinder flow.

Rapid electrokinetic patterning (REP) is an emerging microfluidic tweezer which can dynamically trap and manipulate micro- and nanoparticles via modulation of electrothermal vortices with optical patterns. By analyzing the trajectory of trapped particles with subpixel resolution, we show that the transverse trapping force in REP originates due to axisymmetric Stokes drag experienced by the particles in toroidal electrothermal vortices. The trapping force scales linearly with radial distance from the trap center and trap stiffness is on the order of femtonewtons/μm in the transverse plane. This low trap stiffness is a direct feature of the fluidic nature of the REP trapping and would be useful for measuring femtonewton-scale forces.

Droplets spontaneously move when they are placed at the tip of a cone surface. Using three dimensionally printed structures, we experimentally explore a large panel of configurations regarding the aperture angle of the cone. We evidence a change of the droplet geometry while moving along the conical fiber. This transition is a switch of configuration from barrel to clamshell shape. The consequence is a change in the droplet dynamics. We estimate the position of this geometrical transition and we propose two models to describe the motion of the barrel and the clamshell droplets. While both shapes are driven by capillary forces, the dissipation is dependent on the geometrical configuration. For barrel shape droplets the main dissipation appears to be in the liquid wedge. For clamshell shape droplets the dissipation occurs mainly in the liquid film close to the conical fiber.