This paper is associated with a poster winner of a 2018 APS/DFD Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.P0004

Previous studies on the onset of miscible viscous fingering (VF) have been modeled with two semi-infinite fluid regions, where the more viscous fluid from one region is displaced by the less viscous fluid of the other region. However, most of the experiments were performed by filling the Hele-Shaw cell with a highly viscous fluid and then displacing it by a less viscous fluid through the inlet boundary. This causes the difference in the boundary condition at the inlet, where the reflective boundary arises for the former, and the absorbing boundary is for the latter case, and they correspond to a Neumann- and Dirichlet-type of boundary condition, respectively, in the species transport convection-diffusion equation. The literature on the linear stability analysis (LSA) of miscible VF for the reflective boundary case is largely available. Here we investigate the effects, and we compare both boundary conditions for the onset of miscible VF. In either of the configurations, the base-state is found to be unsteady, which leads to a nonautonomous dynamical system, and perturbations are not localized around the interface in the original coordinate system. To overcome these difficulties, we used the initial value problem (IVP) in a similarity domain, and we found that the onset of VF is delayed in the absorbing boundary case as compared to the reflective one. Interestingly, it is observed from the LSA that there exists a threshold mobility ratio for which the boundary conditions can affect the maximum at the onset of instability. Furthermore, fully nonlinear simulations are carried out using comsol multiphysics, and the results are found to be in good agreement with the LSA.

By smoothing the length-scale independent conic interface under an electric field into a pendant meniscus with finite curvature, dripping dynamics with a unique far-field sensitivity is observed. Two distinct dripping modes are detected: a microdripping regime whose droplet size is independent of the far field and a dripping regime whose droplet size depends on the far field exponentially. The exponential sensitivity is the result of a universal logarithm dependence of the Maxwell force on the droplet dimension for the pendant drop interface topology and the field independence of the former is due to the cutoff of this dependence by the orifice diameter. Universal self-similar scaling based on the local analysis of this dripping droplet is able to collapse the data over a large window of operating parameters. It hence allows precise tuning of the droplet size with this droplet generation mechanism.

Equilibrium boundary layer (EBL) analysis is performed on filtered turbulence flow fields for the purpose of deriving key closure models for scale-resolving simulations (SRS) of turbulence. The objective is to convey the near-wall closure modeling advantages of the Reynolds-averaged Navier-Stokes (RANS) method to SRS methodology. In the context of two-equation SRS turbulence closure, the filtered flow field EBL analysis leads to closure models for turbulent transport of unresolved kinetic energy and dissipation as a function of degree of resolution. The resulting model is then employed to perform SRS-PANS (partially averaged Navier-Stokes method) computations of turbulent channel flow. It is first demonstrated that PANS computations yield flow-field statistics that are consistent with filtered-field closure modeling assumptions. The PANS results are then compared against established direct numerical simulation and experimental data. It is exhibited that mean velocity, Reynolds stresses, and qualitative and quantitative coherent-structure features are well captured at a reasonable computational effort.

Droplet deposition after impact on superhydrophobic surfaces has been an important area of study in recent years for its potential application in reduction of pesticides usage. Minute numbers of long-chain polymers added to water have been known to arrest the droplet rebound effect on superhydrophobic surfaces. Previous studies have attributed different reasons like extensional viscosity, dominance of elastic stresses, or slowing down of the contact line in the retraction phase due to stretching of polymer chains. The present study attempts to unravel the existence of critical criteria of polymer concentration and impact velocity on the inhibition of droplet rebound. The impact velocity will indirectly influence the shear rate during the retraction phase, and the polymer concentration dictates the relaxation timescale of the elastic fluids. Finally, we show that the governing Weissenberg number (at onset of retraction), which quantifies both the elastic effects of polymer chains and the hydrodynamics, is the critical parameter in determining the regime of onset of rebound suppression, and that there is a critical value which determines the onset of bounce arrest. The previous three causes, which are manifestations of elastic effects in non-Newtonian fluids, can be related to the proposed Weissenberg number criterion.

In the past, dual states were reported in turbulent plane Couette flow with spanwise rotation at ${\text{Re}}_w=1300$ and $\text{Ro}=0.2$ based on direct numerical simulations at a computational box $10\pi h\times 2h\times 4\pi h$, where the flow would evolve to a state with three or two pairs of roll cells if the simulation started with the initial flow field $u_i^{3p}$ or $u_i^{2p}$. In the present work, the influence of an initial flow field on the dual states is investigated. Nine new simulations with an initial flow field constructed by $u_i=\alpha u_i^{2p}+(1-\alpha )u_i^{3p}$ ($\alpha =0.1,0.2,...,0.9$) are carried out, and it turns out that the flow will evolve to a state with three pairs of roll cells if $\alpha \le 0.6$, while the flow will have only two pairs of roll cells when $\alpha \ge 0.7$, which documents the robustness of two states. The turbulent statistics is also revisited, and it is found that the turbulent kinetic energy and related dissipation are larger in the state with more roll cells. The terms in the transport equations of the Reynolds stresses are generally of the same shape at two different states, but the state with more roll cells has a larger value. The energy transfer between the secondary and the residual fields shows that the secondary flows are more energetic at the state with more roll cells while the residual field is more energetic in the other state. Furthermore, a local inverse energy cascade is observed in the near wall region at the latter state with fewer roll cells where the energy is transferred from the residual field to the secondary flow field. Our results support the conjecture that the large-scale secondary flows play a very important role in the dual states of spanwise rotating plane Couette flows.

We study the problem of fluid mixing induced by gravity-driven Rayleigh-Taylor convective dissolution in porous media with top and bottom confinement. The competition between buoyancy and diffusion is measured by the Rayleigh-Darcy number, ${\text{Ra}}_0$, the value of which controls the entire dynamics of the flow. In this work, mixing is quantified by the mean scalar dissipation rate, $\langle \chi \rangle$. Our results indicate that the time behavior of $\langle \chi \rangle$ is nontrivial and distinctly different from previous observations in Rayleigh-Bénard configuration. Analyzing a number of simulations for a broad range of ${\text{Ra}}_0$, we clearly show that, in the convection-dominated regime, $\langle \chi \rangle$ exhibits a sublinear growth $\left(\langle \chi \rangle \sim t^{0.3}\right)$, which, in the limit of large ${\text{Ra}}_0$, is very robust, does not seem to depend on ${\text{Ra}}_0$, and can pave the way for new modeling perspectives.

The objective of the present study is to explain the evolution of the transonic buffet phenomenon from two-dimensional airfoils to three-dimensional swept wings by a global stability analysis. With respect to two-dimensional buffet, shock oscillation frequency increases by a factor of 4 to 7 in the case of a swept ${30}^{\circ }$ wing and three-dimensional patterns in the detached boundary layer are convected outboard. Crouch et al. [J. Comput. Phys. 224, 924 (2007)] explained the two-dimensional transonic buffet phenomenon by the appearance of a real positive complex eigenvalue of the linearized Jacobian matrix. In the case of an infinite unswept wing, the present study shows that two unstable modes actually exist: The two-dimensional transonic buffet mode already identified by Crouch et al. [J. Fluid Mech. 628, 357 (2009)] and a strongly amplified three-dimensional zero-frequency mode. The latter exhibits regular patterns in the separated boundary layer, which relates to the so-called buffet cells as named by Iovnovich et al. [AIAA J. 53, 449 (2015)]. The nonzero sweep angle generates a spanwise velocity component on the wing which convects the cells outboard. This impacts both modes identified in the unswept case: The two-dimensional mode is weakly damped by the sweep while the three-dimensional buffet cells mode, even if weakly damped, remains strongly unstable and now exhibits a nonzero frequency which increases with the sweep angle. The frequency and wavelength of the most unstable three-dimensional mode for a sweep angle of ${30}^{\circ }$ agree well with numerical and experimental values of the three-dimensional transonic buffet on wings. The analysis of the wavemaker of the three-dimensional modes indicates that the core of the instability is nearly solely located in the separated region, with a maximum along the separation line. In contrast, the wavemaker of the two-dimensional buffet mode exhibits stronger values all along the shock wave.

A study of the flow around three tandem square prisms may provide us a better understanding of complicated flow physics related to multiple closely spaced structures. In this paper, a numerical investigation on the flow around three tandem square prisms at a Reynolds number $\mathrm{Re}(=U_{\infty }W/\nu )=150$ is conducted for $L/W=1.2–10.0$, where $U_{\infty }$ is the freestream velocity, $W$ is the prism width, $L$ is the prism center-to-center spacing, and ν is the kinematic viscosity of the fluid. Extensive analyses are done of flow structures, Strouhal numbers St, fluid forces, and vorticity, velocity, and pressure fields. Four distinct flow regimes and their ranges are identified, viz., single bluff-body flow (Regime I, $1.2\le L/W<3.0$), alternating reattachment flow (Regime II, $3.0<L/W<4.3$), synchronous coshedding flow (Regime III, $4.3<L/W<7.3$) and asynchronous coshedding flow (Regime IV, $7.3<L/W\le 10.0$). Regime III is further subdivided into two regimes: single St flow (Regime IIIA, $4.3<L/W<5.1$) and dual St flow (Regime IIIB, 5.1 < L/W < 7.3). The dependence on L/W of fluctuating and time-mean fluid forces and St of the three prisms in each regime is studied in detail and connected to the flow structures. A secondary vortex street following the primary vortex street is observed for Regimes IIIB and IV. The detailed physics of the evolution of the primary vortex street to the secondary is imparted. The inherent frequency associated with the secondary vortex street is smaller than that with the primary. The evolution process of the primary vortex street to the secondary leads to a tertiary frequency. Dynamic mode decomposition analysis is proposed for the first time as a useful and quantitative tool to identify and quantify the secondary vortex street and its onset position.

The steady translation of a spherical particle under constant rotation in a viscoelastic incompressible fluid is analytically studied. The fluid is modeled using the finitely extensible nonlinear elastic constitutive equation with the Peterlin approximation (FENE-P) and its limiting case, which is the Oldroyd-B model. Steady state and creeping and isothermal flow conditions are assumed. The solution of the governing equations is found by applying a regular perturbation scheme with the small parameter being the Deborah number $\mathrm{De}=U\lambda /R$, where λ is the single relaxation time of the ambient fluid, $U$ is the sedimentation velocity of the particle, and $R$ is its radius. A high-order asymptotic solution is found for all the flow variables, and a fourth-order expression for the total drag force on the particle is derived. A technique that accelerates the convergence of series is also implemented and an improved solution is derived. Comparison of the latter with numerical results by Castillo et al. [Phys. Rev. Fluids 4, 063302 (2019)] shows excellent agreement, even for high values of the Deborah number, indicating the ability of the analytical methods and techniques used here to capture and predict accurately essential characteristics of the flow.

Understanding macroscopic behaviors of suspensions of active particles is a challenging issue in the study of living fluids. We investigate the response of shape-change driven microswimmers to an external flow. In particular, we calculate the viscosity of the dilute suspension of active microswimmers when the flow timescale is close to that of the swimmer activity, resulting in an ample contribution of the swimmer activity to rheology. We find that the shape activity leads to either an increase or a decrease of the effective viscosity, depending on the shear rate. These opposite behaviors occurring for the same microswimmer originate from a phase-locking phenomenon between the swimmer shape oscillations and the applied flow. A simplified analytical model remarkably reproduces the results of full simulations, and offers a promising framework for the derivation of macroscopic constitutive laws for active matter.

The transition mechanism and unsteady behavior behind a backward-facing step (BFS) in the supersonic regime at $\text{Ma}=1.7$ and ${\text{Re}}_{{\delta }_0}=13718$ is investigated using large-eddy simulation (LES). The visualization of the flow field shows that the transition process behind the step is initiated by a Kelvin-Helmholtz (K-H) instability of the separated shear layer, followed by secondary modal instabilities of the K-H vortices, leading to $\mathrm{\Lambda }$-shaped vortices, hair-pin vortices and finally to a fully turbulent state. The separation system features a broadband low-frequency dynamics in the range of $f{\delta }_0/u_{\infty }=0.003\sim 0.20$ as concluded from the spectral and statistical analysis. Dynamic mode decomposition suggests that the medium frequency motions centered around $f{\delta }_0/u_{\infty }=0.06$ are related to the interactions between reattaching and the shedding of large coherent shear vortices, while the lower ($f{\delta }_0/u_{\infty }\approx 0.01$) and higher ($f{\delta }_0/u_{\infty }\approx 0.1$) frequency unsteadiness are associated with the periodical expansion and shrinking of the separation system and the convection of upstream K-H vortices, respectively. All these three unsteady mechanisms are coupled to the laminar-to-turbulent transition process in the different stages.

We reveal and investigate a type of linear axisymmetric helical magnetorotational instability which is capable of destabilizing viscous and resistive rotational flows with radially increasing angular velocity, or positive shear. This instability is double-diffusive by nature and is different from the more familiar helical magnetorotational instability, operating at positive shear above the Liu limit, in that it works instead for a wide range of the positive shear when $\left(\mathrm{i}\right)$ a combination of axial and azimuthal magnetic fields is applied and $\left(\mathrm{ii}\right)$ the magnetic Prandtl number is not too close to unity. We study this instability first with radially local Wentzel-Kramers-Brillouin (WKB) analysis, deriving the scaling properties of its growth rate with respect to Hartmann, Reynolds, and magnetic Prandtl numbers. Then we confirm its existence using a global stability analysis of the magnetized flow confined between two rotating coaxial cylinders with purely conducting or insulating boundaries and compare the results with those of the local analysis. From an experimental point of view, we also demonstrate the presence of this instability in a magnetized viscous and resistive Taylor-Couette flow with positive shear for such values of the flow parameters, which can be realized in upcoming experiments at the DRESDYN facility. Finally, this instability might have implications for the dynamics of the equatorial parts of the solar tachocline and dynamo action there, since the above two necessary conditions for the instability to take place are satisfied in this region. Our global stability calculations for the tachocline-like configuration, representing a thin rotating cylindrical layer with the appropriate boundary conditions—conducting inner and insulating outer cylinders—and the values of the flow parameters, indicate that it can indeed arise in this case with a characteristic growth time comparable to the solar cycle period.

Pressure-imposed rheometry is used to examine the influence of surface roughness on the rheology of immersed and dry frictional spheres in the dense regime. The quasistatic value of the effective friction coefficient is not significantly affected by particle roughness while the critical volume fraction at jamming decreases with increasing roughness. These values are found to be similar in immersed and dry conditions. Rescaling the volume fraction by the maximum volume fraction leads to collapses of rheological data on master curves. The asymptotic behaviors are examined close to the jamming transition.

We present an experimental study of surface wave fields in single- and double-slit experiments with single wave-driven droplets of silicone oil that bounce on a vertically vibrated bath of the same liquid. During slit passage, we observe significant reduction of the central wave crest behind the droplet and disruption of the horseshoe-shaped wave field that is characteristic of a droplet over flat topography. In the double-slit experiments, we find a weak wave field in and through the slit that is not visited by the droplet, and there are only minute differences between the single- and double-slit experiments in the wave field along the center line of the slit that is visited by the droplet. We discuss our observations in relation to the slit experiments by Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] and Pucci et al. [J. Fluid Mech. 835, 1136 (2018)].

A perspective is presented on how machine learning (ML), with its burgeoning popularity and the increasing availability of portable implementations, might advance fluid mechanics. As with any numerical or experimental method, ML methods have strengths and limitations, which are acknowledged. Their potential impact is high so long as outcomes are held to the long-standing critical standards that should guide studies of flow physics.

A theoretical model of liquid and particle random fluctuations is proposed for gravity-driven flows of inertial homogeneous suspensions. It is based on a paradigm assuming that fluctuations of both liquid velocity and particle slip velocity are driven by fluctuations of the phase indicator function. It is shown that this model accurately predicts the energy of the fluctuations of both the fluid and particle phases measured in a homogeneous solid-liquid fluidized bed over a wide range of particle volume fractions, from $10\%$ to $45\%$.

Viscous fingering on chemically reactive and immiscible interface is simulated by the phase-field method. The reaction produces surfactants on the interface to reduce local interfacial tension. Parametric analysis regarding the influences of reaction, determined by the dimensionless Damköhler number (Da) and the saturated capillary coefficient (${\epsilon }_s$), on the fingering prominence at a prescribed breakthrough time is presented. The injection rate and viscosity ratio are also varied to observe their influences on the patterns. Transported by the fountain flows formed in the fingers, the produced surfactants tend to accumulate on the sides of fingers to weaken the local interfacial tension so that great variation of capillary effect will exist along the interface, especially for an intermediate range of Da. The weaker local capillary effect on a finger's side could result in prominent side-branching instability. Nonmonotonic behavior regarding the prominence of fingering instability for continuously increased injection flow rate observed in experiments is confirmed and explained qualitatively by the simulations. A reference capillary number $\left({\text{Ca}}_R\right)$ is proposed which is capable to monotonically describe the viscous fingering associated with both temporal and spatial changes of interfacial tension by reaction.

In this paper, the subgrid-scale (SGS) force and the divergence of SGS heat flux of compressible isotropic turbulence are modeled directly by an artificial neural network (ANN), which serves as a data-driven SGS modeling tool for large-eddy simulations (LESs). The unclosed SGS force and divergence of SGS heat flux are modeled based on the local stencil geometry with Galilean invariance. The input features include the first-order and second-order derivatives of filtered velocity and temperature, filtered density, and its first-order derivative. It is shown that the proposed ANN-F7 model shows an advantage over the gradient model in the a priori test. Specifically, the ANN-F7 model gives larger correlation coefficients and smaller relative errors than the gradient model. In an a posteriori analysis, the ANN-F7 model performs better than the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the statistical properties of flow fields at the Taylor microscale Reynolds number ${\text{Re}}_{\lambda }$ ranging from 180 to 250. The DSM and DMM models lead to the typical tilted spectral distribution of velocity, where low wave numbers are too energy rich, while those near the cutoff are damped too strongly. In contrast, it is shown that the velocity spectrum predicted by the ANN-F7 model almost overlaps with the filtered direct numerical simulation data. Besides, the ANN-F7 model reconstructs the probability density functions of SGS force and divergence of SGS heat flux much better than the DSM and DMM models. An artificial neural network with reasonable physical input features can deepen our understanding of turbulence modeling.