We find and study the viscoelastic transition in transonic flow focusing when polymers of low molecular weights are dissolved in water at the appropriate concentration. This phenomenon is explained in terms of the coil-stretch transition of the polymers crossing the tapering meniscus, where the airstream produces very large strain rates. The resulting elastic stress stabilizes the flow, reducing the minimum liquid flow rate leading to jetting. As a consequence, we produce jets much thinner and longer than their Newtonian counterparts, which has important consequences at the technological level. We present a scaling analysis to show the role played by the polymer relaxation time and extensional viscosity in the viscoelastic transition.

This study extends the input-output framework for the receptivity analysis of an incompressible boundary layer introduced by Ran et al. [Phys. Rev. Fluids 4, 093901 (2019)] to the laminar adiabatic supersonic case. Spatially distributed in the wall-normal direction, a $\delta$-correlated Gaussian noise is considered as input, both including the velocity and temperature fields. Similarly, components of the resulting velocity and/or temperature fields are chosen as outputs. To study effects on the boundary layer, the measurements of the output are restricted within the ${\delta }_{99}$ boundary layer thickness, implying, however, that effects like acoustic radiation to the free stream are outside the scope of the present analysis. The main goal of the study is twofold: first, to demonstrate the potential of the chosen approach by comparison with familiar results, and second, to extend the current state of knowledge in the compressible regime in selected points by exploiting the extended capabilities of the chosen framework. To this end, the importance of the different inputs—especially the temperature effects—for the amplification of two-dimensional, oblique flow structures and streaks are discussed. Furthermore, the influence of first and second Mach modes (not present in the incompressible regime) is identified within the stochastic framework and results are discussed in light of previous receptivity analyses where the output is restricted to a single mode. By varying the spatial distribution of the forcing, the dependence of the receptivity on the wall-normal position, where the forcing is introduced, is illustrated and discussed. Finally, dominant coherent structures are identified by evaluating the first singular vector of the correlation matrix (proper orthogonal decomposition (POD) modes). By analyzing the dependence of both forcing and response POD modes on the choice of the measured component, further insight is provided about the contribution of temperature fluctuation to the stochastically maintained variance of the system.

Unforced shoaling waves experience growth and changes to wave shape. Similarly, wind-forced waves on a flat-bottom likewise experience growth/decay and changes to wave shape. However, the combined effect of shoaling and wind-forcing on wave shape, particularly relevant in the near-shore environment, has not yet been investigated theoretically. Here, we consider small-amplitude, shallow-water solitary waves propagating up a gentle, planar bathymetry forced by a weak, Jeffreys-type wind-induced surface pressure. We derive a variable-coefficient Korteweg–de Vries–Burgers (vKdV–B) equation governing the wave profile's evolution and solve it numerically using a Runge-Kutta third-order finite difference solver. The simulations run until convective prebreaking—a Froude number limit appropriate to the order of the vKdV–B equation. Offshore winds weakly enhance the ratio of prebreaking height to depth as well as prebreaking wave slope. Onshore winds have a strong impact on narrowing the wave peak, and wind also modulates the rear shelf formed behind the wave. Furthermore, wind strongly affects the width of the prebreaking zone, with larger effects for smaller beach slopes. After converting our pressure magnitudes to physically realistic wind speeds, we observe qualitative agreement with prior laboratory and numerical experiments on breakpoint location. Additionally, our numerical results have qualitatively similar temporal wave shape to shoaling and wind-forced laboratory observations, suggesting that the vKdV–B equation captures the essential aspects of wind-induced effects on shoaling wave shape. Finally, we isolate the wind's effect by comparing the wave profiles to the unforced case. This reveals that the numerical results are approximately a superposition of a solitary wave, a shoaling-induced shelf, and a wind-induced, bound, dispersive, and decaying tail.

Direct pore-scale simulations of fluid flow through porous media are computationally expensive to perform for realistic systems. Previous works have demonstrated using the geometry of the microstructure of porous media to predict the velocity fields therein based on neural networks. However, such trained neural networks do not perform well for unseen porous media with a large degree of heterogeneity. In this study we propose that incorporating a coarse velocity field in the input of neural networks is an effective way to improve the prediction performance. The coarse velocity field can be simulated with a low computational cost and provides global information to regularize the ill-posedness of the learning problem, which is usually caused by the use of local geometries due to the computational resource constraints. We show that incorporating the coarse-mesh velocity field significantly improves the prediction accuracy of the fine-mesh velocity field by comparison to the prediction that relies on geometric information alone, especially for the porous medium with a large interior vuggy pore space. We also show the flexibility of training the network in using coarse velocity fields with various resolutions. The results suggest that even using coarse velocity field with a very low resolution, the predictions are still enhanced and close to the ground truths. The feasibility of the method is further demonstrated by testing the trained network on real rocks. This study highlights the merits of incorporating a coarse-mesh velocity field into the input for neural networks, which provides global, physics-based information for the model, thereby improving the model's generalization capability.

We present an experimental investigation of the electrostatically assisted primary atomization in a coaxial gas-liquid jet. Shadowgraphy imaging reveals the primary breakup dynamics and allows for a semiquantitative assessment of the resulting droplet characteristics. We describe the statistics of the liquid core in terms of the probability distributions of its length, the spray angle, and the virtual origin. A strong axial electric field reduces the liquid core length over a wide range of gas-to-liquid momentum ratios, whereas a predominantly radial electric field influences the atomization process weakly. We characterize the primary breakup dynamics in terms of two frequencies associated with the liquid mass: the flapping frequency and the droplet-shedding frequency. Using a combination of proper orthogonal decomposition and Fourier transforms in time and space, we derive empirical dispersion relations. Observations of the initial interfacial instabilities' growth reveal shorter wavelengths and higher growth rates in the presence of a strong axial electric field. This enhanced growth of the interfacial instabilities is consistent with a mechanism whereby Maxwell's stresses drive liquid ligaments out radially across the high-speed annular gas jet, thus improving the momentum transfer between the two phases and enhancing the breakup process (producing smaller final droplet sizes). These results illustrate the importance of the electric field configuration to assist two-fluid coaxial atomization and establish electrostatic forcing as a potential feedback control input.

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data have shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [J. Bardina, J. Ferziger, and W. Reynolds, Improved subgrid-scale models for large-eddy simulation, in Proceedings of the 13th Fluid and Plasmadynamics Conference, AIAA (1980); C. Meneveau and K. Katz, Scale-invariance and turbulence models for large-eddy simulation, Ann. Rev. Fluid Mech. 32, 1 (2000)]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g., Bardina et al., Proceedings of the 13th Fluid and Plasmadynamics Conference (1980); R. A. Clark, J. Ferziger, and W.C. Reynolds. Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech. 91, 1 (1979); S. Stolz and N. A. Adams, An approximate deconvolution procedure for large-eddy simulation, Phys. Fluids 11, 1699 (1999)]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for large-eddy simulation (LES), vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence, and wall-modeled turbulent channel flow at high Reynolds numbers. The results show favorable agreement with DNS data. It has been shown that DTCSM offers similar predictive capabilities as the dynamic Smagorinsky model for canonical flows. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump (Boeing speed bump) exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to existing static coefficient (Vreman) and dynamic Smagorinsky model. The computational cost of performing LES with this model is up to 15% higher than the dynamic Smagorinsky model.

A phase dynamics concept is employed to study coherent structure formation in a 2D Euler fluid system. We demonstrate that the mean vorticity gradient has a spatial phase pinning effect on the local vortex excitations, which can lead to their phase synchronization and hence coherent structure formation. Criteria for the existence of a fully synchronized state, which are consistent with the classical eigenmode analysis, are given. We report a partially synchronized state. A numerical study shows that the steeper the mean vorticity gradient, the larger the coherent region. Incorporating the nonlinear convection effect, an interesting finding is that the small-scale vortex can induce phase synchronization of a large-scale vortex by flattening the mean vorticity profile, which in essence is similar to the phase-coupling mechanism in the linear scenario. These results can be immediately extended to the more general potential vorticity (PV) -conserved system, i.e., a Charney-Hasegawa-Mima (CHM) system.

The variations of transport efficiency in structured environments between distinct individuals in actively self-propelled systems are both hard to study and poorly understood. Here, we study the transport of a nontumbling Escherichia coli strain, an active-matter archetype with intrinsic size variation but fairly uniform speed, through a periodic pillar array. We show that long-term transport switches from a trapping dominated state for shorter cells to a much more dispersive state for longer cells above a critical bacterial size set by the pillar array geometry. Using a combination of experiments and modeling, we show that this anomalous size dependence arises from an enhancement of the escape rate from trapping for longer cells caused by nearby pillars. Our results show that geometric effects can lead to size being a sensitive tuning knob for transport in structured environments, with implications in general for active matter systems and, in particular, for the morphological adaptation of bacteria to structured habitats, spatial structuring of communities, and for antibiofouling materials design.

An efficient approach for extracting three-dimensional local averages in spherical subdomains is proposed and applied to study the intermittency of small-scale velocity and scalar fields in direct numerical simulations of isotropic turbulence. We focus on the inertial-range scaling exponents of locally averaged energy dissipation rate, enstrophy, and scalar dissipation rate corresponding to the mixing of a passive scalar $\theta$ in the presence of a uniform mean gradient. The Taylor-scale Reynolds number $R_{\lambda }$ goes up to 1300, and the Schmidt number Sc up to 512 (albeit at smaller $R_{\lambda }$). The intermittency exponent of the energy dissipation rate is $\mu \approx 0.23\pm 0.02$, whereas that of enstrophy is slightly larger; trends with $R_{\lambda }$ suggest that this will be the case even at extremely large $R_{\lambda }$. The intermittency exponent of the scalar dissipation rate is ${\mu }_{\theta }\approx 0.35$ for $\text{Sc}=1$. These findings are in essential agreement with previously reported results in the literature. We additionally obtain results for high Schmidt numbers and show that ${\mu }_{\theta }$ decreases monotonically with Sc, either as $1/log\text{Sc}$ or a weak power law, suggesting that ${\mu }_{\theta }\to 0$ as $\text{Sc}\to \infty$, reaffirming recent results on the breakdown of scalar dissipation anomaly in this limit.

In swimming microorganisms and the cell cytoskeleton, inextensible fibers resist bending and twisting, and interact with the surrounding fluid to cause or resist large-scale fluid motion. In this paper, we develop a numerical method for the simulation of cylindrical fibers by extending our previous work on inextensible bending fibers [O. Maxian et al., Phys. Rev. Fluids 6, 014102 (2021)] to fibers with twist elasticity. In our “Euler” model, twist is a scalar function that measures the deviation of the fiber cross section relative to a twist-free frame, the fiber exerts only torque parallel to the centerline on the fluid, and the perpendicular components of the rotational fluid velocity are discarded in favor of the translational velocity. In the first part of this paper, we justify this model by comparing it to another commonly used “Kirchhoff” formulation where the fiber exerts both perpendicular and parallel torque on the fluid, and the perpendicular angular fluid velocity is required to be consistent with the translational fluid velocity. Through asymptotics and numerics, we show that the perpendicular torques in the Kirchhoff model are small, thereby establishing the asymptotic equivalence of the two models for slender fibers. We then develop a spectral numerical method for the hydrodynamics of the Euler model. We define hydrodynamic mobility operators using integrals of the Rotne-Prager-Yamakawa tensor, and evaluate these integrals through a slender-body quadrature, which requires on the order of 10 points along a smooth fiber to obtain several digits of accuracy. We demonstrate that this choice of mobility removes the unphysical negative eigenvalues in the translation-translation mobility associated with asymptotic slender-body theories, and ensures strong convergence of the fiber velocity and weak convergence of the fiber constraint forces. We pair the spatial discretization with a semi-implicit temporal integrator to confirm the negligible contribution of twist elasticity to the relaxation dynamics of a bent fiber. We also study the instability of a twirling fiber, and demonstrate that rotation-translation and translation-rotation coupling change the critical twirling frequency at which a whirling instability onsets by $\sim$20%, which explains some (but not all) of the deviation from theory observed experimentally. When twirling is unstable, we show that the dynamics transition to a steady overwhirling state, and quantify the amplitude and frequency of the resulting steady crank-shafting motion.

We computationally studied the pairwise hydrodynamic interactions for simple two-dimensional dimer model swimmers over a range of intermediate Reynolds numbers $\left(\text{Re}\right)$ and for thousands of initial conditions, varying position and orientation. We found that the swimmers arranged in assemblies that were sensitive to initial conditions and $\text{Re}$. The resulting “phase diagrams” showed regions where the swimmers repel and swim away from one another, regions where they form stable pairs with different symmetries, and locations of transitions between them. The stable pairs fit neatly into combinations of five categories: swimmers in-line and side by side, parallel and antiparallel, and perpendicular to one another. Once arranged into the preferred stable pair, the swimmers swam together or turned into a symmetric immotile pump, in both cases coordinating as one and generating combined fluid flows that stabilized the assembly. By looking at the pairs' steady state velocities, we were able to provide insight on possible benefits of being in a pair versus swimming alone. For some pairs, there seemed to be a clear speed advantage over the single swimmer, while for others the presence of a second swimmer slowed them both down. Moreover, we found that the stable pairs transition their swimming direction at different Reynolds numbers and when compared to the single swimmer. The time-averaged flow fields around each stable pair are also different from one another and from the single swimmer, and evolve as $\text{Re}$ increases. Our results provide a guide for the complex nonlinear interactions that arise between self-propelled particles in fluids at intermediate $\text{Re}$ by using the fluid inertia as a knob to control assembly behavior. They are the basis for scaling up towards many-body interactions and active matter of mesoscale swimmers.

We study the mixed boundary-value problem of finding the concentration distribution surrounding a two-sided (Janus) sphere, with a uniform concentration imposed on one segment of it and the no-mass-flux condition enforced on the other one. This mass transfer problem arises in the analysis of the Marangoni propulsion phenomenon, where a chemically active particle propels itself along a liquid-gas interface via nonuniform release of a chemical species that locally alters the surface tension distribution. Assuming that the mass transfer is purely driven by diffusion (i.e., neglecting advection), we present an approximate form for the concentration field derived from the integral representation of the solution to the corresponding Laplace equation. We demonstrate the high fidelity of the proposed approach by comparing its results with those obtained from a collocation method based on the series solution of the problem. Beyond the motivating problem, our findings are expected to be applicable to the self-diffusiophoresis of catalytic colloids, as well as to the conduction heat transfer and electrostatics problems involving partially insulated spheres. Moreover, our approach can lead to the derivation of similarly accurate approximate solutions to analogous problems in mathematical physics.

We investigate the flow within a liquid-metal battery induced by an externally imposed magnetic field, $B_0$. An analytical model for laminar flow is proposed and this is found to be in excellent agreement with numerical simulations, not only for weakly forced steady flow, but also for the time-averaged velocity in more strongly forced flows where the motion is either unsteady (but laminar) or else weakly turbulent. Our primary conclusion is that surprisingly weak magnetic fields are capable of destabilizing the flow and inducing turbulence, with turbulence first appearing at $B_0\approx 1.0\mathrm{G}$. By comparison, the earth's magnetic field is ∼0.5 G. This extreme sensitivity of liquid-metal pools carrying current to an external magnetic field has long been known in the context of other industrial processes.

The important role of unicellular flagellated micro-organisms in aquatic food webs is mediated by their flagella, which enable them to swim and generate feeding currents. The flagellum in many predatory flagellates is equipped with hairs (mastigonemes) that reverse the direction of thrust compared to the thrust due to a smooth flagellum. Conventionally, the mechanism of such reversal has been attributed to drag-based thrust of individual hairs, neglecting their hydrodynamic interactions. However, at natural densities of hairs, hydrodynamic interactions are important. In fact, using fully resolved three-dimensional computational fluid dynamics, we show here that hydrodynamic interactions are key to thrust-generation and reversal in hairy flagellates, making their hydrodynamics fundamentally different from the slender-body theory governing smooth flagella. We reveal the significant role of the curvature of the flagellum, and using model analysis we demonstrate that strongly curved flagellar waveforms are optimal for thrust-generation. Our results form a basis for understanding the diverse flagellar architectures and feeding modes of predatory flagellates.

The influence of rheological properties on the breakup process of shear-thickening suspensions is studied in this paper. Using high-speed photography, we analyze the breakup morphology of cornstarch-water suspensions with different rheological behaviors. The processes of droplet formation and breakup of the cornstarch-water suspensions is divided into three stages: thinning stage, thickening stage, and diluted stage. In the thickening stage, shear-thickening behavior apparently slows the deformation of the droplet throat, and the throat diameter $D_m$ follows a power law with breakup time, $D_m\propto {\left(t_p-t\right)}^{1/5}$. A unique solidlike phenomenon occurs when the volume fraction of the suspension is $\phi >43\%$ and a slip plane forms, which resembles a cylindrical metal rod stretched by uniaxial tensile loading.

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such base flow variations enter the linearized dynamics as multiplicative sources of uncertainty that can alter the stability of the linearized dynamics and their receptivity to exogenous excitations. Our approach does not rely on costly stochastic simulations or adjoint-based sensitivity analysis. We provide verifiable conditions for mean-square stability and study the frequency response of the flow subject to additive and multiplicative sources of uncertainty using the solution to the generalized Lyapunov equation. For small-amplitude base flow perturbations, we bypass the need to solve large generalized Lyapunov equations by adopting a perturbation analysis. We use our framework to study the destabilizing effects of stochastic base flow variations in transitional parallel flows, and the reliability of numerically estimated mean velocity profiles in turbulent channel flows. We uncover the Reynolds number scaling of critically destabilizing perturbation variances and demonstrate how the wall-normal shape of base flow modulations can influence the amplification of various length scales. Furthermore, we explain the robust amplification of streamwise streaks in the presence of streamwise base flow variations by analyzing the dynamical structure of the governing equations as well as the Reynolds number dependence of the energy spectrum.

Two-dimensional channel flow simulations of FENE-P (finitely extensible nonlinear elastic-Peterlin) fluid in the elasto-inertial turbulence (EIT) regime reveal distinct regimes ranging from chaos to a steady traveling wave which takes the form of an arrowhead structure. This coherent structure provides insights into the polymer/flow interactions driving EIT. A set of controlled numerical experiments and the study of transfer between elastic and turbulent kinetic energies highlight the role of small- and large-scale dynamics in the self-sustaining cycle of chaos in EIT flows.

A large eddy simulation (LES) method employing a one-coefficient dynamic mixed model is used to generate data of two separated hypersonic shock/turbulent boundary layer interactions. The first of these is a Mach 7.2 turbulent boundary layer at ${\text{Re}}_{\theta }=3300$ over a ${33}^{\circ }$ ramp. The second is a Mach 9.1 turbulent boundary layer at ${\text{Re}}_{\theta }=8000$ over a ${34}^{\circ }$ ramp. We document the mean flow statistics including Reynolds stresses, turbulent amplification, turbulent kinetic energy budget, anisotropy tensor invariants, wall pressure distribution, skin friction, and wall heat transfer. Various modeling assumptions typically used in engineering applications such as the Reynolds Analogy Factor, constant turbulent Prandtl number, and Strong Reynolds Analogies are assessed for these conditions. The documentation of the two-dimensional time-averaged flow statistics of these two datasets is the main focus of this article, however, we first demonstrate the reliability of our LES method by simulating both a separated supersonic compression ramp flow and an attached hypersonic compression ramp flow and comparing to existing direct numerical simulation (DNS) data. An excellent comparison of mean flow profiles, turbulence amplification factors, spectral content, and the state of separation is achieved. The practicality of the LES over the DNS method is also emphasized by the typical factor of 32 reduction in grid size as well as a numerical time step increase of three times the DNS. Additional grid size reduction might be possible. A discussion on the accuracy of the mixed model in comparison to the eddy viscosity model is included. We found that at Mach 7, omitting the scale-similar contribution in the subgrid-scale models of shear stress and heat flux resulted in as much as a 32% increase in the separation length and 10% decrease in shear layer spreading rate.

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated.

In this study, we investigate the stability of a thin viscoelastic fluid draining down a uniformly heated slippery inclined plane. A theoretical model is employed consisting of the Navier-Stokes equations coupled with the conservation equation for energy. We apply a Navier slip condition at the solid-liquid interface. To obtain the critical conditions for the onset of instability, we carry out a long-wave linear stability analysis within the Orr-Sommerfeld framework. Furthermore, we derive a first-order Benney-type evolution equation for the local film thickness to analyze the effect of long-wave instabilities. The results reveal that the slippery substrate destabilizes the liquid film flow. We find that the presence of the viscoelastic parameter and Marangoni number always promotes this destabilizing effect. We use the method of multiple scales to investigate the weakly nonlinear stability analysis of the flow which shows that there is a range of wave numbers with a supercritical bifurcation and a range of larger wave numbers with a subcritical bifurcation. The study interprets that the variation of Marangoni number, slip length and viscoelastic parameter have substantial effects on different stable or unstable zones. Different instability zones are also demarcated. Finally, the direct numerical simulations of the full thin-film model clearly demonstrate the role of the viscoelastic parameter, thermocapillary, and slip length. A good agreement between the linear stability analysis and the numerical simulations is found.