In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly useful: the edge states and the minimal seeds. In this nonlinear picture of the transition, the basin boundary of turbulence is set by the edge state's stable manifold and this manifold comes closest in energy to the laminar equilibrium at the minimal seed. We begin this paper by presenting numerical experiments in which three-dimensional perturbations are too energetic to trigger turbulence in pipe flow but they do lead to turbulence when their amplitude is reduced. We show that this seemingly counterintuitive observation is in fact consistent with the fully nonlinear description of the transition mediated by the edge state. In order to understand the physical mechanisms behind this process, we measure the turbulent kinetic energy production and dissipation rates as a function of the radial coordinate. Our main observation is that the transition to turbulence relies on the energy amplification away from the wall, as opposed to the turbulence itself, whose energy is predominantly produced near the wall. This observation is further supported by the similar analyses on the minimal seeds and the edge states. Furthermore, we show that the time evolution of production-over-dissipation curves provides a clear distinction between the different initial amplification stages of the transition to turbulence from the minimal seed.

We put forward the idea of defining vortex boundaries in planar flows as closed material barriers to the diffusive transport of vorticity. Such diffusive vortex boundaries minimize the leakage of vorticity from the fluid mass they enclose when compared to other nearby material curves. Building on recent results on passive diffusion barriers, we develop an algorithm for the automated identification of such structures from general, two-dimensional unsteady flow data. As examples, we identify vortex boundaries as vorticity diffusion barriers in two flows: an explicitly known laminar flow and a numerically generated turbulent Navier-Stokes flow.

We show how fully developed vortex-induced vibration (VIV) of a linearly sprung circular cylinder can be completely suppressed, i.e., driven to zero asymptotically in time, by release of a rotational nonlinear energy sink, consisting of a mass rotating about the axis of the cylinder and a dissipative element damping the rotational motion of the mass. (The nonlinear energy sink is located either inside the cylinder or beyond the spanwise extent of the flow, with which it thus interacts only through inertial coupling to the rectilinear motion of the cylinder.) We also show that VIV can be turned on by locking up the rotating mass. Once VIV is suppressed or turned on, no further action or energy input is required. Thus, this approach provides a true switch. Applications for flow control and for turning mixing on or off are discussed.

The dynamics of an oscillating shear layer when confined is enriched by retarded actions whose physical modeling is not trivial. We present a nonlinear delayed saturation feedback model, which allows us to correctly reproduce the complex shear layer spectra observed experimentally in open cavity flows in the incompressible limit. The model describes the evolution of the amplitude of the shear layer instabilities and considers two hydrodynamic feedback mechanisms directly related to the confinement introduced by the walls. One is associated with reflections of instability waves on the vertical cavity walls and the other to intracavity recirculation flow. These feedback mechanisms provide retarded actions with time lags that are used in the delay differential equation and allow the computation of the model parameters on physical grounds. The frequency components of six experimental cases in different flow regimes are well recovered by the dynamical model. The results show that the model with a single feedback mechanism produces monoperiodic oscillations of the amplitude, while the interplay of two purely hydrodynamic feedback mechanisms allow quasiperiodicity to develop.

This paper considers a single-sensor estimation of vortex shedding in cylinder wakes at $\text{Re}=100$ in simulations and at $\text{Re}=1036$ in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, linear estimation (LE), which implements a Kalman filter to estimate the flow. Second, linear-trigonometric estimation (LTE), which utilizes the same Kalman filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good performance and outperforms LE regarding the reconstruction of vortex shedding. Physically this suggests that, at the Reynolds numbers considered, the higher harmonic motions in the cylinder wake are slave to the fundamental frequency.

Understanding the role of frictional drag in diffusive transport is an important problem in the field of active turbulence. Using a generic continuum model that applies well to living systems, we investigate the role of Ekman friction on the passive transport of Lagrangian tracers that go with the local flow. We find that the crossover from ballistic to diffusive regime happens at a timescale ${\tau }_c$ that attains a minimum at zero friction, meaning that both injection and dissipation of energy delay the relaxation of tracers. We explain this by proposing that ${\tau }_c\sim {\ell }^{*}/u_{\text{rms}}$, where ${\ell }^{*}$ is a dominant length scale extracted from energy spectrum peak, and $u_{\text{rms}}$ is a velocity scale that sets the kinetic energy at steady state; both scales monotonically decrease with friction. Finally, we predict friction scaling laws for ${\ell }^{*},u_{\text{rms}}$, and the diffusion coefficient $\mathcal{D}\sim {\ell }^{*}{u}_{\text{rms}}/2$, that are valid over a wide range of fluid friction. The findings of our report should apply to transport phenomena in generic active systems such as dense bacterial suspensions, microtubule networks, or even artificial swimmers, to name a few.

The present study is on periodic three-dimensional biological flow during batlike flapping as well as fishlike undulation based spanwise symmetric three-dimensional (3D) kinematics and propulsion of batoid fish. For a single parameter based unified study on various types of real and hypothetical batoid fish, a 3D unified-kinematics model is proposed here. Using our immersed interface method based in-house code, the present numerical study is on the effect of various wavelengths (of the wavy undulation of a hydrofoil-shaped lateral cross section) and aspect ratios (of the elliptical span of the body)—corresponding to various types of batoid fishlike locomotion—at a constant nondimensional frequency of 0.5. Furthermore, for Dasyatis and a hypothetical batoid fish, the effect of various nondimensional frequencies is studied at an aspect ratio of 1. The study is done at a maximum nondimensional amplitude of 0.15 of the pitching/undulation and a Reynolds number of 10 000. A 3D vortex structure demonstrates a spanwise symmetric double row of vortex structure at the various wavelengths while a larger wavelength also results in a horseshoe type of vortices with multiple vortex rings. For propulsive performance, the maximum thrust force (propulsive efficiency) is obtained at an intermediate (smaller) wavelength. Further, with increasing aspect ratio, an increase in the thrust force and the propulsive efficiency are found for various wavelengths. A single-row (double-row) vortex structure leading to smaller (larger) thrust force is obtained at a smaller (larger) nondimensional frequency. Using the more realistic 3D kinematics, as compared to the 2D kinematics used earlier, more realistic flow structures and the associated propulsive performance parameters are presented that can be used for the efficient design of underwater vehicles.

Evaporation along a curved liquid vapor interface, such as that of a wetting meniscus, is a classic multiscale problem of vital significance to many fields of science and engineering. However, a complete description of the local evaporative flux over all length scales, especially without arbitrary tuning of boundary conditions, is lacking. A multiscale method to model evaporation from steady meniscus is described such that a need for tuning of boundary conditions and additional assumptions are alleviated. A meniscus submodel is used to compute evaporation flux in the bulk meniscus while a transition film submodel is used to account for enhanced evaporation near the contact line. A unique coupling between the meniscus and transition film submodels ensures smooth continuity of both film and mass flux profiles along the meniscus. The local mass flux is then integrated over the interfacial area to investigate the contribution from the different regions on the surface. The model is evaluated with data from cryoneutron phase-change tests conducted previously at National Institute for Standards and Technology (NIST) [K. Bellur et al., Cryogenics 74, 131 (2016)]. It is found that the peak mass flux in the transition region is two orders of magnitude greater than the flux at the apex. Despite the enhanced evaporation in the thin film region, it was found that 78–95% of the evaporation occurs in the bulk meniscus due to the large area. The bulk meniscus contribution increases with increase in vapor pressure and Bond number but decreases with an increase in thermal conductivity of the substrate. Using a nonuniform temperature boundary suggests that there is a possibility that the adsorbed film may have a nonzero mass flux.

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (nonvolatile solute $+$ solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one-dimensional nonlinear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long timescales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite-time Lyapunov exponent (FTLE) and its relation to the Reynolds number, the lattice size, and the choice of the steptime used to compute the Lyapunov exponents. The results show that using the FTLE method produces Lyapunov exponents that are remarkably stable under the variation of the steptime and lattice size. Furthermore, it reaches such stability faster than other characteristic quantities such as energy and dissipation rate. These results remain even if the steptime is made arbitrarily small. A discrepancy is also resolved between previous measurements of the dependence on the Reynolds number of the Lyapunov exponent. The signal produced by different variables in the steady state is analyzed, and the self-decorrelation time is used to determine the run time needed in the simulations to obtain proper statistics for each variable. Finally, a brief analysis on magnetohydrodynamic flows is also presented as an extension to recent work, which shows that the Lyapunov exponent is still a robust measure in the simulations, although the Lyapunov exponent scaling with the Reynolds number is significantly different from that of magnetically neutral hydrodynamic fluids.

Recent studies of rotating Rayleigh-Bénard convection at high rotation rates and strong thermal forcing have shown a significant discrepancy in total heat transport between experiments on a confined cylindrical domain on the one hand and simulations on a laterally unconfined periodic domain on the other. This paper addresses this discrepancy using direct numerical simulations on a cylindrical domain. An analysis of the flow field reveals a region of enhanced convection near the wall, the sidewall circulation. The sidewall circulation rotates slowly within the cylinder in anticyclonic direction. It has a convoluted structure, illustrated by mean flow fields in horizontal cross sections of the flow where instantaneous snapshots are compensated for the orientation of the sidewall circulation before averaging. Through separate analysis of the sidewall region and the inner bulk flow, we find that for higher values of the thermal forcing the heat transport in the inner part of the cylindrical domain, outside the sidewall circulation region, coincides with the heat transport on the unconfined periodic domain. Thus the sidewall circulation accounts for the differences in heat transfer between the two considered domains, while in the bulk the turbulent heat flux is the same as that of a laterally unbounded periodic domain. Therefore, experiments, with their inherent confinement, can still provide turbulence akin to the unbounded domains of simulations and at more extreme values of the governing parameters for thermal forcing and rotation. We also provide experimental evidence for the existence of the sidewall circulation that is in close agreement with the simulation results.

The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of unsteady motions that can, in principle, lead to energy conversion efficiencies that exceed the Betz limit not only transiently but also in time-averaged performance. Potential physical implementations of those unsteady motions are speculated.

A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and solid phases appears. Depending on the initial conditions, freezing or melting occurs until the interface eventually converges toward a stationary state. This evolution is studied numerically in a two-dimensional configuration using a phase-field method coupled with the Navier-Stokes equations. Varying the control parameters of the model, we exhibit two types of equilibria: diffusive and convective. In the latter case, Rayleigh-Bénard convection in the liquid phase shapes the solid-liquid front, and a macroscopic topography is observed. A simple way of predicting these equilibrium positions is discussed and then compared with the numerical simulations. In some parameter regimes, we show that multiple equilibria can coexist depending on the initial conditions. We also demonstrate that, in this bistable regime, transitioning from the diffusive to the convective equilibrium is inherently a nonlinear mechanism involving finite-amplitude perturbations.

We study the inertial settling of suspensions of flexible and rigid fibers using an immersed boundary method. The fibers considered are inextensible and slender, with an aspect ratio of 20. For a single Galileo number of $\text{Ga}=160$, we examine a range of dimensionless bending rigidities $0.1<\gamma <20$ and fiber concentrations $0.5<n{L}^3<25$, with $n$ being the fiber number density and $L$ the fiber length, that spans dilute and semidilute regimes. The settling fibers form streamers, regions where the fibers are packed and settle faster than the average settling velocity of the suspension, for $n{L}^3>10$. In the low-concentration regions outside the streamers, the fibers either go upward or have low settling velocities. Flexible fibers exhibit higher packing inside the streamers and smaller streamers compared to the streamers formed by the rigid fibers. Due to this higher packing, the flexible fibers settle faster compared to the rigid fibers. The formation of the streamers counterbalances the hindering of the settling velocity at higher concentrations. At higher $n{L}^3$, however, the maximum local concentration of fibers relative to a uniform distribution diminishes for both flexible and rigid fibers as the mobility of the fibers becomes limited due to the presence of other fibers in their vicinity. Due to this limited mobility, the deformation of the fibers and their settling orientation become insensitive to $n{L}^3$ for $n{L}^3>7$. In both the dilute and semidilute regimes, flexible fibers are more aligned with the direction perpendicular to gravity compared to rigid fibers.

In many simulations of turbulent flows, the viscous forces $\nu {\nabla }^2\mathbf{u}$ are replaced by a hyperviscous term $-{\nu }_p{(-{\nabla }^2)}^p\mathbf{u}$ to suppress the effect of viscosity at the large scales. In this work we examine the effect of hyperviscosity on decaying turbulence for values of $p$ ranging from $p=1$ (ordinary viscosity) up to $p=100$. Our study is based on direct numerical simulations of the Taylor-Green vortex for resolutions from ${512}^3$ to ${2048}^3$. Our results demonstrate that the evolution of the total energy $E$ and the energy dissipation $\epsilon$ remain almost unaffected by the order of the hyperviscosity used. However, as the order of the hyperviscosity is increased, the energy spectrum develops a more pronounced bottleneck that contaminates the inertial range. At the largest values of $p$ examined, the spectrum at the bottleneck range has a positive power-law behavior $E\left(k\right)\propto k^{\alpha }$ with the power-law exponent $\alpha$ approaching the value obtained in flows at thermal equilibrium $\alpha =2$. This agrees with the prediction of Frisch et al. [Phys. Rev. Lett. 101, 144501 (2008)] who suggested that at high values of $p$, the flow should behave like the truncated Euler equations (TEE). Nonetheless, despite the thermalization of the spectrum, the flow retains a finite dissipation rate up to the examined order, which disagrees with the predictions of the TEE system implying suppression of energy dissipation. We reconcile the two apparently contradictory results, predicting the value of $p$ for which the hyperviscous Navier-Stokes goes over to the TEE system and we discuss why thermalization appears at smaller values of $p$.

Coupled mixed convective and stratified systems are common in natural flows. To study experimentally the associated dynamics, we use a singular property of water: its nonlinear equation of state is characterized by a maximum density close to $4°\mathrm{C}$. By heating the top of a tank at $35°\mathrm{C}$ and cooling the bottom at $0°\mathrm{C}$, a two-layer configuration spontaneously appears. The convective motion in the bottom layer consists mostly of a large-scale circulation and rising cold plumes. This turbulent flow generates propagating internal gravity waves in the upper stably stratified layer. Particle image velocimetry measurements are performed and spectral characteristics of the convection and internal gravity waves are presented. An horizontal large-scale reversing flow in the stratified layer is observed which is viscously driven by a third, intermediate layer. This buffer layer is located between the convective and stratified layers and is thermally coupled with the convective one, hence sustaining a strong horizontal shear. Three-dimensional direct numerical simulations with geometry and physical parameters close to the experimental ones corroborate our experimental results.

Immiscible displacement of fluids with large viscosity mismatch is inherently unstable due to viscous fingering, even in porous media where capillary forces dominate. Adding polymer to the displacing fluid reduces the viscosity mismatch and suppresses the viscous fingering instability thereby increasing the fluid displacement leading to extensive use in applications such as oil recovery. Surprisingly, however, an increase in displacement occurs even for very large viscosity mismatches. Moreover, significant additional displacement is observed when the polymer solution is followed by additional water flow. Thus, the fundamental physics of this phenomenon remains unclear. To understand this behavior, we use confocal microscopy to visualize the displacement of oil in a three-dimensional micromodel of a porous medium and simultaneously measure the local flow velocities of the displacing fluid. We find that the increased displacement results from a counterintuitive effect: polymer retention in the medium and the resultant local changes in flow. Typically retention is avoided since it reduces the permeability of the medium; instead, we find that large and heterogeneous local changes in flow lead to sufficiently large enough viscous forces at the interface of the immiscible fluids resulting in increased displacement.

The directional motion of sessile drops can be induced by slanted mechanical vibrations of the substrate, which induce drop deformations combining both axisymmetric and antisymmetric modes. In this paper, we establish quantitative trends from experiments conducted within a large range of parameters, namely, the amplitude $A$ and frequency $f$ of the forcing, the liquid viscosity $\eta$, and the angle between the substrate and the forcing axis $\alpha$. These experiments are carried out on weak-pinning substrates. For most parameters sets, the averaged velocity $\langle v\rangle$ grows linearly with $A$. We extract the mobility, defined as $s=\frac{\mathrm{\Delta }\langle v\rangle }{\mathrm{\Delta }A}$. It is found that $s$ can show a sharp maximal value close to the resonance frequency of the first axisymmetric mode $f_p$. The value of $s$ tends to be almost independent on $\eta$ below 50 cSt, while $s$ decreases significantly for higher $\eta$. Also, it is found that for peculiar sets of parameters, particularly with $f$ far enough from $f_p$, the drop moves in the reverse direction. Finally, we draw a relationship between $\langle v\rangle$ and the averaged values of the dynamical contact angles at both sides of the drop over one period of oscillation.

We study the development of interfacial magnetoelastic patterns when an initially circular droplet of a field-activated fluid (ferrofluid, or a magnetorheological fluid), surrounded by a nonmagnetic fluid, is subjected to a radial magnetic field in a Hele-Shaw cell. Elasticity takes effect when the fluids are brought into contact and, due to a chemical reaction, the interface separating them becomes a gel-like elastic layer. By modeling the interface as an elastic membrane having a curvature-dependent bending rigidity, a perturbative mode-coupling theory is employed to investigate the weakly nonlinear dynamics of the system. In this context, we examine how the interface responds to the influence of magnetic, elastic, and yield stress forces. Our findings support the relevance of a curvature weakening effect, in the sense that magnetoelastic fingering structures tend to arise and protrude in regions of lower bending rigidity. We contrast the magnetoelastic patterns with the corresponding usual shapes of magnetic fluid interfaces without bending rigidity, but with surface tension.

In large eddy simulations (LESs), the large scales of turbulent motion are resolved directly, whereas the small scales that are computationally expensive to solve are modeled. The scale separation is performed either in the physical domain (space or time) or in Fourier space, which involves application of an explicit or implicit scale filtering operation, parting the resolved and subfilter-scales (well known as subgrid scales). Proper orthogonal decomposition (POD) of a turbulent flow also leads to the scale separation, where the POD modes represent characteristic scales of motion. In the present work, the similarity between the physical and Fourier scales and the POD modes, in terms of their kinetic-energy content and the interchange of energy among the scales and modes, is used to model the effect of subfilter-scales of motion for the LES. The subfilter-scales stress tensors, namely, Leonard, cross, and Reynolds are expressed directly in terms of the POD modes, while the cross and Reynolds subfilter-scale stresses are modeled, incorporating the energy contribution of the subfilter-scale POD modes. In addition to the mathematical properties of the subfilter-scale stress tensor, the model inherently predicts the near-wall asymptotic behavior and the backward transfer of subfilter-scale energy (the backscatter).