Spatial evolution of electrically conducting submerged jet flow is studied by numerical simulations for the case of a transverse uniform magnetic field. This situation occurs frequently in metallurgical industry where permanent magnetic fields are applied to control the liquid metal jets. We investigate through numerical simulations the flow characteristics for Reynolds $(\mathrm{Re}<4500)$ and for moderate interaction numbers ($N$ < 0.1). The results show the occurrence of far more complex phenomena than the expected magnetohydrodynamics damping effect, in agreement with many of the theoretical predictions made by Davidson [J. Fluid Mech. 299, 153 (2001)]. The Lorentz force indeed acts against the flow within the main jet; however, it simultaneously accelerates the flow in adjacent quiescent regions. It results in a momentum redistribution in the form of a jet flattening in the direction of the applied magnetic field. Adjacent to the main jet, two strong reverse jets develop. The closure of induced currents is found to be responsible for these effects. While small-scale turbulent fluctuations are indeed suppressed, large coherent vortices aligned with the magnetic field develop within the shear region at the boundary between the main jet and the adjacent reverse jets.

The Green's function of the incompressible Stokes equations, the stokeslet, represents the singular flow due to a point force. Its classical value in an unbounded fluid has been extended near surfaces of various shapes, including flat walls and spheres, and in most cases the presence of a surface leads to an advection flow induced at the location of the point force. In this paper, motivated by the biological transport of cargo along polymeric filaments inside eukaryotic cells, we investigate the reaction flow at the location of the point force due to a rigid slender filament located at a separation distance intermediate between the filament radius and its length (i.e., we compute the advection of the point force induced by the presence of the filament). An asymptotic analysis of the problem reveals that the leading-order approximation for the force distribution along the axis of the filament takes a form analogous to resistive-force theory but with drag coefficients that depend logarithmically on the distance between the point force and the filament. A comparison of our theoretical prediction with boundary element computations shows good agreement. We finally briefly extend the model to the case of curved filaments.

Single-fluid-phase porous medium systems are typically modeled at an averaged length scale termed the macroscale, and Darcy's law is typically relied upon as an approximation of the momentum equation under Stokes flow conditions. Standard approaches for modeling macroscale single-fluid-phase flow of generalized Newtonian fluids (GNFs) extend the standard Newtonian model based upon Darcy's law using an effective viscosity and assuming that the intrinsic permeability is invariant with respect to fluid properties. This approach results in a need to perform an experiment for a non-Newtonian fluid, the introduction of effective parameters that are not tied to known microscale physics, and uncertainty regarding the dependencies of the fitted empirical parameter on system properties. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for GNF flow that is consistent with microscale conservation principles and the second law of thermodynamics. A direct connection between microscale and macroscale quantities is used to formulate an expression for interphase momentum transfer for GNF flow in porous medium systems. Darcy's law is shown to approximate momentum transfer from the fluid phase to the solid phase. Momentum transfer is found to depend on the viscosity at the solid surface, which is only invariant for Newtonian flow. TCAT is used to derive a macroscale equation for the hydraulic resistance based on accessible fluid and solid properties. This hydraulic resistance may be used in the same way that hydraulic conductivity is typically used to model flow at the macroscale, and it includes parameters that can be calculated a priori, without the need to carry out microscale simulations, or experiments, for any GNF. The TCAT approach is validated for four model isotropic and anisotropic media and five Cross-model fluids. The traditional shift factor and effective viscosity are related to the newly derived TCAT model, shedding new light on this common empirical approach. The results from this work form a basis for the modeling of GNF flow in porous medium systems under Stokes flow, which is predictive given the rheological properties of the GNF and the resistance observed for Newtonian flow.

The focus of this study is to investigate primary and secondary bifurcations to weakly nonlinear flows (weak branch) in convective rotating spheres in a regime where only strongly nonlinear oscillatory sub- and supercritical flows (strong branch) were previously found [E. J. Kaplan, N. Schaeffer, J. Vidal, and P. Cardin, Phys. Rev. Lett. 119, 094501 (2017)]. The relevant regime corresponds to low Prandtl and Ekman numbers, indicating a predominance of Coriolis forces and thermal diffusion in the system. We provide the bifurcation diagrams for rotating waves (RWs) computed by means of continuation methods and the corresponding stability analysis of these periodic flows to detect secondary bifurcations giving rise to quasiperiodic modulated rotating waves (MRWs). Additional direct numerical simulations (DNS) are performed for the analysis of these quasiperiodic flows for which Poincaré sections and kinetic energy spectra are presented. The diffusion timescales are investigated as well. Our study reveals very large initial transients (more than 30 diffusion time units) for the nonlinear saturation of solutions on the weak branch, either RWs or MRWs, when DNS are employed. In addition, we demonstrate that MRWs have multimodal nature involving resonant triads. The modes can be located in the bulk of the fluid or attached to the outer sphere and exhibit multicellular structures. The different resonant modes forming the nonlinear quasiperiodic flows can be predicted with the stability analysis of RWs, close to the Hopf bifurcation point, by analyzing the leading unstable Floquet eigenmode.

This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable model augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to as “learning and inference assisted by feature-space engineering”, is based on the hypothesis that robustness and generalizability demand a meticulously designed feature space that is informed by the underlying physics and a carefully constructed features-to-augmentation map. The critical components of this approach are: (1) maintaining consistency across the learning and prediction environments to make the augmentation case-agnostic; (2) tightly coupled inference and learning by constraining the augmentation to be learnable throughout the inference process to avoid loss of inferred information (and hence accuracy); (3) identification of relevant physics-informed features in appropriate functional forms to enable significant overlap in feature space for a wide variety of cases to promote generalizability; (4) localized learning, i.e., maintaining explicit control over feature space to change the augmentation function behavior only in the vicinity of available data points. To demonstrate the viability of this approach, it is used in the modeling of bypass transition. The augmentation—in the form of model coefficient functions—is developed using skin friction data from two flat plate cases from the ERCOFTAC dataset. Piecewise linear interpolation on a structured grid in feature space is used as a sample functional form for the augmentation to demonstrate the capability of localized learning. The impact of using a different function class (neural network) is also assessed. The augmented model is then applied to a variety of flat plate cases which are characterized by different freestream turbulence intensities, pressure gradients, and Reynolds numbers. The predictive capability of the augmented model is also tested on single-stage high-pressure-turbine cascade cases, and the model performance is analyzed from the perspective of information contained in the feature space. The results show consistent improvements across these cases, as long as the physical phenomena in question are well-represented in the training.

We employ multiple-sinusoid modulated optical tweezers to measure the frequency-dependent rheological parameters of a linear viscoelastic fluid over five decades of frequency in a single shot, hitherto not achieved using active microrheology alone. Thus, we spatially modulate a trapped probe particle embedded in a fluid medium with a combination of a square wave—which is by definition a superposition of odd sinusoidal harmonics—and a linear superposition of multiple sinusoids at a wideband frequency range, with complete control over the amplitude, frequency, and relative phase of the modulating signals. For the modulating signals, we selectively excite the particle by larger amplitudes at high frequencies where the particle response is low, thereby enabling wideband active microrheology with large signal to noise. This mitigates the principal issue associated with conventional active microrheology—which is low bandwidth—and also renders our method better in terms of signal to noise, and faster compared to passive microrheology. We determine the complex viscoelastic parameters of the fluid by extracting the phase response (relative to input excitation) of the probe from the experimentally recorded time series data of the probe displacement and employing well-known theoretical correlations thereafter. We test the efficacy of our method by studying a variety of linear viscoelastic media—polyacrylamide-water solution, worm-like micelles, and polyethylene oxide—at different concentrations and find good agreement of the measured complex fluid parameters with the known literature values.

In this work we perform reactive control of stochastic disturbances in forced turbulent jets based on destructive interference. The study is motivated by the success of recent studies in applying this type of control on instability waves in transitional boundary layers and free-shear flows. Linear convective mechanisms in the initial region of turbulent jets are explored in order to perform reactive control, wherein the actuation signal is updated in real time based on sensor measurements performed upstream, resulting in an inverse feedforward approach. The control law is based on empirical transfer functions of the jet response to stochastic forcing and actuation, which are measured experimentally. Since turbulent jets have energy content spread in a number of azimuthal wave numbers, we apply axisymmetric forcing at the nozzle lip in order to be able to perform control using a reduced number of sensors and actuators. The external forcing produces axisymmetric wave packets which possess stochastic phases and amplitudes, akin to turbulent fluctuations found in unforced jets. We demonstrate the successful implementation of real-time reactive control of these disturbances, achieving order-of-magnitude attenuations of associated velocity fluctuations. Control is shown to reduce fluctuation levels over an extensive streamwise range.

When a droplet is brought in contact with an undercooled surface, it wets the substrate and solidifies at the same time. The interplay between the phase transition effects and the contact-line motion, leading to its arrest, remains poorly understood. Here we reveal the early solidification patterns and dynamics of spreading hexadecane droplets. Total internal reflection imaging is employed to temporally and spatially resolve the early solidification behavior. With this, we determine the conditions leading to the contact-line arrest. We quantify the overall nucleation behavior, i.e., the nucleation rate and the crystal growth speed and show its sensitivity to the applied undercooling of the substrate. We also show that for strong enough undercooling it is the rapid growth of the crystals which determines the eventual arrest of the spreading contact line. By combining the Johnson-Mehl-Avrami-Kolmogorov nucleation theory and scaling relations for the spreading, we calculate the temporal evolution of the solid area fraction, which is in good agreement with our observations.

Janus particles are a class of artificial swimmers with an anisotropic coverage of catalyst on its surface. This generates a tangential chemical gradient. Solute molecules interact with the particle surface via a short-range potential. The asymmetric distribution of solute molecules gives rise to a tangential pressure gradient near the particle surface. This results in diffusio-osmotic flows in a thin region at the particle surface. The flow inside the thin layer is modeled as an effective slip velocity at the particle scale. This slip results in self-propulsion of a freely suspended particle, even in the absence of externally imposed concentration gradients. Previous studies have shown significant similarity between artificial and biological chemotaxis. Based on the magnitude of Péclet number (ratio of advective to diffusive effects), advective effects can have a moderate effect on the swimming velocity of an artificial swimmer. The current work aims at developing a theoretical framework to capture weak advective effects on the swimming velocity of an active particle under the influence of an external concentration gradient. It can be applied for any active particle with an axisymmetric surface activity distribution. Using Péclet number as a perturbation parameter, we employ a singular perturbation technique along with the method of matched assymptotic expansions to evaluate the concentration field up to $O\left(\mathrm{Pe}\right)$. Using the Lorentz reciprocal theorem, an analytical expression for the translational velocity valid up to $O\left(\mathrm{Pe}\right)$ is obtained. We show $O\left(\mathrm{Pe}\right)$ correction of solute advection always reduces the swimming velocity.

We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $\text{Sv}\equiv v_s/u_{\tau }$ is small ($v_s$ is Stokes settling velocity, $u_{\tau }$ is fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_{\tau }$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechanisms that control the vertical particle velocity and concentration profile. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small Sv is (provided it is finite). Direct numerical simulations confirm the arguments and show that the near-wall concentration is highly dependent on Sv even when $\text{Sv}\ll 1$, and it can reduce by an order of magnitude when Sv is increased from $O\left({10}^{-4}\right)$ to $O\left({10}^{-2}\right)$. The results also show that the preferential sampling of ejection events in the boundary layer by inertial particles when $\text{Sv}=0$ is profoundly altered as Sv is increased, and it is replaced by a preferential sampling of sweep events due to the onset of the preferential sweeping mechanism.

Using a large-scale wind tunnel equipped with an aerodynamic balance mounted on a rotating turntable, we first study the aerodynamic force exerted on a cyclist in time trial position from head to tailwind limits. A theoretical model for the aerodynamic force is developed to show the origin of the different experimental features. The theoretical analysis is then extended to the power dissipated in crosswinds and it is shown that the expression commonly used in the literature only holds in the pure head and tailwind limits but must be corrected in the general case of a crosswind. A new analytical expression for the total aerodynamic power is derived and used to determine the cycling speed in arbitrary crosswind conditions.

We analyze a set of bidirectional wave experiments in a linear wave flume of which some are conducive to integrable turbulence. In all experiments the wavemaker forcing is sinusoidal and the wave motion is recorded by seven high-resolution side-looking cameras. The periodic scattering transform is implemented and power spectral densities computed to discriminate linear wave motion states from integrable turbulence and soliton gas. Values of the wavemaker forcing Ursell number and relative amplitude are required to be above some threshold values for the integral turbulence to occur. Despite the unavoidable slow damping, soliton gases achieve stationary states because of the continuous energy input by the wavemaker. The statistical properties are given in terms of probability density distribution, skewness, and kurtosis. The route to integrable turbulence, by the disorganization of the wavemaker induced sinusoidal wave motion, depends on the nonlinearity of the waves but equally on the amplitude amplification and reduction due to the wavemaker feedback on the wave field.

Spectra of supersaturation and liquid water content (LWC) fluctuations in cloud turbulence are theoretically studied. Equations for the variance spectra are derived using the Lagrangian renormalized approximation and examined through asymptotic analysis. Our results show that the wave-number-dependent Damköhler number, defined as the ratio of the turbulent eddy turnover time to the phase relaxation time of the supersaturation, controls the scalar transfer functions and the supersaturation excitation by turbulence. Additionally, the supersaturation spectrum $E_s\left(k\right)$ has three power-law ranges. Here two ranges follow $k^{-5/3}$; however, their amplitudes differ depending on the large-scale Damköhler number and the input ratio of the supersaturation excitations in the associated range. The third range of $E_s\left(k\right)\propto k^{-1-2C_B{D}_{\mathrm{K}}}$ includes $C_{\mathrm{B}}$ and $D_{\mathrm{K}}$ representing the Bachelor constant and Damköhler number corresponding to the Kolmogorov time, respectively. The LWC spectrum $E_{\varphi }\left(k\right)$ reveals two power-law ranges: $k^{-5/3}$ for $k<k_{\varphi *}$ and $k^{-1}$ for $k_{\varphi *}<k$, in which the transition wave number $k_{\varphi *}\overline{\eta }$ is given by the input ratio of the supersaturation excitations in the two $k^{-5/3}$ ranges by the turbulence and is consistent with field measurement results.

Active nematic fluids confined in narrow channels are known to generate spontaneous flows when the activity is sufficiently intense. Recently, it was demonstrated [R. Green, J. Toner, and V. Vitelli, Phys. Rev. Fluids 2, 104201 (2017)] that if the molecular anchoring at the channel walls is conflicting, i.e., perpendicular on one plate and parallel on the other, flows are initiated even in the zero activity limit. An analytical laminar velocity profile for this specific configuration was derived within a simplified nematohydrodynamic model in which the nematic order parameter is a fixed-magnitude unit vector $\mathbf{n}$. The solution holds in a regime where the flow does not perturb the nematic order imposed by the walls. In this study, we explore systematically active flows in this confined geometry with a more general theoretical model that uses a second-rank tensor order parameter Q to express both the magnitude and orientation of the nematic phase. The Q-model allows for the presence of defects and biaxial, in addition to uniaxial, molecular arrangements. Our aim is to provide a unified picture, beyond the limiting regime explored previously, to serve as a guide for potential microfluidic applications that exploit the coupling between the orientational order of the molecules and the velocity field to finely control the flow and overcome the intrinsic difficulties of directing and pumping fluids at the microscale. We reveal how the nematic-flow coupling is not only dependent on geometrical constraints, but is also highly sensitive to material and flow parameters. We specifically stress the key role played by the activity and the flow aligning parameter, and we show that solutions mostly depend on two dimensionless parameters. We find that for large values of the activity parameter, the flow is suppressed for contractile particles while it is either sustained or suppressed for extensile particles depending on whether they tend to align or tumble when subject to shear. We explain these distinct behaviors by an argument based on the results of the stability analysis applied to two simpler configurations: active flows confined between parallel plates with either orthogonal or perpendicular alignment at both walls. We show that the analytical laminar solution derived for the $\mathbf{n}$ model in the low activity limit is found also in the $\mathbf{Q}$ model, both analytically and numerically. This result is valid for both contractile and extensile particles and for a flow-tumbling as well as aligning nematics. We remark that this velocity profile can be derived for generic boundary conditions. To stress the more general nature of the $\mathbf{Q}$ model, we conclude by providing a numerical example of a biaxial three-dimensional thresholdless active flow for which we show that biaxiality is especially relevant for a weakly first-order isotropic-nematic phase transition.

Active droplets can swim spontaneously in viscous flows as a result of the nonlinear convective transport of a chemical solute produced at their surface by the Marangoni and/or phoretic flows generated by that solute's inhomogeneous distribution, provided the ratio of convective-to-diffusive solute transport, or Péclet number $\text{Pe}$, is large enough. As the result of their net buoyancy, active drops typically evolve at a small finite distance $d$ from rigid boundaries. Yet, existing models systematically focus on unbounded flows, ignoring the effect of the wall proximity on the intrinsically nonlinear nature of their propulsion mechanism. In contrast, we obtain here a critical insight on the propulsion of active drops near walls by analyzing their stability against nonaxisymmetric perturbations and the resulting emergence of self-propulsion along the wall with no limiting assumption on the wall distance $d$. Dipolar or quadrupolar axisymmetric (levitating) base states are identified depending on $d$ and $\text{Pe}$. Perhaps counterintuitively, a reduction in the drop-wall separation $d$ is observed to destabilize these modes and to promote self-propulsion, as a result of the confinement-induced localization of the chemical gradients driving the motion. In addition, quadrupolar states are more unstable than their dipolar counterparts due to the redistribution of the chemical perturbation by the base flow, favoring the emergence of stronger slip forcing on the drop surface.

The reattachment of turbulent flow in canopy wakes is studied in laboratory flume experiments with model submerged aquatic vegetation. Velocity profiles using acoustic Doppler velocimeters were taken in the wakes of homogeneous (single-patch) canopies and within long gaps of discontinuous canopies (two patches). Analysis of the velocity records for mean flow and turbulence statistics suggests the presence of two dominant dynamics and scales: canopy-shear dynamics (CSD) and backward-facing step dynamics (BFSD). The mean streamwise velocities near the bed of the canopy wakes indicate the presence of an adverse pressure gradient, as found in the wake of BFS or other flow expansions. Using this observation, we redefine the reattachment for canopy wakes. Spectral analysis of the streamwise velocity near the bed in the immediate wake of the canopy shows that there is a significant peak centered about a frequency comparable to the streamwise periodicity found in the immediate wake of a BFS. Further from the bed, the vertical velocity spectra maintain a strong spectral peak that corresponds to the coherent structures formed by the canopy-shear instability from the upstream canopy. While different canopy systems have different contributions from the two dynamics, our canopy systems are dominated by canopy-shear dynamics about the canopy height in the wake. For example, CSD has a strong influence on the turbulence in the wake of the canopy because the length of the canopy controls the turbulence development. This in turn has a strong influence on the reattachment length. (However, the BFSD modifies the dominant CSD-induced signal by introducing both larger and smaller scales to the flow.) We find that the reattachment length decreases with increasing canopy length of turbulence, with an asymptotic limit for the canopy length required for fully developed turbulence.

In many environmental and industrial applications, the mass transfer of gases in liquid solvents is a fundamental process during the generation of bubbles for specific purposes or, vice versa, the removal of entrapped bubbles. We address the growth dynamics of a trapped slug bubble in a vertical glass cylinder under a water barrier. In the studied process, the ambient air atmosphere is replaced by a ${\mathrm{CO}}_2$ atmosphere at the same or higher pressure. The asymmetric exchange of the gaseous solutes between the ${\mathrm{CO}}_2$-rich water barrier and the air-rich bubble always results in net bubble growth. We refer to this process as solute exchange. The dominant transport of ${\mathrm{CO}}_2$ across the water barrier is driven by a combination of diffusion and convective dissolution. The experimental results are compared to and explained with a simple numerical model, with which the underlying mass transport processes are quantified. Analytical solutions that accurately predict the bubble growth dynamics are subsequently derived. The effect of convective dissolution across the water layer is treated as a reduction of the effective diffusion length, in accordance with the mass transfer scaling observed in laminar or natural convection. Finally, the binary water-bubble system is extended to a ternary water-bubble-alkane system. It is found that the alkane ($n$-hexadecane) layer bestows a buffering (hindering) effect on bubble growth and dissolution. The resulting growth dynamics and underlying fluxes are characterized theoretically.

A detailed analysis of the effects of uniform blowing, uniform suction, and body-force damping on the turbulent boundary layer developing around a NACA4412 airfoil at moderate Reynolds number is presented. The flow over the suction and the pressure sides of the airfoil is subjected to a nonuniform adverse pressure gradient and a moderate favorable pressure gradient, respectively. We find that the changes in total skin friction due to blowing and suction are not very sensitive to different pressure-gradient conditions or the Reynolds number. However, when blowing and suction are applied to an adverse-pressure-gradient (APG) boundary layer, their impact on properties such as the boundary-layer thickness, the intensity of the wall-normal convection, and turbulent fluctuations are more pronounced. We employ the Fukagata-Iwamoto-Kasagi decomposition [K. Fukagata et al., Phys. Fluids 14, 73 (2002)] and spectral analysis to study the interaction between intense adverse pressure gradient and these control strategies. We find that the control modifies skin-friction contributions differently in adverse-pressure-gradient and zero-pressure-gradient boundary layers. In particular, the control strategies modify considerably both the streamwise-development and the pressure-gradient contributions, which have high magnitude when a strong adverse pressure gradient is present. Blowing and suction also impact the convection of structures in the wall-normal direction. Overall, our results suggest that it is not possible to simply separate pressure-gradient and control effects, a fact to take into account in future studies on control design in practical applications.

An analysis was conducted of the transpiration velocity of the streamwise periodic simulation of the turbulent flat plate boundary layer. As an often imposed quantity in numerical simulation, the transpiration velocity plays an important role in the shape of the wall-normal profile near the outer layer. Unlike other simulation frameworks which impose the transpiration velocity, the recently proposed framework [Ruan and Blanquart, Phys. Rev. Fluids 6, 024602 (2021)] relies on a single-scale rescaling of the wall-normal coordinate to perform streamwise periodic boundary layer simulations. The current manuscript highlights that any error in the transpiration velocity from these simulations is due to a difference in inner and outer layer growth rates. A new multiscale framework to compensate for these differing growth rates is proposed and verified but ultimately has negligible impact on the mean profiles and turbulent intensities. These remain in excellent agreement with previously published values. It is shown that any error in the mean continuity equation expresses itself primarily as an error in transpiration velocity, which decreases with Reynolds number. Overall, the error in the transpiration velocity can be used to quantify the error in single-scale, streamwise periodic simulations.