This article discusses the effect of rotation on the boundary layer in high Reynolds number flow over a ridge using a numerical method based on stabilized finite elements that captures steady solutions up to a Reynolds number of order ${10}^6$. The results are validated against boundary layer computations in shallow flows and for deep flows against experimental observations reported in Machicoane et al. [Phys. Rev. Fluids 3, 034801 (2018)]. In all cases considered the boundary layer remains attached, even at arbitrarily large Reynolds numbers, provided the Rossby number of the flow is less than some critical Rossby number of order unity. At any fixed Rossby number larger than this critical value, the flow detaches at sufficiently high Reynolds number to form a steady recirculating region in the lee of the ridge. At even higher Reynolds numbers no steady flow is found. This disappearance of steady solutions closely reproduces the transition to unsteadiness seen in the laboratory.

Drop impact experiments are performed with very viscous fluids to propose a description of the drop deformation at low Reynolds number. We focus on a specific case where dimensionless parameters other than the Reynolds number play no role, which means that only kinetic energy and viscous dissipation determine the final deformation. The same situation in the case of a Reynolds number larger than ten has been clarified years ago. The maximum diameter of the spread drop is well described by a 1/5 power law of the Reynolds number only. Here the deformation of the drop, defined as the contact diameter rescaled by the drop size, is also a power law of the Reynolds number. From experimental data and scaling arguments, the exponent of the power law is shown to be 1/3.

We illuminate effects of surface-charge convection intrinsic to leaky-dielectric electrohydrodynamics by analyzing the symmetric steady state of a circular drop in an external field at arbitrary electric Reynolds number ${\mathrm{Re}}_E$. In formulating the problem, we identify an exact factorization that reduces the number of dimensionless parameters from four—${\mathrm{Re}}_E$ and the conductivity, permittivity and viscosity ratios—to two: a modified electric Reynolds number $\widetilde{\mathrm{Re}}$ and a charging parameter $\varpi$. In the case $\varpi <0$, where charge relaxation in the drop phase is slower than in the suspending phase, and, as a consequence, the interface polarizes antiparallel to the external field, we find that above a critical $\widetilde{\mathrm{Re}}$ value the solution exhibits a blowup singularity such that the surface-charge density diverges antisymmetrically with the $-1/3$ power of distance from the equator. We use local analysis to uncover the structure of that blowup singularity, wherein surface charges are convected by a locally induced flow towards the equator where they annihilate. To study the blowup regime, we devise a numerical scheme encoding that local structure where the blowup prefactor is determined by a global charging-annihilation balance. We also employ asymptotic analysis to construct a universal problem governing the blowup solutions in the regime $\widetilde{\mathrm{Re}}\gg 1$, far beyond the blowup threshold. In the case $\varpi >0$, where charge relaxation is faster in the drop phase and the interface polarizes parallel to the external field, we numerically observe and asymptotically characterize the formation at large $\widetilde{\mathrm{Re}}$ of stagnant, perfectly conducting surface-charge caps about the drop poles. The cap size grows and the cap voltage decreases monotonically with increasing conductivity or decreasing permittivity of the drop phase relative to the suspending phase. The flow in this scenario is nonlinearly driven by electrical shear stresses at the complement of the caps. In both polarization scenarios, the flow at large $\widetilde{\mathrm{Re}}$ scales linearly with the magnitude of the external field, contrasting the familiar quadratic scaling under weak fields.

Since its discovery in 2005, the hydrodynamic pilot-wave system has provided a concrete macroscopic realization of wave-particle duality and concomitant classical analogs of a growing number of quantum effects. The question naturally arises as to how closely particle-particle correlations achieved with this classical system can mimic those arising on the quantum scale. We here introduce a new platform for addressing this question, a numerical model of cooperative tunneling in a bipartite pilot-wave hydrodynamic system. We execute a static Bell test, in which the system geometry is fixed and the two subsystems are coupled through the intervening wave field. This wave-mediated coupling is not congruent with the assumptions made in deriving Bell's inequality, and so allows one to rationalize the reported violations. Nevertheless, these violations are elusive, and arise only in a limited corner of parameter space.

We examine the linear thermocapillary instability of a two-dimensional gravity-driven shear-imposed incompressible viscous film flowing over a uniformly heated inclined wall when the film surface is covered by an insoluble surfactant. The aim is to expand the prior research [Wei, Phys. Fluids 17, 012103 (2005)] to the case of a nonisothermal viscous film. As a result, the energy equation is incorporated into the governing equations along with the mass conservation and momentum equations. In the present study, we have found two additional thermocapillary S- and P-modes in the low to moderate Reynolds number regime, along with the known H-mode (surface mode) and surfactant mode. The long-wave analysis predicts that the surfactant Marangoni number, which measures the surface tension gradient due to a change in insoluble surfactant concentration, has a stabilizing impact on the H-mode, but the thermal Marangoni number, which measures the surface tension gradient due to a change in temperature, has a destabilizing impact. These opposing effects produce an analytical relationship between them for which the critical Reynolds number for the H-mode instability of the nonisothermal film flow coincides with that of the isothermal film flow. On the other hand, the numerical result exhibits that the surfactant Marangoni number has a stabilizing influence on the thermocapillary S-mode and P-mode. More specifically, these thermocapillary instabilities diminish with an increase in the value of the surfactant Marangoni number. However, these thermocapillary instabilities can be made stronger by increasing the value of the thermal Marangoni number. Furthermore, the thermal Marangoni number destabilizes the surfactant mode instability, but the onset of instability is not affected in the presence of the thermal Marangoni number, which is in contrast to the influence of the surfactant Marangoni number on the onset of surfactant mode instability. Interestingly, the Biot number, which measures the ratio of heat convection and heat conduction, shows a dual role in the surfactant mode instability, even though the threshold of instability remains the same. In the high Reynolds number regime, the shear mode appears and is stabilized by the surfactant Marangoni number but destabilized by the thermal Marangoni number. Moreover, the comparison of results with inertia and without inertia exhibits a stabilizing role of inertia in the surfactant mode.

The second moment correlations between thermodynamic fluctuations in incident shock wave/turbulent boundary layer interaction flows at Mach 2.25 are systematically investigated by direct numerical simulation. The concerned fluctuations are those of pressure, entropy, temperature, and density $\{p^{\prime },s^{\prime },T^{\prime },{\rho }^{\prime }\}$. Effects of wall temperature and Reynolds number are studied. Kovásznay decomposition is introduced to decompose the fluctuations into acoustic and entropic modes. It is shown that all the six concerned correlations are determined by merely two parameters, which are interpreted as intermodal competition and intermodal correlation, respectively. Accordingly, the flow field is divided into several zones, each with distinct physical properties, to analyze the contributing factors to the correlations. In addition, a model is proposed where the correlations are deemed as functions of the root-mean-square values of thermodynamic fluctuations, as in Gerolymos and Vallet [J. Fluid Mech. 851, 447 (2018)] but simpler. The formula for each correlation has the same form. The accuracy of the model is validated in boundary layers where the intermodal correlation is weak.

A parallel-plate rotational rheometer measures the viscosity of a fluid by rotating the top plate relative to the bottom plate in order to induce a shear on the fluid and measuring the torques and forces that result as a function of the induced rotation rate. Manufacturing imperfections can often lead to unintentional misalignment of the plates of the rheometer, where the top and bottom plates are not perfectly parallel, and this misalignment can affect the fluid dynamics inside the rheometer. This study examines the effect that misalignment has on the viscosity measurements of Newtonian fluids in the limit of small rheometer gap heights. A theoretical model for the behavior of a general Newtonian fluid in a misaligned rheometer with a small gap height is derived using perturbation expansions. The theoretical results show that at small gap heights, misalignment can produce additional secondary velocity components and pressures in the fluid, which affect the forces and moments in the rheometer. In such cases at small Reynolds numbers, the dominant forces and moments acting on the top plate of the rheometer are the viscous force in the direction parallel to the tilt axis, the pressure moment in the direction perpendicular to the tilt axis and in the cross-sectional plane, and the viscous moment in the direction along the height of the rheometer. These forces and moments on the top plate were found to increase as the misalignment tilt angle increased, leading to an increase in the error of viscosity measurement by the rheometer. Three-dimensional numerical simulations validate the theoretical predictions.

Modal and nonmodal stability analysis of a channel flow with longitudinal riblets are investigated. To this extent, a method based on the coupling between a two-dimensional stability problem and a computational framework for $n$-periodic systems based on Bloch waves is proposed. Unstable modes from linear stability can be retrieved. The influence of the riblets on the most amplified flow structures is investigated through a transient growth analysis: a resonance is found when the riblet wavenumber is equal to the wavenumber of the optimal streaks in a smooth channel flow. For large riblet spacing, a wavenumber lock-in regime, in which the streaks dynamics and wavelength are totally controlled by the riblet spacing, is observed. Physically, a modulation of the streaks amplitude in the spanwise direction via a beating mechanism is seen. These phenomena are characteristic of dynamic systems spatially forced and may exhibit geometric frustration. Similar results were found in the study of secondary flows in Rayleigh-Bénard convection with wavy walls. A resolvent analysis is also performed: it is found that riblets lead to the development of oblique waves that may trigger an early transition.

Blood rheology and microcirculation are strongly influenced by red blood cell aggregation. We investigate the dissociation rates of red cell aggregates in extensional flow using hyperbolic microfluidic constrictions and image analysis by a convolutional neural network (CNN). Our findings reveal that aggregate dissociation increases sharply when a critical extension rate is reached which falls within the range of microcirculatory conditions, suggesting that large variations of aggregate sizes should be expected in vivo. This work contributes to a deeper understanding of the behavior of red blood cell aggregates in response to extensional stress in microcirculatory networks, provides crucial experimental data to validate theoretical and numerical models, and constitutes the basis for improved evaluation of blood aggregability in clinical contexts.

The formation of small droplets and bubbles in turbulent flows is a crucial process in geophysics and engineering, whose underlying physical mechanism remains a puzzle. In this Letter, we address this problem by means of high-resolution numerical simulations, comparing a realistic multiphase configuration with a numerical experiment in which we attenuate the presence of strong velocity gradients either across the whole mixture or in the disperse phase only. Our results show unambiguously that the formation of small droplets is governed by the internal dynamics which occurs during the breakup of large drops and that the high vorticity and the extreme dissipation associated to these events are the consequence and not the cause of the breakup.

Existing hemolysis algorithms are often constructed for laminar flows that expose red blood cells (RBCs) to a constant rate of shear. It remains an open question whether such models are applicable to turbulent flows, where there is a significant variation in shear rate along cell trajectories. To evaluate the effect of turbulence on hemolysis, we perform cell-resolved simulations of isolated RBCs in turbulent channel flow at ${\text{Re}}_{\tau }=180$ and 360 and compare them against the results obtained from laminar flow simulations at an equivalent wall shear stress. The RBCs are modeled as isolated cells in an unbounded domain with the viscosity of the bulk fluid used for the surrounding fluid. This comparison shows that, while the laminar flow generally induces greater stretch in the cell in a time-averaged sense, cells experience an overall larger deformation in turbulence. This difference is attributed to extreme events in turbulence that occasionally create bursts of high shear conditions, which, consequently, induce a large deformation in the cells. Associating damage with the most extreme deformation regimes, we observe that, in the worst case, the turbulent flow can produce deformation in the cell that is higher than the absolute maximum value in the analogous laminar case approximately $14\%$ of the time. Additionally, the ${\mathrm{Re}}_{\tau }=180$ universally induced greater deformation in the cells than the ${\mathrm{Re}}_{\tau }=360$ case, suggesting that increasing the range of scales in the flow does not necessarily yield greater deformation when all other parameters are kept constant. A strong direct correlation ($R>0.8$) between shear rate and deformation metrics was observed in turbulence. The correlation against $Q$-criterion is inverse and weaker ($R\approx -0.26$), but once the shear contribution is subtracted, it improves in terms of areal dilatation ($R\approx -0.6$).

Atomistic and coarse-grained simulations show the formation of a condensed layer of counterions near a charged surface in contact with multivalent or monovalent electrolytes of high concentration. This condensed layer may overscreen the surface charge, and eventually a coion-dominated region may arise within the electric double layer, which again draws a layer of counterions and so on till the charge density approaches zero. Such a type of overscreening and charge density oscillation cannot be predicted through the mean-field based models as it does not account for the correlations between discrete charges. In the present study the mean-field-based model has been extended to consider the many-body interactions to analyze the electro-osmosis and ion transport of multivalent electrolytes in a highly charged nanopore. The ions are considered to be finite-sized, which is accounted for by considering the hydrodynamic steric interactions and modification of the suspension medium viscosity. Consideration of the electrostatic correlation leads to a fourth-order Poisson-Fermi equation for an electric field. Such a type of continuum model is easy to handle and to use to predict the layered structure of the EDL. Our model captures the existing experimental and molecular dynamics simulation correctly. Based on the modified model, we have analyzed the volume flow rate, current density, and ion selectivity of the pore in multivalent electrolytes for different electrostatic conditions. The present model shows that the counterion size has an impact on the condensed layer and hence overscreening. We demonstrate that the EOF reversal of multivalent electrolytes can be suppressed by mixing with monovalent slats.

The orientation dynamics of and the torque fluctuations due to a spheroidal magnetic particle in an oscillating magnetic field are analyzed in the Stokes flow regime. For a permanent dipole, the dynamics depends on ${\omega }^{†}$, the ratio of the magnetic field frequency, and the viscous relaxation rate. For ${\omega }^{†}\gg 1$, the particle executes oscillations with amplitude $\sim {\left({\omega }^{†}\right)}^{-1}$ about its initial orientation. The average torque is zero because the particle does not execute complete rotations, and the root mean square of the torque fluctuations scaled by the characteristic magnetic torque tends to a constant in this limit. For ${\omega }^{†}\ll 1$, the orientation is close to the magnetic field direction for most of the oscillation period, and it rapidly rotates when the field passes through extrema. The scaled root mean square of the torque fluctuations is proportional to ${\left({\omega }^{†}\right)}^{-1/2}$ in this limit. The particle orientation aligns along the magnetic field direction for different models of induced dipoles if the magnetization is nonhysteretic. For the hysteretic Stoner-Wohlfarth model, the dynamics also depends on the parameter $h_0$, the ratio of the Zeeman energy, and the anisotropy energy. For $h_0\ll 1$, the magnetic moment oscillates about one pole of the orientation vector, and the orientation vector rapidly rotates when the field passes through extrema in a manner similar to that for a permanent dipole. For $h_0\gg 1$, the magnetic moment switches between the two poles of the orientation vector, and the orientation vector executes small amplitude oscillations about the field direction. There is a discontinuous transition between the oscillating and switching magnetic moment which depends on $h_0$ and the initial orientation.

We investigate experimentally the propulsive efficiency of a propeller in water with chordwise flexible blades that deform under the action of fluid loading. Using a scale model experiment, we record the deformation of the blades as well as the thrust and torque generated by the rotor. The use of flexible materials can improve the resilience to changing external conditions: with optimal flexibility, the blades deform and remain efficient under off-design conditions. We derive a theoretical law for blade tip deformation and show good agreement with experiments. Our results suggest that, using only the blade flexibility alone, we are able to program the blade deformation to passively adopt an optimized shape for efficient propulsion within a given parameter range.

Random jet arrays (RJAs) have been shown to be effective in generating zero mean flow homogeneous isotropic turbulence. While many laboratory studies have investigated the flow in these facilities, there are several remaining questions regarding the evolution of turbulence, from the development of turbulence to where it decays, along with understanding how input energy from the jet array transfers into different turbulent flow characteristics. To address these questions, we perform a series of laboratory experiments in which we alter the parameters of the randomized algorithm, along with the jet spacing and outlet velocity of the jets. We first determine the location where turbulence transitions to a fully developed state and show that it is a function of jet penetration length, ${\mathcal{L}}_{\mathcal{J}}$, and effective jet spacing, $S_e$. We identify three distinct regions for the spatial decay of turbulence in RJA facilities and notably, we find different decay rates, unlike previous studies that report only one spatial decay rate using similar facilities. These regions are shown to depend on the variations of input parameters yet independent of the strength of the mean flow. We also find the strength of the mean flow does not affect the homogeneity, nor the production, transport, or advection terms of the turbulent kinetic energy budget equation. Finally, we address a longstanding question toward estimating turbulence metrics with an RJA based on the input parameters. We define an efficiency parameter that provides insight into the transfer rate of input power to the dissipation rate of the generated turbulence.

Surfactant-laden thin liquid films overlaid on solid substrates are encountered in a variety of industrial and biological settings. As these films reach submicron thickness, they tend to become unstable owing to the influence of long-range dispersion forces. In the current study, we investigate how gravitational drainage affects the stability attributes of such thin liquid films. Using scaling arguments, we demonstrate that gravity and dispersion forces can exert their influence simultaneously over a wide range of film thicknesses. In the lubrication limit, we carry out linear stability analysis and nonlinear simulations to understand the evolution of draining thin films. Linear stability indicates the existence of two unstable modes and two cutoff wave numbers, as opposed to a single unstable mode and a unique cutoff wave number observed in stationary films. It is also found that surfactant-laden flowing films are more stable than stationary films with surfactants as well as draining films with clean interfaces. The origin of stabilization is identified as the enhanced surfactant perturbations generated due to drainage. We demonstrate that films exhibiting intermediate levels of surfactant activity and significant drainage exhibit the lowest rates of disturbance growth, leading to extending the time of rupture.

We have conducted a direct numerical simulation of a turbulent round jet at a previously unattained Reynolds number of $\text{Re}=3500$ based on the jet diameter $D$ and jet-inlet bulk velocity $U_{\text{b}}$ in a particularly long box of $75D$. To achieve very fast convergence to self-similarity, we used a turbulent pipe flow at the same Reynolds number and length $5D$ as the upstream inflow boundary condition. This indeed results in a very rapid emergence of self-similarity already at very small axial distances $z$ compared to all turbulent jet data published so far. Not only for the mean velocities and the Reynolds stresses as well as the budgets of the Reynolds stress tensor and the turbulent kinetic energy, a nearly perfect classical scaling based on the normalized radius $\eta =r/z$ in the range $z/D=25-65$ is shown, but also for the probability density function (PDF) of the axial velocity $U_z$ as well as the associated skewness and kurtosis. All budget terms have been calculated directly, resulting in a marginal error in the balance. An almost completely Gaussian behavior of the PDF for the axial velocity is observed on the jet axis, while a clear deviation with increasingly heavy tails is evident with increasing distance from the axis.

The purpose of this paper is to investigate the effects of molecular mixing on the evolution of a reactive Rayleigh-Taylor turbulent mixing zone. In this regard, we derive algebraic relations showing that an increase in the mixing level leads to a slowing of the growth of the mixing zone width. We also show the existence of a maximum displacement velocity of the mixing zone center. These predictions are assessed using both direct numerical simulations and large eddy simulations.

This paper presents analytical solutions for a steady turbulent miscible gravity current flowing along a horizontal rigid boundary of finite length into a quiescent uniform environment. These solutions are obtained from the governing equations (mass, momentum, and buoyancy) originally proposed by Ellison and Turner [J. Fluid Mech. 6, 423 (1959)] for a buoyant layer of fluid in the Boussinesq approximation. For a constant drag coefficient $C_d$ and the specific entrainment law $E\propto {\text{Ri}}^{-1}, \text{Ri}$ being the local Richardson number, we first derived a system of coupled ordinary differential equations describing the longitudinal evolution of the velocity $u$, the height $h$, the density deficit $\eta$, and the Richardson number $\text{Ri}$ of the current. For an initially supercritical flow $\left({\text{Ri}}_0<1\right)$, explicit relations are found for $u\left(x\right), h\left(x\right),$ and $\eta \left(x\right)$ solely as a function of the Richardson number $\text{Ri}\left(x\right)$. The longitudinal evolution of the Richardson number is then theoretically obtained from a universal function $F$ which can be tabulated and, as in the present paper, also plotted. The function $F$ allows us to determine (and only from the knowledge of the boundary conditions at the source) whether the flow remains supercritical over the whole length of the rigid boundary, or might transit towards a subcritical state ($\text{Ri}>1$). In this latter case, the mathematical resolution is modified by including a discontinuity similar to a hydraulic jump. The location and amplitude of this discontinuity are calculated from an additional universal function $G$ and the injection conditions. The method is finally extended to provide analytical solutions for other classical entrainment laws.

We report an experimental study of heat transport in a three-layer turbulent Rayleigh-Bénard convection. The experiments were conducted in a cylindrical cell (with diameter $D$) filled with a FC77 layer with height $H=D$. A very thin layer of water and a very thin layer of mercury were introduced to the top and bottom of the FC77 layer to provide slippery boundary conditions. We performed high spatial resolution temperature measurements across the water-FC77 and FC77-mercury interfaces, determined the temperatures at the two interfaces, the Rayleigh number (Ra) and the Nusselt number (Nu) across the FC77 layer. The experiments were conducted in the Ra range of $2.81\times {10}^9$ to $1.24\times {10}^{11}$ for the FC77 layer. It is found that not only the amplitude but also the scaling exponent (with Ra) of Nu is greatly enhanced in this three-layer system compared to the canonical single-layer system, especially in the high Ra range. In particular, $\text{Nu}$ first scales as ${\text{Ra}}^{0.31}$ and then ${\text{Ra}}^{0.38}$ when Ra exceeds a transitional Rayleigh number ${\text{Ra}}_t=2.52\times {10}^{10}$, whereas in the canonical single-layer FC77 case, $\text{Nu}$ is found to scale as ${\text{Ra}}^{0.26}$. Temperature measurements show that the boundary condition above and below the FC77 layer is asymmetric especially when $\text{Ra}>{\text{Ra}}_t$: the temperature drop across the top half (in contact with the water layer) of the FC77 layer is smaller than that across the bottom half (in contact with the mercury layer), and the top thermal boundary layer (TBL) becomes thinner and follows a steeper scaling with $\text{Ra}$ compared to the bottom TBL. We consider a hypothetical experiment where the top and the bottom boundary conditions are symmetric, denoted as a “water-FC77-water” three-layer system, in which the temperature drop across the bottom boundary layer $\mathrm{\Delta }{T}_b$ would be the same as that across the top boundary layer $\mathrm{\Delta }{T}_t$. We found in this water-FC77-water three-layer system, with the increase of Ra, $\text{Nu}$ vs $\text{Ra}$ scaling transitions from $\text{Nu}\sim {\text{Ra}}^{0.31}$ to $\text{Nu}\sim {\text{Ra}}^{0.46}$ with the transitional Ra the same as ${\text{Ra}}_t$ identified before. A closer check of the evolution of Ra of the water layer, FC77 layer, and the mercury layer reveal that the transition of the $\text{Nu}$ vs $\text{Ra}$ scaling is due to the transition of the thin water layer from a conduction state to a convection state, whereas the mercury layer remains in a conduction state.