In a turbulent premixed flame, the gradient diffusion approximation for the turbulent scalar flux is invalid and countergradient diffusion occurs. The mechanism of countergradient diffusion needs to be clarified to improve turbulence models for turbulent scalar flux. Many processes are related to the countergradient diffusion in the turbulent premixed flame due to the interaction between turbulence and chemical reactions. In this study we focused on the effects of heat release on turbulence. To discuss this, we devised and implemented a direct numerical simulation of the turbulent Rayleigh flow (TRF) generated by isotropic turbulence flowing into the Rayleigh flow. We show that countergradient diffusion of the turbulent heat flux occurs in TRF, and we discuss its mechanism based on the transport equations of the turbulent statistical quantities. It is shown that the released heat amplifies the density-internal energy correlation, resulting in a prominent contribution from the pressure gradient effect, which results in countergradient diffusion.

Acquiring a comprehensive understanding of the interplay between foam friction and surface roughness is essential for achieving precise control over their flow dynamics. In particular, a major challenge is to reduce friction, which can be achieved with rough surfaces in the situation where a liquid infuses the asperities. In this study, we propose to explore self-infused surfaces. We first present simple observations to demonstrate the effectiveness of our surface design by recording the motion of a foam puddle on a smooth surface and self-slippery liquid-infused porous surfaces. To quantify friction reduction, we conduct stress measurements on surfaces moved at a constant velocity. Finally, we interpret the variation of the friction force with the velocity by a model considering an effective slip length of the surface. This research paves the way for a unique approach to mitigate dissipation in liquid foam flows, holding significant implications for reducing energy consumption in conveying foams for industrial processes and various end-use applications.

The hydrodynamic instabilities of propagating interfaces in Hele-Shaw channels or porous media under the influence of an imposed flow and gravitational acceleration are investigated within the framework of Darcy's law. The stability analysis pertains to an interface between two fluids with different densities, viscosities, and permeabilities, which can be susceptible to Darrieus-Landau, Saffman-Taylor, and Rayleigh-Taylor instabilities. A theoretical analysis, treating the interface as a hydrodynamic discontinuity, yields a simple dispersion relation between the perturbation growth rate $s$ and its wave number $k$ in the form $s=(ak-b{k}^2)/(1+ck)$, where $a$, $b$, and $c$ are constants determined by problem parameters. The constant $a$ characterizes all three hydrodynamic instabilities, which are long wave in nature. In contrast, $b$ and $c$, which characterize the influences of local curvature and flow strain on interface propagation speed, typically provide stabilization at short wavelengths comparable to the interface's diffusive thickness. The theoretical findings for Darcy's law are compared with a generalization of the classical work by Joulin and Sivashinsky, which is based on a Euler-Darcy model. The comparison provides a conceptual bridge between predictions based on Darcy's law and those on Euler's equation and offers valuable insights into the role of confinement on interface instabilities in Hele-Shaw channels. Numerical analyses of the instabilities are carried out for premixed flames using a simplified chemistry model and Darcy's law. The numerical results corroborate with the explicit formula with a reasonable accuracy. Time-dependent numerical simulations of unstable premixed flames are carried out to gain insights into the nonlinear development of these instabilities. The findings offer potential strategies for control of interface instabilities in Hele-Shaw channels or porous media. Special emphasis is given to the critical role played by the imposed flow in destabilizing or stabilizing the interface, depending on its direction relative to the interface propagation.

The dynamics of polar vortices has recently regained significant scientific interest due to the observations from the Juno mission of stable patterns of polar cyclones on both the North and the South poles of Jupiter [A. Adriani et al., J. Geophys. Res.: Planets 125, e2019JE006098 (2020)]. In this paper, we present experiments of monopolar barotropic cyclones freely drifting in a rotating free surface fluid. The parabolic fluid height variation leads to spatially inhomogeneous topographic effects, relevant for atmospheric flows in the vicinity of the pole. We show, both experimentally and with idealized quasigeostrophic numerical simulations, that starting from an initial vortex, two different evolution regimes can take place depending on the ratio between the vortex strength and the local gradient of potential vorticity across the vortex. In the linear regime, the relative vorticity of the cyclone is weak in comparison with the local beta effect, which results in the emission of Rossby waves. In our confined experimental setup, this leads to the emergence of Rossby normal modes. In the vortex regime, the generated cyclone remains coherent and drifts from its initial position towards the center of the tank in a north (radial towards the axis of rotation) and west (opposite direction to the background rotation) direction. This phenomenon, known as the “beta drift” on a beta-plane, has been shown numerically and theoretically to result from a dipolar relative vorticity anomaly called the “beta gyre.” We show that a similar mechanism locally applies in our experimental polar plane. We present our experimental measurements of the beta gyre and show that its direction indeed correlates with the direction of vortex motion. In order to distinguish between the three observed trajectory patterns around the pole, we introduce a reduced model that highlights the influence of the boundaries on the vortex trajectory.

This study targets the stability issues of rotating-disk boundary layer in a rotor-stator cavity within the context of the incompressible Navier-Stokes equations, incorporating a drag model representative of roughness elements. Consequently, 32 azimuthally uniformly distributed roughness elements have been positioned within the computational domain. Owing to the inviscid crossflow instability inherent to the rotating-disk boundary layer, the roughness elements induce crossflow vortices with an azimuthal wave number $k=32$. Upon saturation of the crossflow vortices, a transition to turbulence does not immediately ensue; instead, a series of azimuthal Fourier modes constituting self-sustaining, spatiotemporally coherent traveling spiral waves mode emerge downstream. At higher Reynolds numbers, these traveling spiral waves mode reach saturation and are followed downstream by a transition to turbulence. Notably, to the best of the authors' knowledge, this is the first instance where selective excitation of crossflow vortices with a specific wave number in the rotating-disk boundary layer within a rotor-stator cavity has resulted in a transitional process ultimately dominated by traveling mode spiral waves. This process is distinct from the one observed over a single rotating disk, where the crossflow vortices, after reaching a certain Reynolds number, govern the transition to turbulence in the von Kármán boundary layer.

Equilibrium droplet shape and transient dynamics during (di)electrowetting and dewetting on dielectric are electric field–dependent. We present a lubrication model incorporating the Young–Lippmann law that accurately predicts the equilibrium droplet shape and its transient dynamics. The droplet contact line position $x_{cl}$ follows a field-dependent power law $x_{cl}\propto t^n$, where the magnitude of $n$ increases with the applied electric field. When the field strength equals the critical value required for complete wetting, the electrospreading dynamics reduce to the classical Tanner's law ($n=1/7$), in agreement with past experiments. The magnitude of $n$ for electrodewetting is shown to be greater compared with wetting, attributed to a lesser viscous dissipation in the former case. Despite a difference in the power-law exponent $n$, the transient dynamics for both (di)electrowetting and electrodewetting are shown to follow the Cox–Voinov law. These observations qualitatively extend beyond the lubrication regime to large contact-angle droplets as well, as confirmed using Navier–Stokes simulations.

The gradual suppression of the vertical motions and the emergence of large-scale horizontal structures in the late wake are commonly seen in a stratified wake flow. These long-lived coherent patterns are referred to as meandering and their impacts on the statistics are still not well studied. This paper aims to examine the kinematic impacts of the meandering effect in stratified wakes and how it affects the statistics of the velocity profiles, wake width, and wake height. To do this, we isolate wake meandering from the stationary velocity, i.e., the velocity without meandering, by utilizing direct numerical simulations (DNS) covering bulk Reynolds numbers ${\mathrm{Re}}_B=U_{B}D/\nu$ in the range $[10000,50000]$ and bulk Froude number ${\mathrm{Fr}}_B=U_B/ND$ in the range $[2,50]$ ($U_B$ is the free-stream velocity, $D$ is the characteristic length scale, and $N$ is the buoyancy frequency). The results show that the range of meandering increases in both the horizontal and vertical directions as the flow evolves. This complies with the wake width growth in the horizontal direction, but is opposed to the wake height in the vertical direction. The traditional scalings of the velocity, width, and height rely on the assumption of self-similarity and simultaneous transitions for all three scalings. However, the meandering, especially in the horizontal direction, leads to the distortion of the instantaneous velocity and layered flow structures. Thus, the mean velocity profile deviates from two-dimensional self-similarity in the late wake. Apart from the distortion of the velocity profile, the meandering of the wake also imposes anisotropy on the scaling of the statistics. The scaling of the width and the height transitions at different points, and they are related to the scaling of the velocity deficit through the momentum flux equation. Through theoretical analysis, we obtain the superposition of the meandering to the stationary velocity. We can accurately measure how the meandering distorts the self-similar velocity profile and impacts the scaling of the width and height, and thus how the meandering changes the scaling of the velocity deficit.

Pilot-wave hydrodynamics concerns the dynamics of “walkers,” droplets walking on a vibrating bath, and has provided the basis for the burgeoning field of hydrodynamic quantum analogs. We here explore a theoretical model of pilot-wave hydrodynamics that relaxes the simplifying assumption of resonance between the droplet and its pilot wave, specifically the assumption of a fixed impact phase between the bouncing drop and its wave field. The model captures both the vertical and the horizontal dynamics of the drop, allowing one to examine nonresonant effects for both free and constrained walkers. The model provides rationale for a number of previously reported but poorly understood features of free walker motion in pilot-wave hydrodynamics, including collinear swaying at the onset of motion, intermittent walking, and chaotic speed oscillations, all of which are accompanied by sporadic changes in the impact phase of the bouncing drop. The model also highlights the degeneracy in the droplets' vertical dynamics, specifically, the possibility of two distinct bouncing phases and of switching between the two. Consideration of this degeneracy is critical to understanding the droplet dynamics and statistics emerging in confined geometries at high memory and the interaction of walking droplets with standing Faraday waves.

An experimental investigation of the Richtmyer-Meshkov instability is conducted in spherical geometry, where convergence effects are more pronounced and the vorticity distribution is specific to the geometry. The gas lens technique is employed within a conical chamber to generate a spherical converging shock wave. This shock wave triggers the instability at a single-mode $\mathrm{air}/{\mathrm{SF}}_6$ interface for two different initial amplitudes. The displacement and the growth of the perturbations at the interface are monitored using a high-speed Mie-scattering laser tomoscopy method, and the results are compared to numerical simulations and new theoretical predictions. The instability amplitude initially grows, stabilizes, and then reduces before the arrival of the reflected shock wave. Numerical simulations demonstrate good agreement with the experiments, and they indicate a weak effect of the installed grid materializing the perturbation. In addition to the experimental and numerical results, the theoretical model developed here agrees well with the experiments, although a time shift is observed between theory and experiments in the stabilization regime. A comparison to other models available in the literature shows that, in the studied configurations, compressibility has a negligible effect on the development of the instability. Our model demonstrates that convergent Rayleigh-Taylor effects are the main stabilizing mechanisms in these configurations.

Accurate subfilter stress modeling aids in increasing the accuracy of large-eddy simulations. A two neural network architecture for subfilter stress modeling is proposed for its magnitude and tensor structure based on a tensor basis expansion of the subfilter stress tensor. Due to the fully convolutional structure of the neural networks, they are trained on varying filter widths and varying domain sizes with a physics-informed loss function that enforces dissipation directly while allowing for backscatter. This structure is first evaluated a priori for forced homogeneous isotropic turbulence and channel flow conditions, where it is demonstrated that the neural networks can accurately predict the subfilter stress even in domains where, on average, over 20% of the kinetic energy (as compared to direct numerical simulation) is filtered out. The two neural network architecture is also analyzed in a posteriori settings for both forced homogeneous isotropic turbulence and channel flow conditions without clipping, where it is found that the model improves turbulent space-time correlations for forced homogeneous isotropic turbulence and mean velocity profiles for channel flow. In addition, the neural network provides reasonable results in simulations at Reynolds numbers over 30 times the Reynolds numbers in the training set.

Recent works have established the utility of sparsity-promoting norms for extracting spatially localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear dynamics of infinitesimal perturbations about a given baseflow. In this paper, we propose an optimization framework for computing sparse finite-amplitude perturbations that maximize transient growth in nonlinear systems. A variational approach is used to derive the first-order necessary conditions for optimality, which form the basis of our iterative direct-adjoint looping numerical solution algorithm. When applied to a reduced-order model of a sinusoidal shear flow at $\mathrm{Re}=20$, our framework demonstrates that energy injection into a single vortical mode yields comparable energy amplification to the nonsparse optimal solution, which concentrates $92\%$ of the energy in the same mode. Subsequent analysis of the dynamic response of the flow establishes that these sparse optimal perturbations trigger many of the same nonlinear modal interactions that give rise to transient growth when all modes are perturbed in an optimal manner. It is also observed that as perturbation amplitude is increased, the maximum transient growth is achieved at an earlier time. Our results highlight the power of the proposed optimization framework for revealing sparse perturbation mechanisms for transient growth and instability in fluid flows. We anticipate the approach will be a useful tool in guiding the design of flow control strategies in the future.

A floating liquid bridge can be generated when voltage is applied across two beakers in DC or high-frequency AC conditions. However, this leaves a wide range of scanning frequencies unknown for the stability of the floating liquid bridge. In this work, we investigated the stability of a micro-floating liquid bridge under periodic voltage pulses, characterized by a high-speed camera and current recording systems. We found that the electrical current perfectly revealed the stability and dynamics of liquid bridges and, thus, can be used as a new approach to study the liquid bridge in the absence of an imaging system. We found six different states of liquid bridges based on their stability, as well as their current characteristics. The phase diagram indicated that, besides the electrocapillary number, the frequency of voltage pulses is another crucial factor for the liquid bridge stability. We unveiled the strong electrical impacts on the liquid bridge formation and breakup dynamics, and we found that the critical time of liquid bridge formation and breakup is an order of magnitude longer than that predicted value, without considering the charging and discharging process. We corrected the formation and breakup time of the floating liquid bridge, considering the Maxwell stress-reduced capillary force in the charging and discharging process, which well explained our experimental observation. Our study provides new insights into the dynamics and stability of liquid bridges, which may be useful for printing in the future.

The chaotic flow of elastic fluids at low Reynolds number ($Re$) is typically distinguished into elasto-inertial and elastic turbulence (EIT/ET). However, the clear separation among these two turbulent regimes in parallel flows with a gradual $Re$ decrease remains elusive. Here, spanning $Re$ over four orders of magnitude, we investigate the statistical and structural nature of the flows computed by fully resolved 3D numerical simulations, revealing that as inertia becomes subdominant all flows share similar dynamical properties. Supported by the results, we thus propose a unified view of fully developed ET and EIT in parallel flows.

We perform Brownian dynamics simulations of the finitely extensible nonlinear elastic (FENE) dumbbells in spatially periodic turbulence to investigate the relationship between the dynamics of polymers and the hierarchy of coherent vortices. We decompose the velocity field into different scales to directly evaluate the effect of vortices with different sizes on dumbbells. Scale-decomposition analysis provides quantitative evidence that the smallest-scale vortices dominantly stretch dumbbells with a relaxation time shorter than the Kolmogorov time, whereas the contribution from large-scale vortices relatively increases when the relaxation time exceeds the Kolmogorov time. To explore the origin of this scale-dependent stretching mechanism, we investigate the alignment between dumbbells and the scale-decomposed strain-rate tensor. We find that dumbbells with a shorter relaxation time than the Kolmogorov time preferentially align in the most extensional direction induced by the smallest-scale vortices. However, as the relaxation time increases, dumbbells tend to align in the most extensional direction induced by 2–4 times larger vortices than the smallest-scale vortices. We explain this relaxation-time dependence of the effect of vortices with different sizes on dumbbells by focusing on how persistently the vortices stretch dumbbells.

The impact of liquid droplets on nonwetting solid surfaces and their subsequent rebounds have been extensively studied in recent decades, largely because of their robustness in practical scenarios. However, most works were focused on impinging single-phase droplets, while compound droplet impacts, which are more practically important, received only limited attention. In this work, we experimentally investigate the impact of compound droplets, comprising a water shell and an oil core, on superamphiphobic surfaces. Such core-shell droplets have similar surface tensions but higher viscosities than water and can completely rebound from superamphiphobic surfaces under a wide range of Weber numbers as pure water and oil droplets. However, they show distinct dynamic behaviors due to their different physical properties and energy dissipation processes. The enhanced viscosity due to the oil core strongly dampens surface capillary wave propagation, suppressing air bubble entrapment for droplet impacts at low Weber numbers, but, instead, facilitates the entrapment of a water droplet, resulting in complex water-in-oil-in-water droplet configuration. We demonstrate that such a water entrapment phenomenon provides an alternative strategy for producing submillimeter-sized water-in-oil droplets through the impingement of millimeter-sized oil-in-water droplets on slightly inclined superamphiphobic surfaces. Furthermore, the deformation of the oil-water interface during droplet spreading stores part of the impact energy, and it subsequently serves as an additional source driving droplet recoil, eventually shortening the contact time of all bouncing droplets. These findings offer a better understanding of the droplet impact dynamics of complex fluids and provide guidance for surface engineering and microfluidic device manufacturing.

We compute unsteady perturbations that optimally increase the heat transfer (Nu) of optimal steady unidirectional channel flows, for a given average rate of power consumption ${\mathrm{Pe}}^2$. The perturbations are expanded in a basis of modes, and the heat transfer enhancement corresponds to eigenvalues of the Hessian matrix of second derivatives of the Nusselt number with respect to the mode coefficients. Enhanced heat transfer, i.e., positive eigenvalues, occur in a range of temporal periods $\tau$ that scale as ${\mathrm{Pe}}^{-1}$. At small to moderate $\tau \mathrm{Pe}$ values the corresponding flows are chains of eddies near the walls that move as traveling waves at the steady background flow speed. At large $\tau \mathrm{Pe}$ the flows have eddies of multiple scales ranging up to the domain size. We use an unsteady solver to simulate these flows with perturbation sizes ranging from small to large and find increases in Nu of up to 56% at $\mathrm{Pe}=2^{19}$. Large Nu can be obtained by eddies with small spatial and temporal scales and by eddies with a range of spatial scales and large temporal scales.

When a particle moves in a Newtonian flow at a low Reynolds number, inertia is irrelevant, and a linear relationship exists between velocities and forces. For incompressible flows, any force distribution $\mathbf{f}\left(\mathbf{r}\right)$ acting in the fluid bulk induces flow and motion only through its solenoidal component. For force distributions that are spatially localized (i.e., vanish sufficiently fast at infinity), we derive the representation of the rigid-body motion as an explicit linear functional of $\mathbf{\nabla }\times \mathbf{f}$, which automatically selects the solenoidal component of $\mathbf{f}$. This alternative representation complements the usual one in terms of $\mathbf{f}$ and has the advantage of having the incompressibility constraint built-in. We illustrate its utility in avoiding certain ambiguities that arise, for example, when implementing approximations for swimmers.

The thermal drawing method has been widely used in fiber fabrication with thickness down to the microscopic scale, where the flow instability plays an important role in obtaining nanowires or many intriguing patterns. Inspired by this, we performed an exploratory second-order nonlinear analysis to investigate the nonlinear instabilities of a planar liquid sheet under dual mode. The dispersion relations of two modes and the formula for surface waves were obtained. Analysis indicates that van der Waals forces promote perturbation development, and the varicose mode dominates the development of surface waves. As the surface wave evolves, second-order perturbations gradually become dominant, and a portion of the first-order perturbations transfers to the second order takes on a dominant role. The nonlinearity introduced by the second-order perturbations in the development of surface waves has been analytically resolved, which can provide an explanation for the formation of the main and satellite liquid filaments after the rupture of the liquid sheet. Additionally, the application of the theoretical findings in nanowire manufacturing was investigated. Nanowire diameter prediction revealed its dependence on the liquid sheet thickness, with the main filament-to-satellite-filaments diameter ratio ranging 1.91–1.94. The ratio can be modified by adjusting the perturbation amplitude, which influences the diameter ratio positively. The impact of arbitrary microperturbations was also explored, showing negligible effects within the effective wave-number range denoted as $k_e$. These results can provide important guidance to achieve sophisticated nanostructures for functional devices in a single fiber or integrated fabrics.

We study the two-dimensional steady flow of a highly rarefied gas through a right-angled corner element. Driven by an external pressure gradient, the free-molecular regime is analyzed for both diffuse and specular reflecting surfaces, and the solutions are validated through comparisons with direct simulation Monte Carlo calculations at finite Knudsen numbers. Imposing the pressure gradient through differences in the densities and temperatures of the gas reservoirs connected to the channel inlet and outlet, the results for the density- and temperature-drop-driven flows are analyzed and contrasted. The characteristic differences between the diffuse- and specular-wall-system flows, indicating sharper flow gradients and higher flow velocities in the latter, are rationalized. Closed-form expressions for the mass flow rate through the corner are derived, indicating a decrease of more than $40\%$ in its mass transfer permeability due to the bend, compared with a straight channel configuration.

We present an experimental study of the properties of heat transport and flow structures in rotating thermal convection. The heat-transfer efficiency is found to exhibit a scaling transition at a transitional Ekman number ${\mathrm{Ek}}_t$, at which sharp transitions of the dynamical and geometrical properties of the columnar structures also occur. This precise correspondence implies that the behaviors of heat-transfer efficiency are intimately related to the changes in the coherent structures in the bulk flow. The sharp transition at ${\mathrm{Ek}}_t$ provides the first unambiguous experimental evidence for the regime transition from convective Taylor column regime to plume regime, at which the columns break down due to the increased inertial effect. Compared to the heat-transport behaviors, the transitions of the flow-field statistics are much sharper, which suggests that in further investigations of regime transitions, flow-field measurements may be used to provide a more definitive criterion.