Vortex lattices—highly ordered arrays of vortices—are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating fluids. However, the mechanisms governing their formation, stability, and eventual breakdown remain poorly understood. We explore the dynamical stability of vortex lattices in three-dimensional rotating flows. To that end we construct controlled initial conditions consisting of vortex lattices superimposed on turbulent backgrounds. We then characterize their evolution across different Rossby numbers and domain geometries. By introducing an Ekman drag we are able to reach a steady state where vortex lattices persist with near constant amplitude up until spontaneous breakup of the lattice, or an equivalent of “melting,” occurs. We examine an ensemble of runs in order to determine the mean lifetime of the lattice as a function of the system parameters. Our results reveal that the stability of the lattices is a memory-less random process whose mean lifetime depends sensitively on the system parameters that if finely tuned can lead to very long-lived lattice states. These metastable states exhibit statistical properties reminiscent of critical systems and can offer insight into long-lived vortex patterns observed in planetary atmospheres.

In homogeneous and isotropic turbulence, measurements of the longitudinal velocity derivative, ${\partial }_1{u}_1$, make it possible to estimate a surrogate of the rate of energy dissipation per unit mass, $\epsilon$: ${\epsilon }_s=15\nu {\left({\partial }_1{u}_1\right)}^2$, where $\nu$ is the fluid viscosity, in the sense that the averages of $\epsilon$ and ${\epsilon }_s$ are equal. We show here that the $n\text{th}$ moments of the fluctuations $\epsilon$ and ${\epsilon }_s$, for $n>2$, are not exactly proportional to each other, and that the expression for the moment $\langle {\epsilon }_s^n\rangle$ for $n\ge 3$ involves in addition to a term proportional to $\langle {\epsilon }^n\rangle$, other contributions involving the invariant of the strain tensor, $\mathbf{S}$: $\mathrm{tr}\left({\mathbf{S}}^3\right)$. The contribution of this term depends on the distribution of the dimensionless ratio $\mathcal{R}\equiv \mathrm{tr}\left({\mathbf{S}}^3\right)/\mathrm{tr}{\left({\mathbf{S}}^2\right)}^{3/2}$. We find, however, that the relation obtained by assuming that $\mathcal{R}$ is uniformly distributed in the interval $-1/\sqrt{6}\le \mathcal{R}\le 1/\sqrt{6}$, which is obtained when the matrix $\mathbf{S}$ has a Gaussian distribution, differs by no more than a few percent from the exact distribution.

The interaction of vortical structures with boundaries has been extensively studied in Newtonian fluids, where conditions such as no-slip walls, free surfaces, or contaminated surfaces dictate whether vortices rebound, dissipate, or generate secondary structures. In this work, we investigate a related but fundamentally different problem: the interaction of a vortex pair with a finite, nonuniform layer of polymeric fluid. Numerical simulations employing the finitely extensible nonlinear elastic-Peterlin model are used to examine the effects of polymer concentration, relaxation time, polymer layer thickness, and maximum polymer extension on the evolution of kinetic energy and enstrophy. The results show that, while the polymeric fluid dissipates vortical motion, vortex-polymer layer interactions can also generate new coherent structures. In particular, the formation of secondary and tertiary vortices coincides with transient increases in kinetic energy, a behavior absent in the Newtonian case. Unlike classical vortex-boundary interactions, where the primary vortex survives, we find that under certain conditions it completely dissipates upon interaction with the polymer layer. These findings emphasize that fluids with nonuniform polymer concentrations act not only as dissipative agents but also as sources of vorticity, extending the traditional view of polymer-induced drag reduction and providing insights into vortex-polymer interactions.

We investigate the effective rheology of a train of elongated bubbles of negligible viscosity flowing in capillary tubes. Building upon the classical Bretherton theory for a single bubble, we extend the analysis to a train of bubbles in a single capillary tube and finally to an array of parallel, noninteracting capillary tubes, i.e., a capillary bundle. Our goal is to characterize the nonlinear pressure drop-flow rate relation of this simplified two-phase system by incorporating the thin-film hydrodynamics at small capillary numbers. We model the structural heterogeneity of the bundle by assuming that the tube radii follow a truncated power-law distribution and examine deviations of the system from the Darcy law in terms of both its statistical properties and the parameters characterizing the bubble train (i.e., the tube slenderness ratio, the volume fraction, and the number of bubbles). The main result is that two-phase flow alters the effective rheology, leading to deviations from Darcy-type behavior across the entire parameter space investigated. Specifically, for a limited number of bubbles, the flow exhibits a smooth transition from the Bretherton regime, where the pressure drop scales with the flow rate to the power of $2/3$, to weaker sublinear regimes with exponents between $2/3$ and unity. Interestingly, increasing the number of bubbles or narrowing the pore-size distribution leads to only minor deviations from the Bretherton regime. The resulting pressure drop-flow rate exponents are qualitatively similar to those reported in the literature for immiscible two-phase flow in porous media, despite the inherent simplicity of the capillary bundle model.

Cone-and-plate (CP) viscometry is now widely employed to quantify slip lengths on superhydrophobic surfaces owing to its sensitivity at the micrometer scale; however, the presence of wall slip disrupts its intrinsic flow homogeneity. In this study, we present a combined theoretical and numerical investigation on how different slip boundary formulations affect flow homogeneity and its consequences for non-Newtonian fluid flows. Semianalytical solutions are derived under both constant slip-length and constant wall-stress boundary conditions. Numerical simulations are performed to examine the spatial structure of velocity, shear rate, and apparent viscosity in non-Newtonian fluids. The results demonstrate that a fixed slip length induces pronounced spatial variations in shear rate and radial dependence of viscosity for Carreau fluids, whereas a stress-controlled slip condition restores a nearly uniform shear field despite the presence of slip. The drag reduction and effective slip length for shear-thinning Carreau fluids are shown to depend explicitly on the imposed shear rate, with maximum slip enhancement occurring in the intermediate shear-thinning regime. These findings clarify the fundamental limitations of conventional slip interpretations in CP rheometric systems and provide a physically consistent framework for a homogenous flow field.

Unsteady thin-airfoil theory (UTAT) coupled with discrete-vortex methods has been widely employed in reduced-order aerodynamic modeling. Due to the nonuniqueness of potential-flow solutions, the Kutta condition is imposed to determine the circulation around the airfoil. Although the unsteady Kutta condition is commonly associated with the zero-loading condition at the trailing edge, its implications for the continuity of the vortex-sheet strength remain comparatively underexplored. In particular, the classical series expansion employed for the bound vorticity in unsteady thin-airfoil theory is not uniformly convergent at the trailing edge, leading to mathematical inconsistencies in the vortex-sheet and pressure distributions. In this context, the present work seeks to advance the mathematical framework of unsteady thin-airfoil theory through a physically consistent formulation of the bound vortex-sheet strength for the Wagner problem. A recurrence relation is derived for the Wagner coefficients, allowing the construction of a uniformly convergent series expansion for the bound vorticity. The proposed formulation ensures continuity between the bound and wake vortex sheets while simultaneously recovering zero pressure loading at the trailing edge, thereby providing a mathematically consistent representation of the unsteady Kutta condition. To investigate the implications of the modified framework, a discrete-vortex method based on UTAT is developed and compared with the classical formulation. The results demonstrate that the proposed approach eliminates spurious oscillatory behavior near the trailing edge and significantly improves the regularity of the computed vorticity and pressure distributions. Although both formulations appear to approach Wagner's classical lift response at large times, the classical representation remains inconsistent during the transient stage due to the discontinuity of the vortex-sheet strength. The proposed methodology establishes a more robust theoretical foundation for reduced-order unsteady aerodynamic models and provides a consistent basis for future extensions involving arbitrary airfoil kinematics.

We investigate turbulent Rayleigh-Bénard convection (RBC) in a convection cell with square cross section and aspect ratio $\mathrm{\Gamma }=\text{width}/\text{height}=25$ filled with the liquid metal alloy GaInSn at Prandtl number $Pr\approx 0.03$. A dense array of thermocouples and ultrasonic Doppler velocimetry is employed to measure the temperature distributions at the top of the convection cell and horizontal velocity profiles, respectively, in the Rayleigh number range $3.27\times {10}^4\lesssim \mathrm{Ra}\lesssim 2.17\times {10}^5$. Conspicuous thermal structures manifest themselves in the two-dimensional temperature fields and closely resemble the turbulent superstructures predicted in numerical simulations. The velocity data reveal flow features that indicate the presence of “jump rope vortices” (JRV). This can be seen in characteristic oscillations that permeate the entire 3D flow structure. The measured frequencies, $f_0$ correspond very well with the empirical scaling $f_0\propto {\mathrm{Ra}}^{0.419}$. The results thus provide experimental evidence that the jump-rope vortex, which has previously been identified as the striking dynamical feature of large-scale convection (LSC) in geometries with moderate aspect ratios ($1.4\le \mathrm{\Gamma }\le 5$), also persists as a robust, three-dimensional mode embedded within turbulent convective superstructures at very large aspect ratios.

Active grids enable the controlled generation of high Reynolds number turbulence; however, the influence of inlet conditions in the near-grid region remains poorly understood. Here we present a physics-focused experimental study of active-grid-generated turbulence in a water tunnel, focusing on the near-grid region ($x/M<20$), where the flow remains approximately homogeneous but strongly anisotropic. Inlet conditions are varied by independently controlling the operating protocol, the global blockage ratio (25%–74%), the mesh Reynolds number ($\mathrm{Re}{}_{\mathrm{M}}$), and the Rossby number (Ro). At the highest global blockage (74%), trends in large-scale statistics with $\mathrm{Re}{}_{\mathrm{M}}$ and Ro are consistent with measurements reported farther downstream in the literature. In contrast, at substantially lower blockages (≲40.2%), qualitatively different behavior emerges: turbulence intensity decreases monotonically with increasing $\mathrm{Re}{}_{\mathrm{M}}$ and exhibits little sensitivity to Ro. These results demonstrate that global blockage acts as a contributing parameter for the persistence of inlet-condition effects, whereas $\mathrm{Re}{}_{\mathrm{M}}$ and Ro modulate the redistribution of energy across scales. While large-scale quantities differ at lower global blockage relative to the far-grid region, the dissipative length scale exhibits consistent trend with $\mathrm{Re}{}_{\mathrm{M}}$ and Ro across all blockages. Despite persistence of inlet condition in the near-grid region, streamwise velocity spectra exhibit collapse at low and high wave numbers when scaled by the integral and Kolmogorov length scales, respectively, indicating that two distinct length scales are required to describe the near grid. Together, these findings provide insight into how forcing geometry and timescales influence the transition from forcing-dominated toward more universal turbulence behavior, and establish global blockage as an important parameter controlling near-grid active-grid turbulence.

Flame-generated nanoparticles, such as soot, caused by the incomplete combustion of hydrocarbon fuels in reacting flows, have adverse effects on human health and the environment. Understanding the interaction between soot and flow dynamics is critical to reducing particle emissions from engine combustors. This is because soot formation and evolution are highly sensitive to the flow dynamics encountered, especially in confined turbulent swirling flows, where strong shear layers and recirculation regions introduce complex, coherent patterns of both fast and slow timescales. These patterns are often crucial for understanding soot evolution and for controlling its formation and emission. To this end, large-eddy simulations (LES) of an aeroengine model combustor, with and without dilution jets, are conducted using state-of-the-art soot models. Then, modal analysis of flow and soot dynamics in the combustor is performed using the spectral proper orthogonal decomposition (SPOD) method with transient LES data. To the best of the authors' knowledge, this work is the first study to utilize SPOD and raw LES data to reveal the dynamics of coherent structures in swirl sooting flames. The frequency bands of both high-frequency dynamics (HFD, 234.375–468.75 Hz) and low-frequency dynamics (LFD, 0–156.25 Hz) are identified without any prior filtering. It is found that HFD primarily exists in the shear layer and inner recirculation zone, whereas LFD is present throughout the entire combustor. Compared to LFD, the HFD has a significant impact on velocity and gas-phase soot precursors (PAH), while LFD plays a crucial role in soot evolution. Furthermore, the results show that the evolution of velocity, PAH, and soot is closely coupled within the LFD frequency band. It is found that for soot and PAH, the impact of dilution jets on HFD modes is minor and on LFD modes is significant, while the opposite trend is observed for velocity modes.

Hair-covered appendages serve a variety of purposes in Nature, from chemical sensing and particle capture on the antennae of a crustacean to drag generation on bristled wings. At low to intermediate Reynolds numbers, these finite porous media experience three flow regimes. At low Reynolds numbers, the flow goes around the porous structure; this is the paddle or rake regime. As the Reynolds number increases, so does the relative flow rate through the array. If the fluid exits the structure mostly laterally, the flow is in the deflection regime. If the fluid exits downstream, the flow is in the sieve regime. Confining structures, such as the animal body or larger hairs, have been hypothesized to focus the flow on the hair-covered region. We investigate the influence of confinement on the flow through and around an array of cylinders, using a combination of experiments and numerical simulations. Experimentally, we vary the cylinder spacing, channel dimension, and flow rate and measure the velocity field using Particle Image Velocimetry. After comparing the results of finite element analysis with the experimental data, we numerically investigate a broader range of system geometries and flow parameters. Our results show that the confinement focuses the flow in the array and shifts the domains of existence of the three regimes. We present an analytical model that relies on the permeability of rectangular slits to predict the relative flow rate through and around the array. The model is in quantitative agreement with the numerical results, demonstrating that the flow through the array increases with increasing confinement, while the flow angle decreases. These results should provide insight into the morphology of hairy surfaces and have implications in the design of bioinspired flow sensors and filters.

We investigate the influence of a temperature-dependent viscosity on the flow over a heated flat plate, with a slip velocity condition at the wall as can occur with flow past solvophobic surfaces. This slip velocity can reduce the local shear stress on the wall compared to a no-slip boundary condition. An applied heating at the wall decreases viscosity in this region, which can further decrease wall stress. The extent of the contribution to this reduction in stress by the applied heating will depend on the temperature-dependent viscosity and the Prandtl number. We explore the link between the slip parameter, temperature-dependent viscosity, and the Prandtl number to investigate the drag reduction and heat transfer. We expand the momentum and energy boundary-layer equations assuming the slip parameter is small and use similarity solutions to solve for the first- and second-order corrections to the velocity and temperature fields. The asymptotic solutions show that the slip contributions to the flow are enhanced by temperature-dependent viscosity and the Prandtl number and we show their combined effect on the coefficients of friction and the Nusselt number. Our results indicate that increasing the coefficient of the temperature-dependent viscosity and the slip parameter complimentarily reduces friction and heat transfer effectiveness in the small slip parameter limit.

Polymeric turbulence, the flow of fluid with polymer additives at large Reynolds numbers, exhibits striking deviations from the Kolmogorov-like behavior of Newtonian turbulence. Recent experiments and simulations have uncovered a robust self-similar energy spectrum scaling as $k^{-2.3}$, in sharp contrast to the $k^{-5/3}$ scaling of Newtonian flows. The origin of this novel scaling, however, has remained unresolved. In this work we identify the physical mechanism underlying this emergent behavior using fundamental governing equations aided by scaling arguments. We show that the fluid energy cascade is depleted by polymers across a wide range of scales at a constant rate, which emerges as a second invariant alongside the total energy flux. The new invariant sets the novel scaling behavior, and the two invariants together allow for a minimal model description of polymeric turbulence. Concisely, our results reveal that polymeric turbulence is governed by two simultaneous invariants, unlike the single-invariant structure of Newtonian turbulence, and hint at turbulence control through suitably engineered and targeted polymer design.

When wind blows over the surface of a viscous liquid, a clear transition from irregular small-amplitude streamwise-oriented wrinkles to well-defined nearly two-dimensional regular waves is observed at a critical wind velocity. We examine how free-stream turbulence in the air influences the growth of wrinkles and regular waves, as well as the transition between these two regimes. Experiments are carried out in a wind tunnel, in which air is blown over a tank filled with silicone oil whose viscosity is 50 times higher than that of water. The free-stream turbulence is enhanced using upstream grids, achieving relative turbulence intensities up to $8\%$. Surface deformations are measured using free-surface synthetic Schlieren with micrometer accuracy. Velocity measurements are performed using hot-wire anemometry above the interface and particle image velocimetry in the liquid. Results reveal two primary effects of grid-enhanced free-stream turbulence: an increase in the wrinkle amplitude and a reduction in the critical wind speed at the onset of regular waves. Nevertheless, the wrinkle-wave transition still corresponds to an approximately constant friction velocity. We also observe a nonmonotonic evolution of the wave amplitude with fetch, which we rationalize using a wave energy balance model that accounts for the downstream decrease in friction velocity.

The shock-induced evolution of a multilayer fluid system featuring three distinct interfaces is investigated theoretically and numerically. This system exhibits not only adjacent-interface coupling but also significant cross-interface coupling, which substantially complicates the growth of interfacial perturbations. To isolate and elucidate the effects of both coupling mechanisms on the perturbation development at each interface, we develop an alternative linear analytical model. By imposing total transmission condition at the two downstream interfaces, reverberating waves within the layers are effectively eliminated, thereby isolating pure coupling effects. The study examines seven fluid layer configurations with varying initial thicknesses and amplitude combinations to validate the model and explore the influence of interface coupling on hydrodynamic instabilities. Both the initial amplitude and the interinterface distance are found to exert a bidirectional influence, either enhancing or suppressing, on interface development. Leveraging the model, a predictive framework is established to identify initial parameters that lead to amplitude growth stagnation at individual interfaces through tailored interface-coupling effects. These results provide valuable insights into complex interfacial instability mechanisms in multilayer systems and offer practical guidance for engineering applications involving shock-accelerated fluid layers.

We study the self-diffusiophoresis of a spherical chemically active particle near a planar, impermeable wall, with a focus on the influence of particle orientation on propulsion. We analyze a Janus particle with asymmetric surface chemical activity, consisting of a small inert region within a catalytically active cap. While numerical simulations have been used to study such particles, they encounter difficulties resolving the flow and transport in the near-wall regime due to geometric confinement and steep solute concentration gradients. We address this limitation through an asymptotic analysis in the lubrication limit, where the gap between the particle and the wall is narrow. In particular, we consider the distinguished limit in which the inert region is asymptotically comparable in size to the lubrication region. We analyze an axisymmetric configuration in which the inert face is oriented parallel to the wall and extend the analysis to slightly tilted orientations. We find that the cap size determines whether a tilted particle rotates back toward the axisymmetric state or continues to reorient, thereby characterizing its rotational stability in the near-contact regime.

We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially infinitesimal perturbations via twin simulations and decorrelator diagnostics. At short times, perturbations exhibit exponential growth, allowing us to define a (largest) Lyapunov exponent. We systematically examine how this exponent depends on stratification strength, quantified by the Brunt-Väisälä frequency and the Froude number, in a parameter regime relevant to oceanic flows. We find that increasing stratification leads to a monotonic reduction of the Lyapunov exponent, indicating suppressed chaoticity. Despite this reduction, uncertainty growth retains the universal temporal sequence observed in homogeneous isotropic turbulence—initial decay, exponential growth, and saturation. The growth phase is characterized by self-similar decorrelator spectra, but exhibits strong anisotropy: uncertainty spreads much more slowly along the stratification direction than horizontally, with the disparity increasing with stratification strength. An analysis of the decorrelator evolution equation reveals that the suppression of chaos arises primarily from strain-mediated alignment dynamics rather than direct buoyancy coupling. Our results provide a quantitative characterization of predictability and uncertainty growth in stratified turbulence and highlight the utility of decorrelator-based methods for anisotropic geophysical flows.

Droplets impacting on liquid pools have been extensively studied because of their complex dynamics and relevance to many natural and industrial processes. However, most of the research has focused on droplets of Newtonian fluids, and much less is known about droplets containing suspension particles, which adds another layer of complexity of non-Newtonian effect. To address this gap, we studied droplets containing cornstarch particles impacting a deep water pool over a range of impact velocities $u_0$ $(0.5–3\text{m/s})$ and particle volume fractions $\varphi$ $(36.8–47.5\%)$. We identified five distinct impact phenomena, several of which are absent in the impacts of Newtonian droplets, and collected them in a regime map in the nondimensional space of Weber number and $\varphi$. Through an energy-based scaling analysis, we elucidated the origins of and transitions between these phenomena, revealing that the competition between the pool cavity dynamics and the rheological properties of the suspension is the key factor governing the observed impact behaviors. Our results deepen the understanding of the complex interplay between impact dynamics, cavity evolution, and suspension rheology, offering practical guidance for a range of engineering applications.

This paper proposes the moment gas kinetic flux solver (MGKFS) for the simulation of flows from a continuum regime to a rarefied regime. Its fundamental innovation lies in the dual-flux strategy, which extends the conventional gas kinetic flux solver (GKFS) paradigm by directly calculating numerical fluxes not only for the conservation equations (mass, momentum, and energy) but also for the high-order moment equations (stress and heat flux) at cell interfaces. Thus, MGKFS effectively overcomes the critical limitation identified in the Grad-13-based GKFS (G13-GKFS). G13-GKFS locally interpolates stress and heat flux at cell centers from their values at cell interfaces. This approach neglects their global evolution equations, leading to insufficient global accuracy. MGKFS directly captures the evolution of these high-order moments with flux reconstruction from the local solution of the Boltzmann equation at the cell interface. Numerical validations demonstrate that MGKFS significantly outperforms G13-GKFS, achieving superior accuracy. This improvement is particularly notable in boundary layers, where global fidelity is essential.

Buoyancy-driven natural convection in porous media, known as Rayleigh-Darcy convection (RDC), is ubiquitous in geological and engineering systems, where it is induced by natural or anthropogenic temperature and concentration gradients under which higher density fluid lays above lower density fluid. Although medium heterogeneity is widely recognized as a key factor governing subsurface fluid flow, its role in regulating RDC remains poorly understood. Using high-resolution numerical simulations over a broad range of Rayleigh numbers ($Ra$), we show that the interplay between the permeability correlation length ($\mathcal{L}$) and the characteristic flow-structure length fundamentally controls RDC dynamics. In the stable convective-cell regime ($Ra<1300$), $\mathcal{L}$ constrains the horizontal extent of convection cells and therefore modifies transport efficiency. In the transition regime ($1300\le Ra\le 7500$), heterogeneity disrupts the transverse coherence of the boundary layers and suppresses the merging of microplumes into large-scale megaplumes, which significantly amplifies convective instability and enhances transport. In the chaotic regime ($Ra>7500$), heterogeneity with small $\mathcal{L}$ has a negligible effect, whereas that with large $\mathcal{L}$ regulates the boundary-layer thickness through local permeability variations. These results provide a unified physical framework for understanding how heterogeneity regulates buoyancy-driven convection in porous media.

We investigate the detachment of bubbles from an orifice on a horizontally translating plate in a quiescent liquid through experiments and force-based modeling. By varying the plate velocity, orifice diameter, and air volume flow rate, we identify two representative regimes of bubble detachment: buoyancy-driven rise and shear-controlled lift off. For each regime, the balance of dominant forces acting on the bubble yields a critical bubble radius under given conditions, which initiates a transition from the growth phase to the detachment phase. Using the critical radii derived for the extreme cases of the two detachment regimes, a critical radius ratio is proposed to unify the trends of the inclination angle and the bubble radius in the intermediate range where both vertical rise and horizontal lift off are effective. This study develops a foundational model to describe the detachment characteristics of bubbles from a moving solid surface.