A general formula is established for traveling speed of an axisymmetric toroidal vortex with magnetic flux concentrated in a thin core embedded in electrically conducting fluid subject to the Hall effect. We extend Helmholtz-Lamb's method to include magnetic flux. The resulting formula admits viscous diffusion of vorticity and magnetic diffusion. The Hall effect only modifies the distribution of magnetic field. In the other extreme of fat cores, an exact solution is constructed of the ideal Hall-magnetohydrodynamics (HMHD) for a steadily traveling spherical magnetic vortex. This vortex is accompanied by a spherical-boundary vortex sheet as in the MHD case. The toroidal magnetic field acts to enhance the traveling speed, but the Hall effect causes the discrepancy in the traveling speed, whether the magnetic field is parallel or antiparallel to the vorticity, by modifying the distribution of the magnetic field. The traveling speed of a thin vortex ring is increased or decreased for parallel or antiparallel cases, respectively. For the spherical vortex, the opposite trend is brought by the surface vortex sheet. Besides, a particular solution is found for a spherical vortex pertaining only to the HMHD.

Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral proper orthogonal decomposition (SPOD) produces orthogonal, energy-ranked spatial modes at discrete temporal frequencies for statistically stationary flows. However, SPOD requires long stretches of sequential, uniformly sampled, time-resolved data. These data requirements limit SPOD's use in experimental settings where the maximum capture rate of a camera is often slower than the Nyquist sampling rate required to resolve the highest turbulent frequencies. However, if two particle image velocimetry systems operate in tandem, pairs of data can be acquired that are arbitrarily close in time. The dynamic mode decomposition (DMD) uses this pairwise data to resolve frequencies up to the Nyquist frequency associated with the small time step within a pair. However, these modes do not form a basis and have no set ranking. The present work attempts to compute SPOD modes from pairwise data with a small time step but with large gaps between pairs. We use DMD on pairwise data to estimate segmentwise, uniformly sampled series that can then be used to estimate the SPOD modes, intending to resolve frequencies between the gap and pair Nyquist limits. The method is tested on numerically obtained data of the linearized complex Ginzburg-Landau equation, as well as a Mach 0.4 isothermal turbulent jet. For the jet, pairwise SPOD can accurately dealias the SPOD spectrum and estimate mode shapes at frequencies up to $\text{St}\approx 1.0$ while using more than 90% fewer data.

The quasistatic growth of a bubble in a shear flow is investigated. Experiments are performed in a horizontal rectangular channel with air bubbles growing in water. The bubbles are generated on the bottom wall of the channel on two substrates (glass and treated glass) with different wetting conditions. During its growth and detachment, the bubble is recorded with high-speed video camera allowing the measurements of several geometric parameters. These parameters are then used to evaluate the static and hydrodynamic forces acting on the bubble. On the glass substrate, the bubble foot expands outside the injection cavity as the liquid flow rate increases, resulting in an elongation of the bubble foot, while on the treated glass substrate, the bubble foot remains almost constant at a value close to injection cavity radius. Using the force balance acting on the bubble allows us to determine the drag coefficient of the bubble versus the bubble Reynolds number, which is well predicted by expression deduced from numerical simulation by Shi et al. [Phys. Rev. Fluids 5, 073601 (2020)]. Furthermore the theoretical expressions for the drag and lift forces by Shi et al. [Phys. Rev. Fluids 5, 073601 (2020)] allows us to verify the force balance throughout the bubble growth with an error less than $15\%$. Using these theoretical expressions with the experimental observation that the detachment occurs when the advancing (upstream) contact angle reaches a critical value depending on the surface wettability, allows us to build a new criteria for the bubble detachment that is in good agreement with the measurement.

We investigate the basal melting of ice in fresh water under the influence of external shear flow, and focus on the effects of density inversion and shear strength. Density inversion is modeled by a nonlinear equation of state and characterized by the inversion stability ratio $R$, while shear strength is quantified by the effective Richardson number $R{i}_e$. Different flow regimes are identified. When the density inversion is strong, a stably stratified layer suppresses convection, leading to pure conductive heat transfer and a flat ice-water interface. When density inversion is weak, convection motions are dominated by cells under weak shear and long rolls under strong shear, which result in different morphologies of ice interface. The average height of the surface and convection layer is strongly influenced by $R$ but only weakly by $R{i}_e$, while the interface roughness exhibits nonmonotonic dependence on both parameters due to different flow structures and nonuniform growth of the stably stratified layer. A single scaling relation is determined for the effective Rayleigh number and Nusselt number. Theoretical models are also developed for the heights of interface and convection layer, and the parameters for regime transitions, and agree well with numerical results.

The impact of permeability heterogeneity on reactive buoyancy-driven convective dissolution is analyzed numerically in the case of a bimolecular $\text{A}+\text{B}\to \text{C}$ reaction across varying Rayleigh numbers. The convective dynamics is compared in homogeneous, horizontally stratified, vertically stratified, and log-normally distributed permeability fields. Key variables, such as the total amount of product, mixing length, front position and width, reaction and scalar dissipation rates, and dissolution fluxes, are strongly influenced by the type of permeability heterogeneity. Vertically stratified and log-normally distributed permeability fields lead to larger values for all variables compared to homogeneous fields. Horizontally stratified fields act as an obstacle to convective flow, resulting in slower front progression, thicker fingers, wider reaction fronts, and the lowest dissolution fluxes among all cases. When the reaction stabilizes convection, flow stagnation occurs near the extremum of the nonmonotonic density profile, even in vertically stratified systems, highlighting the complex interaction between reactions and dissolution-driven convection. In log-normally distributed fields, the flow behavior depends on the permeability structure: smaller horizontal correlation lengths cause fingers to spread more horizontally, while larger horizontal correlation lengths promote more vertical movement with shorter wavelengths. Overall, a shorter horizontal correlation length relative to the vertical one leads to an increase in the value of all aforementioned variables and thus to a more efficient mixing. These findings reveal how heterogeneity affects convective dynamics by influencing the reaction front, dissolution rates, mixing behavior, and mass transport efficiency, emphasizing the intricate role of permeability structure in reactive convective processes.

We study the spatial dependence of pair correlation functions of velocity field components in a rotating turbulent fluid on a background of a coherent geostrophic vortex. The statistics of the turbulent pulsations are determined by their dynamics, which is the dynamics of inertial waves affected by the differential rotation in the vortex and a weak viscous damping. We are interested in distances which are larger than the scale of the wave forcing but smaller than the radius of the coherent vortex. We establish the anisotropy of the velocity field correlation function at the distances. All the diagonal elements of the correlation function decay logarithmically in the streamwise direction and power-like in radial direction, and the direction along the rotation axis is independent of the details of the forcing correlation function that indicate “coherency” of the flow. On the contrary, the cross-correlation function of the radial-azimuth velocity components, which turns into the Reynolds stress for zero distance, demonstrates strong dependence on the forcing correlation function and decays quickly at distances larger than the forcing scale.

Water wave interaction with a large number of floes is investigated, based on the linearized velocity potential theory for fluid flow, and elastic thin plate theory for ice floes. The solution procedure starts from a domain decomposition approach, and equations for velocity potentials are constructed via the boundary integral method in the free-surface and ice-covered subdomains, separately. The velocity potentials and normal velocities at the interface of different domains are expressed in terms of eigenfunction expansions in the vertical direction. This allows the three-dimensional equation to be reduced to a set of two-dimensional ones. Continuity of velocity and pressure are then imposed at the interface. A formula for evaluating hydrodynamic forces is derived, which requires only the results on the floe edge. When the number of ice floes becomes large, an efficient scheme is introduced to reduce computational effort, while the desired accuracy is maintained. The procedure is applicable to ice floes of arbitrary shapes and arrangements. Case studies are conducted for single and double arrays of circular and elliptical ice floes. Extensive results are provided for the hydrodynamic forces and far-field scattered wave energy. Their features and corresponding physics are discussed.

Gas-liquid-solid (GLS) three-phase interactions play a significant role in many essential areas but present many critical challenges for computational fluid dynamics methods to study. In this paper, we present a GLS contact condition-enforced immersed boundary method (IBM) for simulating multiphase flow problems with curved and moving boundaries on simple Cartesian meshes. Together with the phase field conditions, a GLS contact condition is introduced in the Cahn-Hillard model and then dealt with by the IBM to effectively eliminate mass leakage at the solid boundary. Both the phase field and contact conditions are consistently enforced by proposing a second-order moving-least-squares (MLS)-based IBM. In addition, the velocity correction IBM is applied to enforce the no-slip condition at the solid surface. The flow field is solved by using the multiphase lattice Boltzmann flux solver (MLBFS), which is suitable for multiphase flows at large density ratios. The performance of the present method is well examined through many challenging benchmark tests, including both steady and unsteady GLS problems, such as droplet spreading and impacting circular solid surfaces with different wettabilities. The good agreements with theoretical and available numerical data published in the literature show that the present GLS contact condition-enforced IB-MLBFS can accurately enforce the Dirichlet and Neumann boundary conditions and efficiently restrain nonphysical liquid/mass penetrations near the solid surfaces. Applications of the present method to study more complex GLS problems at large density ratios $O\left({10}^3\right)$, including droplets impacting porous solid structures and a flapping wing, have also been carried out to further demonstrate its reliability and high potential.

Instability of a viscoelastic swirling liquid jet in static ambient gas is studied theoretically and numerically. The theoretical model is established based on the azimuthal Rankine vortex and axial nonuniform velocity distribution, enabling the initially unrelaxed elastic stress in the axial direction of the jet. Linear instability analysis is carried out to study the transition of predominant modes through comparing the maximum perturbation growth rates between different azimuthal modes, and energy budget analysis is employed to reveal the physical mechanism of modes transition. As the rotation is slow, the jet instability is dominated by the unrelaxed axial elastic stress, thus resulting in axisymmetric evolution of the liquid jet. However, when the jet rotates faster, the effect of unrelaxed axial elastic stress weakens rapidly, while the centrifugal force which originates from the inertial effect of the swirling jet starts to play a primary role, leading to the predominant modes transition to larger azimuthal wave numbers. With the enhancement of liquid elasticity, the jet instability would be dominated by a larger azimuthal wave number. To further identify the effect of elastic force on jet instability quantitatively, the numerical simulations based on the open-source platform Basilisk are carried out. It is found that the elastic force plays a stabilizing role on axial, radial, and azimuthal directions of the swirling jet. However, this stabilizing effect weakens with the enhancement of elasticity, leading to the increase of jet kinetic energy with a quicker growth of disturbance at jet interface. Moreover, the centrifugal force and the Coriolis force increases with the enhancement of elasticity, thereby promoting the predominant modes transition to larger azimuthal wave numbers.

Based on mesoscale lattice Boltzmann numerical simulations, we characterize the Rayleigh-Bénard (RB) convective dynamics of dispersions of liquid droplets in another liquid phase. Our numerical methodology allows us to modify the droplets' interfacial properties to mimic the presence of an emulsifier (e.g., a surfactant), resulting in a positive disjoining pressure which stabilizes the droplets against coalescence. To appreciate the effects of this interfacial stabilization on the RB convective dynamics, we carry out a comparative study between a proper emulsion, i.e., a system where the stabilization mechanism is present (stabilized liquid-liquid dispersion), and a system where the stabilization mechanism is absent (nonstabilized liquid-liquid dispersion). The study is conducted by systematically changing both the volume fraction $\varphi$ and the Rayleigh number $Ra$. We find that the morphology of the two systems is dramatically different due to the different interfacial properties. However, the two systems exhibit similar global heat transfer properties, expressed via the Nusselt number $Nu$. Significant differences in heat transfer emerge at smaller scales, which we analyze via the Nusselt number defined at mesoscales ${Nu}_{\mathrm{mes}}$. In particular, stabilized systems exhibit more intense mesoscale heat flux fluctuations due to the persistence of fluid velocity fluctuations down to small scales, which are instead dissipated in the interfacial dynamics of nonstabilized dispersions. For fixed $Ra$, the difference in mesoscale heat-flux fluctuations depends nontrivially on $\varphi$, featuring a maximum in the range $0.1<\varphi <0.2$. Taken all together, our results highlight the role of interfacial physics in mesoscale convective heat transfer of complex fluids.

The internal-kinetic energy exchange and the effect of the Mach number in a 2D compressible Taylor-Green vortex flow are investigated, using direct numerical simulation with initial Mach numbers (${\mathrm{Ma}}_0$) ranging from 0.2 to 1.0 and a Reynolds number of 1600. Kinetic energy is decomposed into dilatational and solenoidal components using Helmholtz decomposition. The flow evolution is described in three stages, which are the generation of compressibility, transition, and oscillatory decay stages, respectively. In the generation stage, the dilatational kinetic energy is analytically derived to increase quadratically with time, which is generated by advection from solenoidal kinetic energy and partially transformed into internal energy via pressure-dilatation. In the transition stage, pressure-dilatation reaches a minimum and scales linearly with initial Mach number. Shock waves emerge at high initial Mach numbers, enhancing both the dilatational and solenoidal dissipations. In the oscillatory decay stage, the kinetic energy is dominated by the solenoidal component, which decays exponentially with superimposed oscillations. These oscillations are explained as acoustic energy exchange between internal energy and the negligible dilatational kinetic energy. The oscillation frequency and initial Mach number are found to follow an inverse proportionality for ${\mathrm{Ma}}_0<0.6$. As a first simplified example, this research sheds light on the understanding of internal-kinetic energy exchange in compressible flows.

We employ interface-resolved direct numerical simulations of a dense suspension in turbulent channel flow laden with finite-size spherical particles at a high solid volume fraction of $\mathrm{\Phi }=0.2$. By systematically varying particle diameters ($a/h=1/12,1/18,1/24$) and density ratios (${\rho }_r=0.5,1,10$), we show that low-inertia particles homogenize flow topology across wall-normal regions by generating symmetric vortex stretching and biaxial strain at the particle–fluid interface, recovering a uniform “tear-drop” shape in the joint probability density functions of the invariants $Q$ and $R$. With increasing inertia, this homogenization weakens first in the viscous sublayer and the buffer layer since heavy particles cannot follow small-scale vortices; their wakes break the symmetry in $Q–R$, fragmenting the classical energy cascade. High-inertia particles preferentially cluster in the channel core, suppress near-wall sweep or ejection events, flatten vortex cores, elevate drag by amplifying particle-induced stresses while reducing both Reynolds and viscous stresses; meanwhile, near-wall turbulent kinetic energy is enhanced by localized intense shear. These results bridge interphase interactions and bulk modulation and quantify how particle inertia reorganizes turbulent structures in dense suspensions.

This study employs direct numerical simulations to investigate wake-induced laminar-to-turbulent transition in separated laminar boundary layers (SLBs) at a moderate gap ratio ($s=0.9$) with ${\text{Re}}_D=800,1575,3900$, and ${\text{Re}}_{\theta }=150$. We characterize the transition process, driven by coherent vortex dynamics synchronized with cylinder wake shedding, through detailed analysis of mean flow, Reynolds stresses, and spatial evolution of velocity spectra. Remarkably, turbulence emerges at such low ${\text{Re}}_{\theta }$ because the transition process follows a hybrid pathway that combines SLB instability and wake-driven $\mathrm{\Lambda }$-vortex formation. The transition unfolds in distinct stages: linear disturbance amplification, nonlinear saturation via superharmonic resonance, and turbulent breakdown. Unlike classical SLB transitions, the wake's periodicity imposes unique spectral signatures on transition dynamics. These findings characterize wake-boundary interactions inherent to turbomachinery and aerodynamic systems, offering insights for potential flow control strategies.

Bubble coalescence can promote bubble departure at much smaller bubble sizes than those required for buoyancy-driven detachment. This can critically enhance the efficiency of gas-evolving electrochemical processes, such as water electrolysis. In this study, we integrate high-speed imaging experiments and direct numerical simulations to dissect how and under which conditions bubble coalescence on surfaces leads to detachment. Our transparent electrode experiments provide insights into contact line dynamics, demonstrating that the bubble neck generally does not contact the surface during coalescence. We reveal that whether coalescence leads to bubble departure or not is determined by the balance between surface energy, adhesion forces, and viscous dissipation. For the previously unexplored regime at low effective Ohnesorge number, a measure of viscosity that incorporates the effect of asymmetry between the coalescing bubbles, we identify a critical dimensionless adhesion energy threshold of $\approx 15\%$ of the released surface energy, below which bubbles typically detach. We develop a global energy balance model that successfully predicts coalescence outcomes across diverse experimental conditions.

Nanoscale fluid morphologies, including adsorbed layers and thin liquid films, are strongly influenced by intermolecular forces. We present a continuum model for nanoscale wetting that incorporates a nonlocal, Lennard-Jones-like solid-fluid interaction potential into the Navier-Stokes-Korteweg framework. This approach enables the study of nanoscale fluid phenomena such as vapor adsorption and thin film dynamics with a continuum description. Our results indicate that the added potential compresses fluid near the solid substrate, forming adsorbed layers in the vapor regime and modifying the density within liquid films. In thin liquid films, purely attractive interactions initially compress the film, leading to transient rearrangements in density gradients before stabilizing with a higher near-wall density. Under thermally driven phase change, the solid-fluid potential modulates liquid-vapor phase change by altering local equilibrium conditions. Near-wall compression inhibits late-time evaporation, stabilizing the film at a finite thickness. In condensation, the film thickens similarly to the no-potential case initially, but then gradually stabilizes as the near-wall region approaches equilibrium. Our analyses show that solid-fluid interaction forces control nanoscale phase change and liquid-vapor coexistence, providing a continuum description that complements molecular and classical continuum methods. Our key contribution is to treat the wall-fluid interaction as a nonlocal bulk potential within the NSK-DGT free energy, which reorganizes near-wall density and modulates interfacial mass transfer while preserving thermodynamic consistency.

Particles are common in biological and environmental flows and are widely used in industrial and pharmaceutical applications. Their motion and flow dynamics are strongly affected by interactions with the surrounding flow structure. While particle-flow interactions have been extensively studied in low Reynolds number (Re) flows as well as in fully developed turbulence, the transport mechanisms of these particles in intermediate flow regimes remain less explored. Here, we investigate the response of neutrally buoyant spherical particles to a single vortex flow field. Using a microfluidic cross-slot geometry, we generate a well-characterized, stationary, three-dimensional streamwise vortex at moderate Re ($\sim 50$). Our experimental results, supported by numerical simulations, show that with increasing particle diameter, they are progressively excluded from the vortex core. Small particles follow a Burgers vortexlike self-similar motion, but for larger particle diameters, deviations from this trend emerge due to fluid inertia and finite-size effects. These findings enhance our understanding of particle dynamics in vortical flows and have implications for microfluidic applications involving particle sorting and separation.

Zonal jets are a fascinating natural example of how a rapidly rotating turbulent flow self-organizes at large scale in the presence of a $\beta$ effect. Understanding the long-term, nonlinear equilibration of zonal jets and the feedback with the underlying turbulence and waves is still a challenge. Following a similar approach as in the Holton-Lindzen-Plumb model for mean flow reversals in stratified fluids, this study describes a novel, quasilinear semianalytical model to discuss the emergence and coalescence of zonal winds from the radiation of Rossby waves. This model emphasizes the role of Rossby waves in exchanging momentum with the zonal flow and the feedback of the zonal flow on the waves. It employs a Wentzel-Kramers-Brillouin expansion of the wave field to obtain an explicit expression for the Reynolds stress, leading to a closed mean flow equation. Two key feedback effects control the properties of the wave-driven zonal flow: the Doppler shift, leading to the emergence of critical latitudes, and the modification of the background $\beta$ effect by the zonal flow curvature. Motivated by previous experimental observations, we integrate this quasilinear model in time with an increasing number of latitudes of wave radiation. We observe a transition between locally driven jets that remain individual and globally driven jets that coalesce and equilibrate at a new scale. In the weak wave damping limit, coalescence occurs when critical latitudes of neighboring jets overlap. This is the first purely zonal closure which self-consistently leads to an equilibrium flow with zonal jets separated by a Rhines scale. These results are further supported by quantitative comparison with experiments and nonlinear direct numerical simulations.

This article presents our experimental study of the nonlinear destabilization of an internal wave standing mode in a uniformly stratified fluid within a rectangular domain. We measure the linear response of the system and target its resonances to generate a high-amplitude standing mode, prone to instabilities. Using modal decomposition tools, we determine the characteristics of the secondary waves and show that they have a standing-mode spatial structure. Box resonance conditions associated with nonlinear resonance conditions lead to a significant deviation from the internal wave dispersion relation and complex nonlinear interaction dynamics. Following previous work, we develop a weakly nonlinear analysis to understand the secondary wave characteristics. This approach, validated by experimental results, shows that the secondary wave characteristics as well as the general nonlinear dynamics are highly sensitive to the domain geometry and to the forcing mode.

A real-time adaptive control framework based on the single-step deep reinforcement learning (SDRL) algorithm is proposed and implemented in numerical simulations for attenuating Tollmien-Schlichting (TS) wave instabilities in a two-dimensional incompressible boundary layer over a flat plate. The perturbation formulation of the Navier-Stokes equations is solved in the time domain using a finite-volume discretization scheme. The controller utilizes volume-distributed body forces as proxies for dielectric barrier discharge plasma actuators, with instantaneous wall-pressure feedback in a closed-loop configuration to dynamically adjust the amplitude of the controlling body force. By learning an opposition control strategy—generating TS waves with the same amplitude but opposite phase to the incoming TS instabilities—the SDRL-based controller achieves effective suppression of both single- and multifrequency TS waves. The performance of the SDRL-based controller is evaluated against a classical model-free adaptive approach, the filtered-x least mean square– (FXLMS) based controller, focusing on effectiveness in terms of TS wave suppression and convergence speed. The SDRL-based controller achieves up to $94.81\%$ suppression of TS waves, demonstrating superior suppression performance and faster convergence than the FXLMS-based controller in most control cases. Additionally, the robustness of the controllers against measurement and actuation noises is examined. These results establish the SDRL framework as a low-cost, model-free control approach for robust real-time control of convective flow instabilities in the presence of noise sources. Relying on compact neural networks and minimal sensor feedback, the methodology enables a practical and experimentally feasible artificial intelligence-based controller for convective instabilities.

The behaviors of an oscillating bubble near a water surface can be classified as forming a toroidal shape resulting from a re-entrant jet and an open bubble completely exposed to the atmosphere. In this study, we observe a phenomenon of partial ventilation. As the bubble expands, perturbations induced by the Rayleigh-Taylor instability grow rapidly on the water's surface and eventually penetrate the bubble wall, allowing ambient air to rapidly enter its interior. The bubble loses its transparency due to the considerable disturbance caused by high-speed airflow and various-sized droplets across its entire wall. Three distinct types of bubble behaviors with decreasing dimensionless standoff distance $\gamma$ are summarized in this study as follows: (i) nonventilation; (ii) partial ventilation; and (iii) complete ventilation, depending on the exposure of a bubble's interior to the surrounding air. The study investigates the partial ventilation phenomenon by combining laboratory experiments, numerical simulations, and analytical modeling. The analytical model comprises two components: a small-amplitude model that explains the growth of perturbations and a bubble-oscillation model that describes the bubble dynamics. Solving the model obtains the boundaries for the partial ventilation regime. These boundaries encompass upper and lower limits for both the dimensionless timing for starting ventilation $t_v^{\prime }$ and the dimensionless standoff distance $\gamma$. The analytical estimates agree well with the experimental observations and numerical results.