Miha Rot, Gregor Kosec
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency. Meshless methods approximate differential operators based on the values of the field in computational nodes, offering a natural approach to adaptivity. The density of computational nodes can either be increased to enhance accuracy or decreased to reduce the number of numerical operations, depending on the properties of the intermediate solution. In this paper, we utilise an adaptive discretisation approach for the numerical simulation of natural convection in non-Newtonian fluid flow. The shear-thinning behaviour is interesting both due to its numerous occurrences in nature, blood being a prime example, and due to its properties, as the decreasing viscosity with increasing shear rate results in sharper flow structures. We focus on the de Vahl Davis test case, a natural convection driven flow in a differentially heated rectangular cavity. The thin boundary layer flow along the vertical boundaries makes this an ideal test case for refinement. We demonstrate that adaptively refining the node density enhances computational efficiency and examine how the parameters for adaptive refinement affect the solution.
Yiqing Wang, Chao Xu, Riccardo Scarcelli, Ben Cantrell, Jon Anders, Sameera Wijeyakulasuriya
A numerical study for a hydrogen (H2) jet in an air crossflow (JICF) was performed using direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) approaches, based on a geometry representative of key aspects of port fuel injection (PFI) in a H2-fueled heavy-duty internal combustion engine. The focus was placed on the H2 mixing process and the turbulent species flux model used in the latter two approaches. Based on the DNS data, the performance of LES and RANS on predicting the turbulent flow fields and mixing process was comprehensively evaluated. Results showed that LES performs very well in predicting both the mean velocity and the Reynolds stress. In contrast, RANS significantly under-predicts all Reynolds stress components, while predicting the mean flow field relatively well. Regarding the H2 mixing prediction, LES shows an excellent agreement with DNS, while RANS significantly under-predicts the mixing process. The underlying reasons for the poor performance of RANS were identified by extracting turbulent transport properties used in RANS approach from DNS data. It was found that the turbulent diffusivity used in RANS is much smaller than that derived from DNS, which is attributed to the over-prediction on turbulent Schmidt number (Sct), as well as the under-prediction on turbulent viscosity. By further analyzing the anisotropic components of Sct and the misalignment angle between turbulent species fluxes directly obtained from DNS and those predicted by the RANS mixing model, the commonly used assumption of isotropic turbulent diffusivity in RANS was demonstrated to be invalid for the present configuration. This study provided a unique DNS dataset for H2 jet in a crossflow relevant to H2 PFI engines and generated new insights on improved modeling of turbulent mixing.
Tong Wu, Chensheng Luo, Le Fang, Michael Wilczek
Statistical moments of velocity gradients provide fundamental information on the small-scale properties of turbulence. In this work, we propose a systematic method to derive exact expressions for statistical moments of arbitrary order for both longitudinal and transverse velocity gradients in isotropic turbulence. The approach is applicable to both compressible and incompressible flows and expresses the moments in terms of invariants of the velocity gradient tensor. The derivation combines isotropic tensor theory, orientational averaging, and an algorithmic implementation, enabling the computation of high-order moments in a unified framework. We show that longitudinal velocity gradient moments of order higher than three depend not only on $\mathrm{tr}(\boldsymbol{S}^2)$, which is proportional to the dissipation rate, but also on $\mathrm{tr}(\boldsymbol{S}^3)$, which reflects strain self-amplification, where $\boldsymbol{S}$ denotes the strain-rate tensor. The resulting theoretical expressions are validated through comparisons with existing theoretical results and direct numerical simulations.
Aditya Singh, Joseph Samuel, Chien-chia Liu, Luiza Angheluta, Andrés Concha, Mahesh Bandi
We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.
Bodhinanda Chandra, Sachith Dunatunga, Ken Kamrin
This work presents a unified viscoelastic-viscoplastic continuum framework for modeling rate-dependent granular flows across regimes. The formulation incorporates two distinct rate-dependent mechanisms, namely micro-inertia and viscoelastic dissipation, within a single continuum description. A central contribution is an explicit link between the coefficient of restitution and a continuum viscosity, derived from an analysis of wave attenuation in granular assemblies, thereby establishing a direct connection between particle-scale collision physics and macroscopic damping. This relation is introduced while retaining inertia-dependent plastic flow governed by the classical $μ(I)$ rheology. The constitutive model is constructed by meticulously partitioning elastic and viscous responses within the model and corresponding stress-update routine, such that viscous dissipation governs wave propagation and collisional processes without altering the plastic flow rule. The framework is implemented within the material point method to simulate transient processes involving large deformations, material separation, and subsequent reconsolidation. A range of numerical examples, including steady, transient, vibrational, and impact-driven flows, demonstrates that the model captures wave propagation, diffusion, and rate-dependent granular behavior within a unified continuum setting.
Haotian Cheng, Hongna Zhang, Wenhua Zhang, Yuke Li, Xiaobin Li, Fengchen Li
Elasto-inertial turbulence (EIT) is primarily driven by polymer elasticity, yet the modulating role of fluid inertia is non-negligible and remains largely unexplored. To investigate the effect of inertia, we perform direct numerical simulations of two-dimensional EIT in channel flow over a wide range of Reynolds numbers ($Re$). We show that increasing inertia promotes both the enhancement of dynamic amplitudes and the wallward migration of core structures. Specifically, inertia intensifies the turbulent fluctuations, facilitates the fragmentation of large-scale structures, and amplifies statistical quantities such as the root-mean-square of velocity fluctuations and polymer extension. The peak location of nonlinear elastic shear stress follows a scaling law $y^+ \propto Re_τ^{1/2}$, closely resembling that of Reynolds shear stress in Newtonian turbulence, indicating a change of the momentum transfer mechanism. Meanwhile, the peak location of energy conversion between elastic and turbulent kinetic energies exhibits a $y^+ \propto Re_τ^{0.1}$ scaling law migration, remaining mostly confined to the near-wall region. Remarkably, despite the inertial modulation, the probability density functions (PDFs) of velocity and elastic stress fluctuations extracted at the energy-conversion peak collapse convincingly over the range of $Re$ investigated. This reveals a robust statistical self-similarity across a wide range of inertia magnitude. Furthermore, the PDFs of wall-normal velocity and elastic stress fluctuations exhibit pronounced exponential heavy tails.
Aditya Sai Pranith Ayapilla, Kazuya Miyashita, Yuki Yasuda, Ryo Onishi
Data assimilation (DA) improves prediction of chaotic systems by combining model forecasts with sparse, noisy observations. Many DA methods are inherently probabilistic, but accurate probabilistic DA is often computationally expensive because it requires repeated high-resolution (HR) forecasts and large ensembles. In this study, we develop DiffSRDA, a probabilistic spatiotemporal super-resolution data assimilation framework based on denoising diffusion models, and evaluate it on an idealized barotropic ocean jet instability testbed. DiffSRDA is trained offline to generate short HR analysis windows conditioned on (i) a time series of low-resolution (LR) forecast frames and (ii) sparse HR observations. Repeated reverse diffusion sampling then produces an ensemble of HR analyses, providing both point estimates and uncertainty information. Despite relying only on low-cost LR forecasts, DiffSRDA achieves reconstruction quality close to that of an Ensemble Kalman Filter (EnKF) driven by HR forecasts, while improving over deterministic CNN-based SRDA baselines. The sampled ensemble also yields physically meaningful uncertainty patterns, with spread concentrated in dynamically active regions similarly to EnKF. A key practical result is that accurate base DiffSRDA cycling does not require long reverse chains: most of the full-chain accuracy is retained with only a few reverse steps, making diffusion-based SRDA practical for repeated cycling. Finally, by exploiting the score-based structure of diffusion sampling, we demonstrate training-free observation-consistency guidance for deployment-time sensor-layout shifts, enabling improved use of changed observation configurations without retraining. Overall, diffusion models provide a practical, uncertainty-aware, and computationally efficient approach for spatiotemporal SRDA in chaotic fluid flows.
M. Moriche, M. García-Villalba, M. Uhlmann
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study of cluster dynamics. The current approach removes vertical periodicity and employs a moving reference frame, enabling efficient simulations of both single- and many-particle cases. We illustrate the method with two examples of increasing complexity: a single particle in the steady vertical regime, and a many-particle case at a parametric point where collective effects were previously observed and recovered here. A converged, free-of-corrections time interval of approximately $600 D/U_g$ is simulated in the many-particle case, representing the first simulation of this kind to date. New physical insights can be explored thanks to this new configuration, for example the effect of still fluid on the first layer of particles encountered by the fluid, or the turbulent character of the flow after a swarm of particles has passed by. Finally, the method only requires parameter tuning, allowing implementation within existing solvers without changes to their core formulation: for a standard configuration with an imposed free stream velocity at the inlet, only the input velocity (or the viscosity of the fluid) and the time step need to be updated.
Xiaowei He, Kenneth Breuer
A fin-body configuration is tested in a water tunnel to study the hydrodynamic loads and vortex evolution under dynamic fin-flapping motions, which is an idealized approximation of the pectoral fins of fish. The fin flaps about its leading edge, which is attached to the side of the body, at a range of combinations of amplitudes ($0^\circ-30^\circ$) and frequencies ($0.25\,\mathrm{Hz}-2\,\mathrm{Hz}$ or $k=0.16-1.26$), so the Strouhal number ($St=0.013-0.419$). The quasi-steady hydrodynamic loads exhibit significant hysteresis during the upstroke and downstroke phases of the fin flapping. Particle image velocimetry (PIV) measurements show the details of the shear layer and vortex development in dynamic flapping cases. Orbiting behaviors of the fin tip vortices are observed in larger Strouhal number cases. PIV results also reveal the influence of vortices on hydrodynamic loads in terms of lift fluctuations and thrust generation. The strong dependency on the reduced frequency and Strouhal number leads to scalings of the hydrodynamic loads using a data-driven method to select highly correlated terms. The most significant terms selected by the scaling process are quadratic terms of the Strouhal number and its nonlinear combinations with the reduced frequency.
Suraj Kumar Nayak, Vishwanath Shukla, Akshay Bhatnagar
We study the dynamics of gyrotactic microswimmers suspended in homogeneous and isotropic turbulence by using direct numerical simulations (DNS). The swimmers are characterized by three non-dimensional parameters: their aspect ratio ($γ$), a dimensionless swimming speed ($φ$), and a dimensionless reorientation time ($ψ$). Strong gyrotaxis (smaller $ψ$) promotes vertical alignment of the swimmers, while weak gyrotaxis leads to nearly isotropic orientations. At low swimming numbers, the orientation distribution is largely shape-independent with spheres and spheroids showing marginally greater vertical alignment than rods, whereas at higher activity the peaks of the distributions exhibit largely shape-independent behavior and the tails show a clear dependence on particle shape. However, at large $ψ$ rods exhibit a stronger alignment along the vertical. We observe that at small $ψ$ the rod-shaped swimmers respond to shear by aligning with the stretching direction of the strain-rate tensor, while at large $ψ$ the alignment with the vorticity vector is preferred. The orientation autocorrelation is found to decay exponentially, with a decay rate that scales as $1/(2ψ)$. Analysis of the mean-squared displacement (MSD) reveals a transition from a ballistic motion at short times to a diffusive regime at longer times. To assess the efficiency of vertical migration, we compute the probability distributions of vertical displacement over a fixed time interval and the time taken to migrate a specific vertical distance. Furthermore, we use a simplified two-dimensional model for spherical swimmers that qualitatively reproduces the key trends observed in the full three-dimensional (3D) simulations.
Megan Mazzatenta, Samuel M. Koblensky, Luc Deike
Bubbles entrained by breaking waves rise to the ocean surface where they cluster and burst, emitting sea spray aerosols into the atmosphere. Bubble bursting thereby links seawater biogeochemistry and aerosol chemistry, influencing the ability of emitted aerosols to serve as cloud condensation nuclei or ice nucleating particles. The mechanisms of film drop and jet drop production are modulated by organic material present in seawater, which may affect the size, number, and composition of resulting aerosols. We disentangle the effect of surfactant on collective bursting processes using laboratory experiments with detailed bubble and aerosol measurements down to small sizes, multiple bubble size configurations, and measurements of bubble lifetime. Submicron aerosol emission, linked to film drop production, increased with surfactant up to an optimal concentration, while production of supermicron aerosols emitted through jet drop production was shut down. Our work paves the way to integrate organic composition into sea spray emission functions.
Gelin Chen, Chen Song, Chao Yang
Self-excited limit-cycle oscillations (LCOs) from Hopf bifurcations are a key feature of nonlinear aeroelasticity and depend sensitively on structural and aerodynamic parameters. Classical center-manifold and normal-form theory describe this local behavior, but can be cumbersome to apply in large discretized models and standard reduced-order modeling (ROM) workflows. A renormalization-group (RG)-based reduction is developed that directly yields a Hopf-type amplitude equation on a local invariant manifold, specialized for polynomial nonlinearities in tensor-based discretizations and compatible with finite-element-type settings. The method provides explicit coefficients governing the Hopf threshold, criticality, and leading LCO amplitude/frequency trends, and admits a companion slow-manifold approximation with selected stable modes retained as static coordinates. Representative nonlinear-aeroelastic examples illustrate how the proposed framework supplies compact, parameter-aware Hopf/LCO descriptors suitable for local ROM construction near flutter.
Yuto Yokoyama, Vincenzo Calabrese, Fabian Hillebrand, Henry J. London, Simon J. Haward, Amy Q. Shen
Orientation and relaxation dynamics of rod-like colloids under flow govern the optical and mechanical properties of many emerging soft materials. In polydisperse suspensions, particles of different lengths exhibit distinct rotational diffusion timescales, yet how this polydispersity influences relaxation following flow cessation remains unclear. In particular, it is not well understood how the pre-shear rate determines the subsequent orientation relaxation dynamics. To address this question, we performed simple shear on dilute cellulose nanocrystal (CNC) suspensions in a narrow-gap Taylor-Couette cell and measured birefringence relaxation after flow cessation using high-speed polarization imaging. To interpret the experiments, we formulated a polydisperse Fokker-Planck model parameterized by the measured length distribution. As a result, the average orientation relaxation time systematically decreases with increasing pre-shear rate. Moreover, when organized by the Péclet number based on the rotational diffusion coefficient of the weighted average rod length, the data agree well with the theory over a wide range of shear rates. This trend arises because the rod sub-population contributing most strongly to the orientation shifts from longer rods to shorter rods as the pre-shear rate increases, showing that the flow history governs the orientation relaxation dynamics. In polydisperse systems, the orientation relaxation time is no longer a material-specific constant but is determined by both the flow conditions and the polydispersity. This study provides a quantitative framework for understanding orientation dynamics in polydisperse rod suspensions and for interpreting rheo-optical measurements.
L. Westrich, B. Shergelashvili, H. Fichtner, V. N. Melnik
Apr 22, 2026·astro-ph.SR·PDF Polytropic models of stellar winds remain to be useful tools because they allow for a simple description of the energy balance of the expanding plasma without explicitly specifying potentially complex energy transport processes like, e.g., heat conduction or extended wave heating. Among recent applications to stellar winds and to the solar wind was a study of the consequences of strongly localized heating in the latter, possibly due to acoustic waves. Such 'nonuniform' heating can result from a time- and space-localized damping of wave modes and allows, as an extreme case, an adiabatic expansion of particular wind streams outside the heating region. The present study generalizes the modeling from the first analytical as well as numerical studies, that were limited to this extreme case, towards a more realistic non-adiabatic behaviour. The additional energy due to heating is demonstrated to be in a plausible range in view of typical flare energies and low compared to the gravitational energy of the plasma in this region. The corresponding solutions may be of interest for stellar winds, in general, and w.r.t. recent observations made with the Parker Solar Probe, which revealed strongly varying wind streams and the presence of acoustic waves near the Sun, for the solar wind, in particular. Potential observational evidence for the solar wind is discussed.
An-Xiao Han, Peng-Yu Duan, Ming-Ze Ma, Xi Chen
A particular interest on two-dimensional turbulence is the inverse energy cascade from small to large sales, which leads to an energy condensation accompanied by the formation of large-scale vortical structures. Indeed, such a phenomenon is observed in the two-dimensional channel (2DCH) with large Reynolds numbers, where prominent large-scale wavy structures play a central role in the momentum and energy transfer across the inhomogeneous wall-normal direction \citep{Falkovich2018}. Yet, the instability of these wavy structures remains poorly understood, and it is unknown whether they have the capacity to generate turbulence. To address this, we first conduct the direct numerical simulation (DNS) of Navier-Stokes equations for 2DCH, then extract the large-scale wavy structures through the singular value decomposition, and finally perform a Floquet-based secondary instability analysis. Two bulk Reynolds numbers are examined in particular, i.e. $Re = 3000$ and $Re = 200000$, which lie on opposite sides of the transitional regime near $Re \approx 10000$ and cover the previously reported simulation domain. At $Re = 3000$, the large-scale wavy structure is found to be linearly stable, consistent with the laminar-like DNS flow field. However, at $Re = 200000$, a subharmonic torsional mode is identified, which leads to a definite growth rate ($λ_r = 0.18$) for the wavy structures with a half wave-length shift. Temporal reconstruction shows that this unstable mode deforms and splits into multiple wave trains and evolves in the opposite phase. Compared to the TS (Tollmien-Schlichting) wave of laminar flow, the subharmonic mode found here offers a novel understanding for the generation of turbulence in larger Reynolds number two-dimensional channels.
Christian Tantardini, Fernando Alonso-Marroquin
Global-pressure formulations recast multiphase Darcy flow in terms of a single pressure driving the total flux. Their exact equivalence to phase-pressure formulations, however, holds only when the constitutive data satisfy the compatibility conditions required for a total-differential structure and its generalized nonisothermal extension. In this work, we derive the corresponding exactness criterion for temperature-dependent mobilities and capillary pressures. We show that equivalence is governed by the closure of a mobility-weighted capillary one-form on the augmented state space of saturation and temperature. This yields both the classical compatibility conditions within the saturation sector and a distinct mixed saturation--temperature condition that arises only in the nonisothermal setting. We then incorporate this structure into a reduced matrix--fracture model with heat transport, matrix--fracture thermal exchange, and evolving fracture aperture. Numerical benchmarks recover the three regimes predicted by the theory: globally exact, exact on each fixed-temperature slice but not on the full saturation--temperature space, and fully nonexact. In fractured systems, thermal forcing alone can drive transitions between these regimes, while aperture evolution changes the path through state space. When exactness fails, a least-squares projection performed independently on each fixed-temperature slice provides a conservative scalar-pressure surrogate together with quantitative defect diagnostics. The resulting framework unifies nonisothermal exactness theory, fractured-flow dynamics, and conservative reduced closure within a single global-pressure formulation.
Pramodt Srinivasula, Doyel Pandey
Gate-modulated nanopores have emerged as a promising platform for achieving ion selectivity and ionic current rectification (ICR) with the advantage of active field-based control. However, the mechanistic origin of these experimentally reported phenomena, arising from electrostatic coupling between the prescribed radial pore surface potential and the axial transmembrane electric field, remains insufficiently understood. Here, using coupled Poisson--Nernst--Planck and Navier--Stokes simulations supported by asymptotic analysis, we show that a uniform surface potential inherently interacts with the axial driving field to generate a three-dimensional, axially nonuniform electric double layer (EDL). This field-induced EDL heterogeneity effectively mimics a linear axial variation in zeta potential, breaking translational symmetry within an otherwise uniform pore. As a result, the system exhibits coupled electrokinetic responses, including ion selectivity, ionic current rectification, and non-canonical electroosmotic flow, all governed by a single asymmetry parameter $α$ derived from the EDL structure. Critical transitions occur at specific values of $α$; in particular, at $α=0$, the EDL becomes axially antisymmetric, leading to reversal of ion selectivity, significant ICR and the emergence of a peculiar negative electroosmotic flow rectification accompanied by internal vortical structures. These findings establish the electrostatic mechanism for axial symmetry breaking as the underlying principle for transport in voltage-gated nanopores, enabling a unified framework for designing tunable electrokinetic functionalities beyond geometry- and chemistry-based strategies.
Ramdhan Wibawa, Birendra Jha
We report the first systematic evidence of hallucination in AI models of fluid dynamics, demonstrated in the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities remains challenging because rapidly evolving, multiscale fingering patterns are difficult to resolve accurately. We identify solutions that appear visually realistic yet are physically implausible, analogous to hallucinations in large language models. These hallucinations manifest as spurious fluid interfaces and reverse diffusion that violate conservation laws. We show that their origin lies in the spectral bias of AI models, which becomes dominant at high flow rates and viscosity contrasts. Guided by this insight, we introduce DeepFingers, a new framework for AI-driven fluid dynamics that enforces balanced learning across the full spectrum of spatial modes by combining the Fourier Neural Operator with a Deep Operator Network to predict the spatiotemporal evolution of viscous fingers. By conditioning on both time and viscosity contrast, DeepFingers learns mappings between successive concentration fields across regimes. The framework accurately captures tip splitting, finger merging, and channel formation while preserving global metrics of mixing. The results open a new research direction to investigate fundamental limitations in AI models of physical systems.
Amareshwara Sainadh Chamarthi
Compressible multiphase and multicomponent solvers require accurate interface representation without spurious pressure oscillations. At material interfaces, pressure and velocity are continuous while density and the equation of state exhibit abrupt discontinuities. Standard approaches reconstruct primitive or characteristic variables to capture these properties, but do not clarify the failure mechanisms of conservative reconstruction or fully leverage the wave-decoupling advantages of characteristic decomposition. This work derives the complete eigenstructure of the Allaire five-equation model for two variable sets. In the fully conservative~(FC) formulation, $\mathbf{U} = [α_1ρ_1,\,α_2ρ_2,\,ρu,\,ρv,\,ρE,\,α_1]^T$, eigenvectors contain a thermodynamic jump term~$Ψ$ that enforces $dp=0$ and $du=0$ at material contacts by compensating for compressibility mismatches. In the semi-conservative~(SC) formulation, $\mathbf{V} = [α_1ρ_1,\,α_2ρ_2,\,ρu,\,ρv,\,p,\,α_1]^T$, the volume-fraction eigenvector carries a structural zero in the pressure slot, enforcing equilibrium without thermodynamic correction. Explicit left and right eigenvectors are derived for one- and two-dimensional stiffened-gas flows. Both formulations satisfy Abgrall's equilibrium condition when reconstruction is performed in characteristic space; reconstruction in physical space yields $\mathcal{O}(1)$ pressure and velocity errors at interfaces regardless of the variable set. The eigenvector structure further reveals that the shear wave is decoupled from all thermodynamic and interface fields in both formulations, extending this result from single-species to compressible multiphase flows including gas-liquid configurations. One- and two-dimensional gas-gas and gas-liquid test cases confirm oscillation-free, accurate results.
Alexandre D. Leonelli, Lukas Widmer, Eckart Meiburg
Due to attractive inter-particle forces, cohesive particles suspended in turbulence undergo a complex process of aggregation, breakup, and restructuring. Despite a growing body of knowledge on the ``flocculation'' of cohesive granular materials suspended in homogeneous isotropic turbulence, little focus has so far been placed on wall-bounded flows where turbulence and shear are inhomogeneous. This study presents a first investigation of a fully developed wall-bounded flow of resolved cohesive particles. Five direct numerical simulations of turbulent channel flows laden with finite-sized particles at successively increasing cohesive strength are performed. A population balance equation (PBE) framework is used to analyze aggregate dynamics. When integrated over the full domain, the PBE is closed by aggregation and breakup alone. However, this balance is found to not hold locally in the wall-normal direction, where regions of net aggregate production and depletion are identified. This imbalance is shown to be compensated by the size-dependent wall-normal transport of aggregates, revealing a mean circulation: larger aggregates are preferentially produced in the channel center and migrate toward the wall where they break, while smaller aggregates are transported away from the wall, grow, and reenter the cycle.