The team’s motivation stems from a long-standing debate about whether the scale-dependent power observed in photospheric velocity maps reflects the intrinsic dynamics of solar convection or merely artifacts introduced at the boundaries between bright granules and dark intergranular lanes. Because intergranular lanes form a network of sharp, high-contrast features across the solar surface, any abrupt discontinuity in velocity values at their edges could, in principle, contaminate the Fourier transform and produce spurious oscillatory signatures known as ringing. If such contamination were significant, decades of turbulence studies based on photospheric power spectra would need to be reinterpreted, with profound consequences for our understanding of solar convection and the energy cascade that shapes it.

To resolve the issue, the researchers designed a series of controlled numerical experiments using three-dimensional magnetohydrodynamic simulations of the quiet Sun, which reproduce the realistic interplay between plasma flows and magnetic fields in the photosphere. Their strategy was deliberately provocative: they replaced the natural intergranular lanes with artificially sharp edges, imposing velocity discontinuities of -0.2, -2, and -5 kilometers per second at those boundaries. In a second round of experiments, they introduced noise of varying bin sizes into the intergranular lanes to generate different types of edges. Finally, they degraded the spatial resolution of their data by re-binning it onto grids up to sixteen times coarser than the original, mimicking the limitations of real observational instruments.

The results were striking in their clarity. When the artificially sharpened edges were introduced, the overall shape and consistency of the power spectra remained essentially unchanged compared with the original, unperturbed data. The distortions that did appear were confined to undersampled datasets, where too few independent realizations were available to average out the artifacts, and even these effects diminished drastically when statistically significant samples were considered. In other words, the edge-related contamination that had worried solar physicists behaves not as a systematic bias but as an unsynchronized perturbation that cancels itself out when enough data are combined.

To understand why this cancellation occurs, the authors turned to complementary Monte Carlo simulations with synthetic data, a mathematical exercise described in detail in the paper’s appendix. They constructed arrays of modified two-dimensional Gaussian functions, each multiplied by an inverse-distance term so that the resulting power spectrum resembled that of turbulence. When a single such profile was truncated and shifted, its spectrum displayed the characteristic ringing of an edge effect, with oscillatory features rippling across the scales. But when the spectra of ten to fifty snapshots were summed, the ringing vanished, leaving a smooth spectrum indistinguishable from that of unperturbed data. The artifacts from individual snapshots, being random in phase and position, destructively interfere when aggregated.

This finding has immediate practical implications for how solar observations are analyzed. Modern instruments such as the Hinode spacecraft, the Sunrise balloon-borne observatory, and the Daniel K. Inouye Solar Telescope routinely deliver high-resolution velocity maps of the photosphere, and researchers routinely average power spectra over many snapshots to improve statistical significance. The new study confirms that this standard practice is not merely a convenience but a robust safeguard: as long as the sample of snapshots is sufficiently large, edge effects, Gibbs phenomena, and noise-like ringing are effectively suppressed. Only in limited cases involving small or poorly sampled datasets do researchers need to exercise caution, and the study provides a quantitative framework for recognizing when such caution is warranted.

Beyond validating the reliability of the method, the research delivered an unexpected bonus for turbulence studies. When the team analyzed the positive component of the vertical velocity, corresponding to the upflowing plasma within granules, separately from the full velocity field, they found that it exhibited a more extended power-law range than the complete signal. In turbulence theory, the power-law range, often called the inertial range, is the regime where energy cascades from large eddies down to smaller ones in a self-similar fashion, and identifying its boundaries is central to characterizing the physics of the flow. The extended power-law range in the upflow data therefore suggests that researchers can gain improved access to the inertial-range dynamics of solar convection by isolating the positive vertical velocity component.

The significance of this work extends to some of the most fundamental questions in solar physics. The photospheric velocity field is the visible manifestation of convection, the engine that transports heat from the solar interior and, through its interaction with magnetic fields, drives phenomena ranging from the small-scale dynamo to the heating of the upper atmosphere. Power spectra of photospheric flows have been used to probe the turbulent energy cascade, to test numerical simulations against observations, and to inform the design of next-generation solar telescopes such as the European Solar Telescope. By demonstrating that these spectra predominantly reflect genuine physical processes rather than edge artifacts, the Algerian team has strengthened the evidentiary foundation on which much of this research rests.

The study also illustrates a broader methodological lesson that resonates across the physical sciences: the importance of stress-testing standard analytical tools rather than assuming their validity. Fourier analysis is among the most widely used techniques in all of physics, yet its susceptibility to edge effects is a well-known theoretical concern that is rarely tested with the rigor applied here. By combining realistic magnetohydrodynamic simulations with deliberately perturbed data and Monte Carlo experiments on synthetic fields, the authors created a controlled environment in which the contribution of edges could be isolated and quantified. The approach could serve as a template for similar validation efforts in other domains where sharp features in data complicate spectral analysis, from astrophysical imaging to fluid dynamics experiments.

For now, the solar physics community can breathe easier. The Fourier power spectra that have illuminated the turbulent photosphere for half a century, from early analyses of the photospheric convection spectrum to modern comparisons between telescope observations and cutting-edge simulations, remain a trustworthy window onto the Sun’s surface dynamics. The artifacts that lurk at the edges of granules and at the boundaries of data fields are real, but they are also transient and self-canceling, fading away as the statistics build up. In the quiet granulation of the solar photosphere, it turns out, the signal is stronger than the noise at its edges, and the physics of convection shines through.

Subject of Research: Reliability of Fourier power spectra for analyzing the solar photospheric velocity field

Article Title: Are Fourier Power Spectra a Reliable Tool to Explore the Solar Photospheric Velocity Field?

Article References: Are Fourier Power Spectra a Reliable Tool to Explore the Solar Photospheric Velocity Field?. (n.d.). https://doi.org/10.1007/s11207-026-02717-y

Image Credits: AI Generated

DOI: 10.1007/s11207-026-02717-y

Keywords: solar physics, photosphere, Fourier power spectra, solar convection, granulation, turbulence, magnetohydrodynamic simulations, edge effects, Monte Carlo simulation, inertial range, quiet Sun, velocity field

The problem begins with the sheer range of scales involved. In the final orbit before two neutron stars merge, the stellar cores slam into one another at a substantial fraction of the speed of light, generating a shear layer roughly a kilometer wide that becomes Kelvin-Helmholtz unstable. This instability, the same mechanism that shapes wind-blown clouds on Earth, shreds the interface between the stars into vortices that fragment into ever smaller eddies, producing a turbulent cascade that spans from kilometer scales down to about a nanometer, where viscosity finally converts kinetic energy into heat. The Reynolds number of this flow, a measure of the ratio of inertial to viscous forces, is a staggering ten to the power of sixteen. Simulating every eddy directly, the approach known as direct numerical simulation, would require computational resources that scale as the Reynolds number cubed, making it utterly impossible for the foreseeable future.

Turbulence is not confined to the moment of contact. Once the stars have merged, the remnant, whether a massive neutron star or a newly formed black hole, is typically encircled by a hot, dense accretion disk. There, the magnetorotational instability stirs the plasma, redistributing angular momentum and governing how matter spirals inward or is flung outward. The way turbulence transports angular momentum determines whether the remnant neutron star collapses promptly to a black hole or survives as a long-lived object, and it controls the mass ejection that powers the kilonova flashes and the nucleosynthesis of r-process elements. It may also amplify magnetic fields to magnetar levels, potentially launching the relativistic jets that produce short gamma-ray bursts. In short, nearly every observable signature of a neutron star merger is touched by turbulence somewhere along the way.

The mathematical machinery for handling unresolved turbulence has a long history in Newtonian fluid dynamics. The classic approach, Reynolds averaging, splits the flow into a mean component and fluctuations, yielding equations for the mean motion that contain an extra term, the Reynolds stress, which encapsulates the momentum carried by the unresolved eddies. A more practical alternative for simulations is large-eddy simulation, or LES, in which the equations are filtered over a length scale comparable to the numerical grid. The filtered equations resemble the original ones but include subgrid-scale stresses that must be modeled. The central difficulty, known as the closure problem, is that these stresses depend on information about the small scales that the simulation does not compute, so modelers must supply approximate relations, or closures, that capture the net effect of the missing physics using only the resolved quantities.

Extending this framework to general relativity introduces subtleties that have no Newtonian counterpart. Radice and Hawke review how averaging or filtering the equations of relativistic hydrodynamics produces effective stresses even when the underlying fluid is ideal, and how the nonlinear structure of the fluxes demands additional closure relations, including one for turbulent mass diffusion. More troubling still is the question of covariance: the averaging operations used in practice are tied to a particular slicing of spacetime, which breaks the four-dimensional symmetry of Einstein’s theory. Recent work has explored building the averaging procedure around a physical observer rather than a coordinate slice, showing that the coarse-grained equations then take the form of a non-ideal relativistic fluid, complete with bulk viscosity, shear stresses, and heat transport terms that arise purely from the turbulence. Even the equation of state, the relation linking pressure, density, and energy, is modified by averaging, since fluctuations in density generate corrections that behave like an additional pressure.

In practice, most published neutron star merger simulations to date have used the simplest possible strategy: implicit large-eddy simulation, which sets the subgrid stresses to zero and relies on the intrinsic numerical dissipation of shock-capturing schemes to mimic the effect of unresolved turbulence. This approach has been remarkably successful in other fields, but the review is blunt about its limitations in this context. The modified equation analysis shows that numerical dissipation can indeed act like an effective viscosity, but implicit methods require a significant fraction of the inertial range to be resolved before results converge, and no neutron star merger simulation has yet been demonstrated to be in that regime. The alternative is explicit modeling. Radice’s own general-relativistic large-eddy simulations employ a relativistic version of the Smagorinsky closure, in which the turbulent viscosity is estimated from a mixing length set by the local scale of the flow and the speed of sound. A third family of methods, gradient or approximate-deconvolution models, reconstructs the effect of the filter algebraically and has the advantage of introducing no tunable parameters beyond the filter width itself.

The payoff of these techniques is already visible in the study of magnetic field amplification. Early Newtonian simulations suggested that the Kelvin-Helmholtz instability could amplify even weak seed fields to magnetar strengths of around ten to the fifteenth gauss, but general-relativistic calculations initially failed to reproduce this, simply because their grids were too coarse. Later, extraordinarily high-resolution simulations by Kenta Kiuchi and collaborators showed that the saturated field strength kept climbing with resolution, with no sign of convergence, precisely because the magnetic back-reaction only halts the cascade at centimeter scales, far below anything a global simulation can resolve. When subgrid models were introduced, the picture changed dramatically. Gradient-model simulations by Ricard Aguilera-Miret, Carlos Palenzuela, and colleagues achieved converged results, confirming that weak fields are indeed amplified to ten to the sixteenth gauss and that the statistical properties of the resulting turbulence are remarkably insensitive to the unknown initial magnetic configuration inside the stars, a reassuring result for predictive modeling.

The same simulations revealed tantalizing evidence of an inverse cascade, in which the characteristic scale of the magnetic field grows from roughly half a kilometer immediately after merger to several kilometers a hundred milliseconds later, as turbulent resistivity rearranges field lines into larger structures. Meanwhile, measurements of the effective viscosity generated by magnetic stresses suggest it remains modest in the dense core of the remnant, implying that turbulence is unlikely to distort the post-merger gravitational-wave signal enough to compromise plans to probe the equation of state of nuclear matter with next-generation detectors such as the Einstein Telescope and Cosmic Explorer. On the other hand, turbulence and dynamo action are expected to leave a significant imprint on the long-term evolution of the remnant, its mass ejection, and its multi-messenger emission, from kilonova light curves to the engines of short gamma-ray bursts.

Much remains to be done. The review highlights open questions about whether angular momentum transport accelerates or delays the collapse of the remnant neutron star, about the topology of the amplified magnetic fields and whether tangled configurations better explain the energetics of gamma-ray bursts, and about the formidable challenge of uncertainty quantification in a parameter space already crowded with uncertain inputs. Validation is particularly thorny: unlike wind tunnels, neutron stars offer no laboratory tests, so models must be calibrated against resolved simulations whose own fidelity is uncertain, and tuned to observables, such as gravitational waves and neutrino signals, that differ from the statistical quantities conventionally used in closure validation. The authors anticipate rapid progress on three fronts: simulations that combine sophisticated microphysics, magnetohydrodynamics, and large-eddy closures; improved phenomenological subgrid models tested in local calculations; and data-driven, machine-learned closures that learn the missing physics directly from high-resolution data. As gravitational-wave astronomy enters its next generation, taming turbulence may prove the key to turning collisions of dead stars into precision measurements of matter at its densest.

Subject of Research: Turbulence modelling in general-relativistic simulations of binary neutron star mergers

Article Title: Turbulence modelling in neutron star merger simulations

Article References: Radice, D., & Hawke, I. (2024). Turbulence modelling in neutron star merger simulations. Living Reviews in Computational Astrophysics, 10(1), Article 1. https://doi.org/10.1007/s41115-023-00019-9

Image Credits: AI Generated

DOI: 10.1007/s41115-023-00019-9

Keywords: neutron star mergers, turbulence, large-eddy simulation, gravitational waves, magnetohydrodynamics, Kelvin-Helmholtz instability, magnetic field amplification, subgrid models, numerical relativity, accretion disks, r-process nucleosynthesis, equation of state

Fine-scale turbulence occupies a middle ground in ocean physics. It sits between the vast, slow-moving gyres that dominate ocean circulation and the microscopic mixing that dissipates energy into heat. At scales of roughly one to ten kilometres, this turbulence takes the form of eddies, filaments and fronts that stir water masses horizontally and vertically. Although individually small, these structures collectively perform much of the ocean’s stirring, controlling how tracers such as heat, salt, carbon and plankton are redistributed beneath the surface. Measuring them directly from ships is extraordinarily difficult, because the features evolve over hours to days and shift position rapidly, making the Mediterranean’s interior a patchwork that in situ campaigns can only sample piecemeal.

The team behind the new work turned to an increasingly powerful alternative: satellite altimetry. Modern altimetry missions measure the height of the sea surface with centimetre-level precision, and because surface currents leave their imprint on the shape of that surface, the data can be transformed into maps of surface geostrophic flow. By applying a fine-scale processing approach that resolves structures far smaller than the traditional eddy fields captured by standard altimetric products, the researchers were able to extract a proxy for surface turbulence intensity across the entire Mediterranean basin, month by month, over a multi-year record.

The central finding is striking: fine-scale turbulence in the Mediterranean is strongly seasonal, and the pattern of that seasonality differs from region to region. In the northwestern Mediterranean, turbulence activity intensifies markedly in winter, when vigorous atmospheric cooling and strong winds such as the mistral and tramontane destabilise the upper ocean and energise mesoscale and submesoscale eddies. In summer, by contrast, a thin, warm, stratified layer caps the sea and suppresses vertical motion, and the turbulent activity quietens. The Gulf of Lion, a known site of deep water formation, emerges as a winter hotspot where fine-scale stirring is at its most intense.

In the eastern basin, the seasonal signal is more nuanced but equally revealing. Areas influenced by the major currents of the region, including the Atlantic Water jet entering through the Strait of Gibraltar and the flow along the North African coast, show turbulence maxima tied to the seasonal behaviour of these currents rather than to local wind forcing alone. When the currents intensify or become unstable, they shed eddies and meanders that show up unmistakably in the satellite-derived turbulence maps. The Strait of Sicily, the shallow sill that separates the western and eastern basins, also stands out as a persistent zone of elevated fine-scale activity, reflecting the energetic exchange of water masses funnelling through this narrow gateway.

The technical foundation of the study lies in how the researchers quantified turbulence from the surface velocity fields. They computed surface kinetic energy and, crucially, the fine-scale component of that kinetic energy: the portion associated with motions at the smaller end of the resolvable scale range, after removing the large, slowly varying background circulation. By examining the ratio of fine-scale to total kinetic energy, they obtained a robust indicator of turbulence intensity that is less sensitive to errors in the absolute current speed. They then averaged this indicator over many years for each month of the annual cycle, producing basin-wide climatologies that expose the seasonal heartbeat of Mediterranean turbulence with a clarity never previously achieved.

Validation against independent data sources was a key part of the analysis. The satellite-derived turbulence patterns align well with what is known from drifter measurements, which trace currents directly as floating instruments ride the flow, and with numerical model simulations of the Mediterranean circulation. The agreement between the space-based proxy and these ground-truth sources gives confidence that the seasonal signals are real features of the ocean rather than artefacts of the satellite processing. It also demonstrates, more broadly, that current-generation altimetry can be pushed to resolve fine-scale dynamics in semi-enclosed seas, where conventional coarse-resolution products have historically fallen short.

Why does this seasonal turbulence cycle matter? The answer lies in the role of fine-scale stirring as the ocean’s mixing engine. In winter, intense turbulence in the northwestern Mediterranean helps to homogenise the water column and ventilate the deep layers, a process central to the Mediterranean’s thermohaline circulation, often described as a miniature version of the global conveyor belt. Enhanced winter stirring also replenishes surface nutrients after the depleted summer months, setting the stage for the spring phytoplankton bloom that anchors the basin’s marine food web. In summer, weakened turbulence and strong stratification trap heat and carbon near the surface, influencing air-sea gas exchange and the fate of waters that will eventually spill over the Sicily sill into the eastern basin.

The findings also carry implications for climate science. The Mediterranean is warming faster than the global ocean average, and models of its future evolution depend on accurately representing the mixing processes that distribute heat vertically. If fine-scale turbulence follows predictable seasonal rhythms, then climate models must capture those rhythms to reproduce the sea’s heat uptake correctly, particularly during the critical winter period of deep water formation. Moreover, as surface warming strengthens stratification, the seasonal suppression of turbulence may intensify, potentially reducing winter ventilation and altering the nutrient supply that sustains Mediterranean ecosystems. The satellite record, extending back years and continuing into the future, offers a way to monitor whether such changes are already underway.

Beyond the Mediterranean, the study opens a template for observing fine-scale ocean dynamics in other semi-enclosed and marginal seas, from the Black Sea to the Gulf of Mexico, where ship-based sampling is logistically demanding and conventional altimetry struggles. As new high-resolution altimetry missions come online and processing techniques continue to improve, oceanographers expect to resolve turbulence at ever finer scales from orbit, closing one of the most stubborn observational gaps in physical oceanography. For now, the Mediterranean has become the proving ground, and it has delivered a vivid message: even the smallest, most turbulent motions of the sea obey the great clock of the seasons, and from hundreds of kilometres above, we can finally watch them turn.

Subject of Research: Seasonal variability of fine-scale turbulence in the Mediterranean Sea observed from satellites.

Article Title: Seasonality of fine-scale turbulence in the Mediterranean Sea observed from space

Article References: Barabinot, Y., Lopez, G., Mourre, B., & Pascual, A. (2026). Seasonality of fine-scale turbulence in the Mediterranean Sea observed from space. Communications Earth & Environment. https://doi.org/10.1038/s43247-026-04046-1

Image Credits: AI Generated

DOI: 10.1038/s43247-026-04046-1

Keywords: fine-scale turbulence, Mediterranean Sea, satellite altimetry, mesoscale eddies, ocean mixing, seasonality, deep water formation, thermohaline circulation, submesoscale dynamics, Gulf of Lion, fine-scale, turbulence

The study was led by César Santos of the University of Beira Interior in Portugal, together with Marco La Capra of the University of Bayreuth, Sven Frei of Wageningen University and Research, Benjamin Gilfedder of the University of Trier, and Cristina Fael of the University of Beira Interior. Bubble barriers work by pumping compressed air through a perforated hose or diffuser laid across a waterway, generating a continuous curtain of bubbles that rises to the surface. The upward flow of air drags water with it, creating a vertical circulation cell that, in principle, deflects floating debris toward a collection point at the bank. The technology has already attracted attention in pilot projects in Europe for intercepting macroplastics, but whether it could meaningfully stem the flow of particles smaller than five millimeters remained an open question.

To answer it, the team built a laboratory flume experiment designed to reproduce realistic open-channel hydraulics. Flow conditions were turbulent and subcritical, with a Reynolds number of approximately 4.7 × 10³ and a Froude number of about 0.03, meaning the water was slow and deep enough that gravitational effects on the free surface were modest. They ran the bubble barrier at three air pressures, 500, 750, and 1000 mbar, and tracked two things simultaneously: how the water itself moved, and how different classes of microplastic particles traveled through the system. The hydrodynamic analysis combined velocity field measurements, including particle image velocimetry, with particle tracking techniques, giving the researchers a full picture of the turbulent structure the bubbles imposed on the water column.

A key innovation of the experimental design was the use of fluorescein, a fluorescent dye that acts as a conservative tracer, meaning it moves with the water without decaying or reacting. By injecting the tracer upstream and measuring breakthrough curves downstream, the team could quantify exactly how the bubble barrier changed the timing and distribution of water transport. The results were unambiguous: the barrier created both preferential flow paths, where water was channeled more quickly through certain regions, and recirculation zones, where water was trapped and recirculated in slow-moving eddies. Together, these effects extended the residence time of fluorescein in the flume by up to 24 percent, a clear demonstration that the bubble curtain fundamentally rewires local mass and momentum transfer rather than merely aerating the water.

Velocity contour analysis confirmed and visualized these mechanisms. The bubble stream drove strong upward convection, pulling water from the depths toward the surface and generating localized turbulence that redistributed velocities around the barrier. This vertical flow component turned out to be the crucial variable for particle capture. Naturally buoyant microplastics, represented by low-density polyethylene and high-density polyethylene, were swept upward along the rising current and accumulated at the water surface near the bubble curtain. Downstream recovery of these buoyant particles dropped to less than 20 percent, meaning that more than four-fifths of them were effectively retained by the barrier. For a passive technology that consumes only compressed air, that level of capture for floating microplastics is a significant result.

The picture changed dramatically for polystyrene, which is denser than water and therefore non-buoyant. The smallest polystyrene particles tested, ranging from 75 to 125 micrometers, behaved almost exactly like the fluorescein tracer. Because of their tiny size and low inertia, these particles were so strongly coupled to the surrounding flow that the turbulent structures generated by the barrier had essentially no trapping effect; downstream recoveries reached 80 percent, indicating that the vast majority sailed straight through the bubble curtain. Mid-sized particles between 200 and 400 micrometers showed moderate interaction with the barrier-induced turbulence, occupying an intermediate zone between flow-following and inertial behavior, while the largest polystyrene particles, at 600 to 1000 micrometers, were governed mainly by gravitational settling. For that largest fraction, the low downstream recovery was attributed primarily to early deposition on the flume bed rather than to retention by the barrier itself.

One of the most intriguing findings concerns the role of air pressure. Velocity contours measured at the higher experimental pressures revealed that strong upward convection near the bubble stream can remobilize smaller, non-buoyant microplastics that had already settled into the sediments. In other words, the same force that lifts buoyant plastics to the surface can also pluck tiny sunken particles back into the water column, where they might be exposed to further transport. This observation cuts both ways. On one hand, it suggests that carefully tuned bubble systems could help resuspend trapped microplastics and give a second chance at capturing them. On the other hand, it raises the possibility that a poorly designed barrier could re-entrain sediment-stored contamination rather than locking it away, a risk that future field deployments will need to quantify.

The broader significance of the study lies in its mechanistic approach. Rather than reporting a simple capture efficiency, the researchers mapped how the bubble barrier modulates the flow field and connected those hydrodynamic changes directly to particle fate. This pressure-dependent control of the local flow field is what gives bubble barriers their versatility, and also what limits them. The upward convective currents are exquisitely suited to intercepting materials with a tendency to rise, which is why the technology performs so well for buoyant polyethylene particles and for macroplastics floating at the surface. Dense, small particles, however, follow the streamlines of the flow almost perfectly, and no amount of gentle turbulence will separate them out unless the flow itself is interrupted by settling zones, filtration, or secondary treatment steps downstream.

The authors emphasize that the results should guide the next generation of barrier designs. To expand the technology’s reach beyond buoyant plastics, future systems will need to optimize turbulent interactions, particularly the vertical flow components, so that non-buoyant particles experience enough drag and lift to be diverted rather than bypassed. That could mean adjusting bubble density, diffuser geometry, air pressure, or even combining bubble curtains with sediment traps or collection booms that exploit the recirculation zones the barrier naturally creates. The study also highlights the value of tracer-based diagnostics: because the fluorescein breakthrough curves predicted the behavior of the smallest particles so accurately, dye tracing could become a cheap field technique for estimating whether a given barrier is likely to retain fine microplastics at a real site.

As concern grows over microplastic pollution in rivers, lakes, and coastal waters, and as bubble barriers move from novelty to infrastructure, this work provides a rigorous scientific foundation for deciding where the technology belongs in the treatment chain. It confirms that bubble curtains are genuine hydrodynamic tools, capable of reshaping how water and particles move through a channel, and that they can deliver impressive retention of large buoyant microplastics before runoff reaches marine environments or effluent exits wastewater treatment plants. At the same time, it delivers an honest accounting of their blind spot: the smallest, densest fragments of plastic pollution, which are also among the most abundant and hardest to remove, remain largely beyond their grasp. Closing that gap, the researchers conclude, will require refined designs that intentionally sculpt the turbulence itself, turning the invisible architecture of the flow into an active filter.

Subject of Research: Laboratory evaluation of air bubble barrier hydrodynamics and their capacity to retain microplastic particles of varying size and buoyancy in flowing water.

Article Title: Can bubble barriers retain microplastics? An evaluation using laboratory and hydrodynamic analysis of transport and retention

Article References: Santos, C., La Capra, M., Frei, S., Gilfedder, B., & Fael, C. (2026). Can bubble barriers retain microplastics? An evaluation using laboratory and hydrodynamic analysis of transport and retention. Microplastics and Nanoplastics. https://doi.org/10.1186/s43591-026-00230-4

Image Credits: AI Generated

DOI: 10.1186/s43591-026-00230-4

Keywords: bubble barrier, microplastics, polyethylene, polystyrene, particle tracking, flow hydrodynamics, fluorescein tracer, turbulence, microplastic retention, air pressure, wastewater treatment, river pollution

The review, led by Hubert Klahr, Hans Baehr, Julio David Melon Fuksman, and Thomas Pfeil of the Max Planck Institute for Solar System Research, arrives at a moment when observational facilities such as the Atacama Large Millimeter/submillimeter Array are delivering breathtaking images of planet-forming disks. Rings, gaps, spiral arms, and hints of long-lived vortices appear routinely in the data, but interpreting these structures requires models that faithfully capture the underlying physics. The authors argue that the first step is deceptively simple: before adding magnetic fields, self-gravity, or dust feedback, a simulation must correctly reproduce the pure hydrodynamic behavior of an irradiated disk, and that behavior is far from trivial.

Disks around young stars are born as byproducts of star formation, a buffer for the excess angular momentum of a collapsing molecular cloud core. During the first tens of thousands of years, the star acquires most of its mass through the disk, a phase in which the disk’s own self-gravity supplies the main torque driving accretion. But after this main accretion phase, enough material remains to build planetary systems over the following ten million years, until winds and photoevaporation strip the gas away. Crucially, for planet formation, an overly vigorous accretion flow toward the star can wash away nascent planets, so understanding when and how disks settle into a calmer state matters enormously.

One of the review’s central themes is baroclinicity, the misalignment between surfaces of constant pressure and constant density in a disk. Because stellar irradiation heats the disk surface while viscous dissipation may warm the midplane, disks develop both radial and vertical temperature gradients. In such a configuration, pressure and density contours are inclined with respect to one another, a situation familiar from Earth’s atmosphere and oceans that also drives instabilities in disks. These effects were long missed in simulations because they are too weak to emerge at low resolution or with overly dissipative numerical schemes. Only recently, with increased computing power, have researchers been able to confirm the analytic predictions of thermal baroclinic instability theory with full numerical experiments.

The review catalogues the family of instabilities that radiation hydrodynamic simulations must capture. The vertical shear instability, or VSI, arises from the vertical gradient of rotation in a baroclinic disk and operates best when thermal relaxation is extremely fast, since rapid cooling prevents the stable vertical stratification from suppressing the unstable shear. The convective overstability, in contrast, is strongest when the thermal relaxation time is comparable to the orbital period; it grows from epicyclic oscillations of gas parcels displaced radially in a weakly convective environment. The Goldreich-Schubert-Fricke instability, a close cousin of the VSI inherited from the theory of rotating stars, operates alongside the convective overstability, and recent work has shown that any disk unstable to one is unstable to the other, because both depend equally on the disk’s baroclinicity. A third mechanism, the subcritical baroclinic instability, generates long-lived anticyclonic vortices from radial entropy gradients combined with thermal relaxation, though it lacks a linear growth-rate prediction and is therefore harder to use as a code benchmark.

To help researchers validate their codes, the authors lay out a systematic testing procedure. The method begins by constructing an equilibrium disk model, typically through a so-called 1+1-dimensional calculation that solves for vertical hydrostatic balance at each radius while enforcing energy conservation with flux-limited diffusion and physically motivated dust opacities. This equilibrium serves both as an initial condition for multidimensional simulations and as the basis for perturbation theory: analytic linear analysis yields predicted growth rates for unstable modes. A code that reproduces those growth rates in the linear regime can then be trusted to explore the nonlinear turbulence that follows. If a code fails to match the predicted growth, the review notes, this signals insufficient resolution or a numerically dissipative scheme rather than a failure of the underlying theory.

The practical details of such tests are demanding. In local axisymmetric simulations carved from a global disk model, the authors demonstrate that resolving roughly 256 cells per pressure scale height is required to reproduce growth rates down to ten thousandths of the orbital frequency. Numerical schemes matter as well: high-order reconstruction methods combined with accurate Riemann solvers recover the predicted linear growth, whereas more diffusive approximate solvers can suppress instability entirely. Even the handling of cooling, implemented through thermal relaxation of the pressure toward an equilibrium value, must be treated carefully, with operator splitting modified so that relaxation times shorter than the dynamical step remain stable. These benchmarks, the authors argue, should become standard practice for any group embarking on radiation hydrodynamic disk simulations.

Beyond linear tests, the review surveys how different radiative transfer approximations shape the outcomes of full three-dimensional simulations. Flux-limited diffusion, the workhorse of earlier decades, is computationally efficient and accurate in optically thick regions but smears out shadows and introduces unphysical diffusion where radiation streams freely. The M1 two-moment method, implemented in codes such as PLUTO, preserves the direction of radiative fluxes and captures shadowing, but it artificially merges crossing beams of light, which can overestimate midplane temperatures by more than 40 percent in single-group calculations. A newer half-moment scheme reduces that error to a few percent, while discrete ordinates and Monte Carlo methods offer the greatest accuracy at the highest cost. The review’s message is that no single method suits every problem, and the choice must weigh computational expense against the physics one needs to capture, whether self-shadowing, scattering, or frequency-dependent heating.

The consequences of getting radiation transport right extend deep into planet formation theory. Global simulations of the vertical shear instability show that the resulting turbulence generates stresses whose strength depends on the square of the radial temperature gradient and on the local cooling time, challenging the classical assumption that turbulent viscosity scales simply with gas pressure. VSI turbulence can spawn long-lived anticyclonic vortices, provided simulations span the full azimuthal extent of the disk, and these storm systems are expected to act as efficient traps for pebbles and dust, potentially accelerating planetesimal formation. In irradiated disks, radiation hydrodynamical studies reveal that the instability can be localized to the surface layers when dust depletion lengthens midplane cooling times, producing a quiescent midplane beneath a vigorously turbulent atmosphere, a stratification with direct consequences for where dust can settle and planets can grow.

The review closes with a forward-looking agenda. The authors recommend abandoning fixed-temperature disk models in favor of self-consistent thermal evolution, since every realistic disk structure is subject to thermal baroclinic instabilities that fixed-temperature setups either suppress artificially or misrepresent. Future work must couple evolving dust populations to the opacity and cooling calculations, treat the separate temperatures of gas, dust, and radiation, and develop well-balanced or low-Mach-number schemes that resolve subsonic fluctuations in a supersonically rotating medium. The payoff is substantial: radiation hydrodynamic simulations calibrated against linear theory will underpin the interpretation of molecular line kinematics and scattered-light images from current and next-generation telescopes, transforming stunning pictures of planet-forming disks into quantitative tests of how worlds are born.

Subject of Research: Numerical radiation hydrodynamics methods and stability tests for simulating protoplanetary disks around young stars

Article Title: Numerical radiation hydrodynamics for circumstellar disks

Article References: Klahr, H., Baehr, H., Melon Fuksman, J. D., & Pfeil, T. (2026). Numerical radiation hydrodynamics for circumstellar disks. Living Reviews in Computational Astrophysics, 12(1), Article 3. https://doi.org/10.1007/s41115-026-00026-6

Image Credits: AI Generated

DOI: 10.1007/s41115-026-00026-6

Keywords: protoplanetary disks, radiation hydrodynamics, planet formation, vertical shear instability, convective overstability, baroclinic instability, radiative transfer, turbulence, numerical simulations, stellar irradiation, computational astrophysics, disk stability