Convective Time Scale Research Articles

Ordering of time scales predicts applicability of quasilinear theory in unstable flows

We discuss the applicability of quasilinear-type approximations for a turbulent system with a large range of spatial and temporal scales. We consider a paradigm fluid system of rotating convection with vertical and horizontal temperature gradients. In particular, the interaction of rotation with the horizontal temperature gradient drives a ‘thermal wind’ shear flow whose strength is controlled by the horizontal temperature gradient. Varying this parameter therefore systematically alters the ordering of the shearing time scale, the convective time scale and the correlation time scale. We demonstrate that quasilinear-type approximations work well when the shearing time scale or the correlation time scale is sufficiently short. In all cases, the generalised quasilinear approximation systematically outperforms the quasilinear approximation. We discuss the consequences for statistical theories of turbulence interacting with mean gradients.

One month convection timescale on the surface of a giant evolved star

The transport of energy through convection is important during many stages of stellar evolution1,2, and is best studied in our Sun3 or giant evolved stars4. Features that are attributed to convection are found on the surface of massive red supergiant stars5–8. Also for lower-mass evolved stars, indications of convection are found9–13, but convective timescales and sizes remain poorly constrained. Models indicate that convective motions are crucial to produce strong winds that return the products of stellar nucleosynthesis into the interstellar medium14. Here we report a series of reconstructed interferometric images of the surface of the evolved giant star R Doradus. The images reveal a stellar disk with prominent small-scale features that provide the structure and motions of convection on the stellar surface. We find that the dominant structure size of the features on the stellar disk is 0.72 ± 0.05 astronomical units. We measure the velocity of the surface motions to vary between −18 and +20 km s−1, which means that the convective timescale is approximately one month. This indicates a possible difference between the convection properties of low-mass and high-mass evolved stars.

Unified framework for laser-induced transient bubble dynamics within microchannels

Oscillatory flow in confined spaces is central to understanding physiological flows and rational design of synthetic periodic-actuation based micromachines. Using theory and experiments on oscillating flows generated through a laser-induced cavitation bubble, we associate the dynamic bubble size (fluid velocity) and bubble lifetime to the laser energy supplied—a control parameter in experiments. Employing different channel cross-section shapes, sizes and lengths, we demonstrate the characteristic scales for velocity, time and energy to depend solely on the channel geometry. Contrary to the generally assumed absence of instability in low Reynolds number flows (<1000\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$<1000$$\\end{document}), we report a momentary flow distortion that originates due to the boundary layer separation near channel walls during flow deceleration. The emergence of distorted laminar states is characterized using two stages. First the conditions for the onset of instabilities is analyzed using the Reynolds number and Womersley number for oscillating flows. Second the growth and the ability of an instability to prevail is analyzed using the convective time scale of the flow. Our findings inform rational design of microsystems leveraging pulsatile flows via cavitation-powered microactuation.

Offline tagging of radon-induced backgrounds in XENON1T and applicability to other liquid xenon time projection chambers

This paper details the first application of a software tagging algorithm to reduce radon-induced backgrounds in liquid noble element time projection chambers, such as XENON1T and XENONnT. The convection velocity field in XENON1T was mapped out using Rn222 and Po218 events, and the rms convection speed was measured to be 0.30±0.01 cm/s. Given this velocity field, Pb214 background events can be tagged when they are followed by Bi214 and Po214 decays, or preceded by Po218 decays. This was achieved by evolving a point cloud in the direction of a measured convection velocity field, and searching for Bi214 and Po214 decays or Po218 decays within a volume defined by the point cloud. In XENON1T, this tagging system achieved a Pb214 background reduction of 6.2−0.9+0.4% with an exposure loss of 1.8±0.2%, despite the timescales of convection being smaller than the relevant decay times. We show that the performance can be improved in XENONnT, and that the performance of such a software-tagging approach can be expected to be further improved in a diffusion-limited scenario. Finally, a similar method might be useful to tag the cosmogenic Xe137 background, which is relevant to the search for neutrinoless double-beta decay. Published by the American Physical Society 2024

Convergence of ensemble forecast distributions in weak and strong forcing convective weather regimes

AbstractThe constraint of computational power and the huge number of degrees of freedom of the atmosphere means a sampling uncertainty exists in probabilistic ensemble forecasts. In our previous study, the uncertainty could be quantified, creating a convergence measure which converges proportional to in the limit of large ensemble size . This power law can then be extrapolated to determine how sampling uncertainty would decrease with larger ensemble sizes and hence find the necessary ensemble size. It is unknown, however, how the sampling uncertainty depends on different weather regimes. This study extends the previous idealised ensemble developed, by including weak and strong forcing convective weather regimes, to look at how sampling uncertainty convergence differs in each. Two ‐member ensembles were run, with weak and strong forcing respectively. Comparisons with a kilometre‐scale weather prediction model ensured realistic weak and strong forcing regimes by comparing the rain, convective available potential energy (CAPE), convective adjustment timescale, and distribution shapes throughout the diurnal cycle. Differences in distribution shape between the regimes led to differences in the convergence measure. Large differences in spread between weak and strong forcing runs throughout the hr period led to large differences in sampling uncertainty of the mean and standard deviation, which could be quantified according to well‐known equations. The timing of these differences was case‐dependent. For extreme statistics such as the quantile and for cases where there was precipitation, the moisture variables for the weak forcing case had the largest sampling uncertainty and required the most members for convergence proportional to . This was due to the tails of the weak forcing moisture variables containing the least amount of density. Different ensemble sizes will hence be required depending on whether one is in the weak or strong forcing convective weather regime.

Laminar separation bubble formation and bursting on a finite wing

The transient processes of laminar separation bubble (LSB) formation and bursting on a rectangular NACA 0018 wing are studied experimentally. A two-dimensional airfoil model is used as a baseline for the assessment of finite wing effects. The models are subjected to ramp changes in free-stream velocity causing the flow to switch between a state where an LSB forms and a state without reattachment. Lift force and particle image velocimetry measurements are used to relate the flow development to the aerodynamic loading. The lift coefficient of the airfoil exhibits substantial hysteresis, and the duration of the lift transients range from $10$ to $22$ convective time scales for bubble formation and $22$ to $30$ convective time scales for bursting. In contrast, the transient lift coefficients of the wing change gradually, with less hysteresis. The wing tip causes greater three-dimensionality in the separation bubble, whose thickness increases near the midspan where bursting is initiated. During bubble formation, the region of separated flow contracts towards the midspan. The gradual change in lift of the wing is linked to slower spanwise expansion and contraction of the separated flow region relative to the airfoil. On both models, the wavenumbers and amplitudes of disturbances in the separated shear layer rapidly change when reattachment initiates or ceases. Applying the bursting criterion of Gaster (Tech. Rep. Reports and Memoranda 3595. Aeronautical Research Council, London, 1967) to the bubble on the wing shows that bursting of the bubble at a single spanwise location is insufficient to cause complete spanwise failure of reattachment, and that the relationship between bursting parameters depends on spanwise position.

3D hydrodynamic simulations of massive main-sequence stars – II. Convective excitation and spectra of internal gravity waves

ABSTRACT Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light-curve observations. We present the oscillation properties of high-resolution hydrodynamic simulations of a $25\,\,{\rm{M}_\odot }$ star performed with the PPMstar code. The model star has a convective core mass of $\approx 12\,\,{\rm{M}_\odot }$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time-scale in addition to significant power across a forest of low and high angular degree l modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes of the order of 10s of days. Thanks to the still significant power at higher l and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt–Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with the same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.

A rapidly time-varying equatorial jet in Jupiter’s deep interior

Planetary magnetic fields provide a window into the otherwise largely inaccessible dynamics of a planet’s deep interior. In particular, interaction between fluid flow in electrically conducting interior regions and the magnetic field there gives rise to observable secular variation (time dependency) of the externally observed magnetic field. Secular variation of Jupiter’s field has recently been revealed1–3 and been shown to arise, in part, from an axisymmetric, equatorial jet2. Whether this jet is time dependent has not previously been addressed, yet it is of critical importance for understanding the dynamics of the planet’s interior. If steady, it would probably be a manifestation of deep dynamo convective flow (and jets are anticipated as part of that flow4–9) but if time dependent on a timescale much shorter than the convective turnover timescale of several hundred years, it would probably have a different origin. Here we show that the jet has a wavelike fluctuation with a period of roughly 4 years, strongly suggestive of the presence of a torsional oscillation10 (a cylindrically symmetric oscillating flow about the rotation axis) or a localized Alfvén wave in Jupiter’s metallic hydrogen interior. This opens a pathway towards revealing otherwise hidden aspects of the magnetic field within the metallic hydrogen region and hence constraining the dynamo that generates Jupiter’s magnetic field.

Classification of Warm-Season Precipitation in High-Resolution Rapid Refresh (HRRR) Model Forecasts over the Contiguous United States

Abstract This study uses the convective adjustment time scale to identify the climatological frequency of equilibrium and nonequilibrium convection in different parts of the contiguous United States (CONUS) as modeled by the operational convection-allowing High-Resolution Rapid Refresh (HRRR) forecast system. We find a qualitatively different climatology in the northern and southern domains separated by the 40°N parallel. The convective adjustment time scale picks up the fact that convection over the northern domains is governed by synoptic flow (leading to equilibrium), while locally forced, nonequilibrium convection dominates over the southern domains. Using a machine learning algorithm, we demonstrate that the convective adjustment time-scale diagnostic provides a sensible classification that agrees with the underlying dynamics of equilibrium and nonequilibrium convection. Furthermore, the convective adjustment time scale can indicate the model quantitative precipitation forecast (QPF) quality, as it correctly reflects the higher QPF skill for precipitation under strong synoptic forcing. This diagnostic based on the strength of forcing for convection will be employed in future studies across different parts of CONUS to objectively distinguish different weather situations and explore the potential connection to warm-season precipitation predictability. Significance Statement An objective classification metric that can delineate a wide range of forecasts into distinct scenarios can serve as a valuable tool. This study represents a pioneering effort in utilizing the convective adjustment time scale to identify the climatological frequency of warm-season precipitation under varying levels of synoptic forcing in different parts of the contiguous United States (CONUS). The results demonstrate that the convective adjustment time scale is a robust metric for categorizing precipitation events and establishing a direct link to their predictability. Overall, this study provides a valuable framework for future studies focused on the CONUS domain, offering guidance on how to employ the convective adjustment time scale to classify weather regimes and explore the influence of environmental conditions on predictability of convection.

Mitigating thermoacoustic instabilities in premixed hydrogen flames using axial staging

In this paper we demonstrate how axial staging can be utilised to mitigate thermoacoustic instabilities in a combustion system by flame redistribution. This is achieved by moving flow to a second stage flame while keeping the combined thermal power and total flow fixed. The stability of the system was first characterised for premixed H2-CH4-air flames operated with hydrogen volume fraction in the range 80%–100%. As observed in recent work, increasing the hydrogen concentration led to the onset of strong self-excited instabilities. Increasing the flow velocity for a fixed hydrogen concentration was shown to have the same effect. Both of these are linked to a decrease in the convective time scale — causing the flame to become more convectively compact and responsive to higher frequencies. We then show that these instabilities could be reduced for all conditions, by distributing flow to the secondary flame. Two main driving mechanisms causing suppression were observed and analysed. Firstly, a reduction in the flow rate provided to the first stage flame, leading to a corresponding change in the flame structure. This leads to an increase in the convective time scale. This effect is quantified by a reduced gain at higher frequencies, and a change in the time delay of the flame transfer function. Secondly, introducing a second flame with a different convective time scale results in interference between the two flames. This acts to suppress or enhance the global fluctuations in heat release rate and hence, the amplitude of the pressure oscillations in the system.

Turbulent dynamo action and its effects on the mixing at the convective boundary of an idealized oxygen-burning shell

Convection is one of the most important mixing processes in stellar interiors. Hydrodynamic mass entrainment can bring fresh fuel from neighboring stable layers into a convection zone, modifying the structure and evolution of the star. Because flows in stellar convection zones are highly turbulent, multidimensional hydrodynamic simulations are fundamental to accurately capture the physics of mixing processes. Under some conditions, strong magnetic fields can be sustained by the action of a turbulent dynamo, adding another layer of complexity and possibly altering the dynamics in the convection zone and at its boundaries. In this study, we used our fully compressible SEVEN-LEAGUE HYDRO code to run detailed and highly resolved three-dimensional magnetohydrodynamic simulations of turbulent convection, dynamo amplification, and convective boundary mixing in a simplified setup whose stratification is similar to that of an oxygen-burning shell in a star with an initial mass of 25 M⊙. We find that the random stretching of magnetic field lines by fluid motions in the inertial range of the turbulent spectrum (i.e., a small-scale dynamo) naturally amplifies the seed field by several orders of magnitude in a few convective turnover timescales. During the subsequent saturated regime, the magnetic-to-kinetic energy ratio inside the convective shell reaches values as high as 0.33, and the average magnetic field strength is ∼1010 G. Such strong fields efficiently suppress shear instabilities, which feed the turbulent cascade of kinetic energy, on a wide range of spatial scales. The resulting convective flows are characterized by thread-like structures that extend over a large fraction of the convective shell. The reduced flow speeds and the presence of magnetic fields with strengths up to 60% of the equipartition value at the upper convective boundary diminish the rate of mass entrainment from the stable layer by ≈20% as compared to the purely hydrodynamic case.

Inviscid evolution of a uniform vortex dipole in a strain field

Competing models employing anti-parallel vortex collision in search of a finite-time singularity of Euler's equation have arisen recently. Both the vortex sheet model proposed by Brenner et al. (Phys. Rev. Fluids, vol. 1, 2016, 084503) and the ‘tent’ model proposed by Moffatt &amp; Kimura (J. Fluid Mech., vol. 861, 2019, pp. 930–967) consider a vortex monopole exposed to a strain flow to model the evolution of interacting anti-parallel vortices, a fundamental element in the turbulent cascade. Herein we employ contour dynamics to explore the inviscid evolution of a vortex dipole subjected to an external strain flow with and without axial stretching. We find that for any strain-to-vorticity ratio $\mathcal {E}$ , the constituent vortices compress indefinitely, with weaker strain flows causing flattening to occur more slowly. At low $\mathcal {E}$ , the vortex dipole forms the well-documented head–tail structure, whereas increasing $\mathcal {E}$ results in the dipole compressing into a pair of vortex sheets with no appreciable head structure. Axial stretching effectively lowers $\mathcal {E}$ dynamically throughout the evolution, thus delaying the transition from the head–tail regime to the vortex sheet regime to higher strain-to-vorticity ratios. Findings from this study offer a bridge between the two cascade models, with the particular mechanism arising depending on $\mathcal {E}$ . It also suggests limits for the ‘tent’ model for a finite-time singularity, wherein the curvature-induced strain flow must be very weak in comparison with the vorticity density-driven mutual attraction such that the convective time scale of the evolution exceeds the core flattening time scale.

Impact of central mixing scheme and nuclear reaction network on the extent of convective cores

Convective cores are the hydrogen reservoirs of main sequence stars that are more massive than around 1.2 solar masses. The characteristics of the cores have a strong impact on the evolution and structure of the star. However, such results rely on stellar evolution codes, in which simplistic assumptions are often made on the physics in the core. Indeed, mixing is commonly considered to be instantaneous and the most basic nuclear networks assume beryllium at its equilibrium abundance. Those assumptions lead to significant differences in the central composition of the elements for which the timescale to reach nuclear equilibrium is lower than the convective timescale. In this work, we show that those discrepancies impact the nuclear energy production and, therefore, the size of convective cores in models computed with overshoot. We find that cores computed with instantaneous mixing are up to 30% bigger than those computed with diffusive mixing. Similar differences are found when using basic nuclear networks. Additionally, we observed an extension of the duration of the main sequence due to those core size differences. We then investigated the impact of those structural differences on the seismic modeling of solar-like oscillators. Modeling two stars observed by Kepler, we find that the overshoot parameter of the best models computed with a basic nuclear network is significantly lower, compared to models computed with a full nuclear network. This work is a necessary step in improving the modeling of convective cores, which is key to determining accurate ages in the framework of future space missions such as Plato.

Is the Madden‐Julian Oscillation a Moisture Mode?

AbstractThe governing thermodynamics of the Madden‐Julian Oscillation (MJO) is examined using sounding and reanalysis data. On the basis of four objective criteria, results suggest that the MJO behaves like a moisture mode–a system whose thermodynamics is governed by moisture–only over the Indian Ocean. Over this basin, the MJO shows a slow convective adjustment timescale, its zonal scale is smaller, and it exhibits slow propagation, allowing moisture modes to exist. Elsewhere, the faster‐propagating wavenumber 1–2 components are more prominent preventing weak temperature gradient (WTG) balance to be established. As a result, temperature and moisture play similar roles in the MJO's thermodynamics outside the Indian Ocean.

MJO in Different Orbital Regimes: Role of the Mean State in the MJO’s Amplitude during Boreal Winter

Abstract The Madden–Julian oscillation (MJO) exhibits pronounced seasonality, with one of the key unanswered questions being the following: what controls the maximum in MJO precipitation variance in the Southern Hemisphere during boreal winter? In this study, we examine a set of global climate model simulations in which the eccentricity and precession of Earth’s orbit are altered to change the boreal winter mean state in an attempt to reveal the processes that are responsible for the MJO’s amplitude in the boreal winter. In response to the forced insolation changes, the north–south asymmetry in sea surface temperature is amplified in boreal fall, which intensifies the Hadley circulation in boreal winter. The stronger Hadley circulation yields higher mean precipitation and stronger mean lower-tropospheric westerlies in the southern part of the Indo-Pacific warm pool. The MJO precipitation variability increases significantly where the mean precipitation and lower-tropospheric westerlies strengthen. In the column-integrated moisture budget of the simulated MJO, only surface latent heat flux feedback shows a trend that is consistent with the MJO’s amplitude, suggesting an important role for the surface latent heat flux feedback in the MJO’s amplitude during the boreal winter. An analysis of the moisture–precipitation relationship in the simulations shows that the increase in the mean precipitation lowers the convective moisture adjustment time scale, leading to the increase in precipitation variance. Our results suggest that the mean-state precipitation plays a critical role in the maintenance mechanism of the MJO.

The Departure from Mixed-Layer Similarity During the Afternoon Decay of Turbulence in the Free-Convective Boundary Layer: Results from Large-Eddy Simulations

This study analyses the departure of the velocity-variances profiles from their quasi-steady state described by the mixed-layer similarity, using large-eddy simulations with different prescribed shapes and time scales of the surface kinematic heat flux decay. Within the descriptive frames where the time is tracked solely by the forcing time scale (either constant or time-dependent) describing the surface heat flux decay, we find that the normalized velocity-variances profiles from different runs do not collapse while they depart from mixed-layer similarity. As the mixed-layer similarity relies on the assumption that the free-convective boundary layer is in a quasi-equilibrium, we consider the ratios of the forcing time scales to the convective eddy-turnover time scale. We find that the normalized velocity-variances profiles collapse in the only case where the ratio (widetilde{r}) of the time-dependent forcing time scale to the convective eddy-turnover time scale is used for tracking the time, supporting the independence of the departure from the characteristics of the surface heat flux decay. As a consequence of this result, the knowledge of widetilde{r} is sufficient to predict the departure of the velocity variances from their quasi-steady state, irrespective of the shape of the surface heat flux decay. This study highlights the importance of considering both the time-dependent forcing time scale and the convective eddy-turnover time scale for evaluating the response of the free-convective boundary layer to the surface heat flux decay.

The influence of free stream turbulence on the development of a wind turbine wake

The wake of an isolated model-scale wind turbine is analysed in a set of inflow conditions having free stream turbulence intensity between 3 % and 12 %, and integral time scales in the range of 0.1–10 times the convective time scale based on the turbine diameter. It is observed that the wake generated by the turbine evolves more rapidly, with the onset of the wake evolution being closer to the turbine, for high turbulence intensity and low integral time scale flows, in accordance with literature, while flows at higher integral time scales result in a slow wake evolution, akin to that generated by low-turbulence inflow conditions despite the highly turbulent ambient condition. The delayed onset of the wake evolution is connected to the stability of the shear layer enveloping the near-wake, which is favoured for low-turbulence or high-integral time scale flows, and to the stability of the helical vortex set surrounding the wake, as this favours interaction events and prevents momentum exchange at the wake boundary which hinder wake evolution. The rate at which the velocity in the wake recovers to undisturbed conditions is instead analytically shown to be a function of the Reynolds shear stress at the wake centreline, an observation that is confirmed by measurements. The rate of production of Reynolds shear stress in the wake is then connected to the power harvested by the turbine to explain the differences between flows at equivalent turbulence intensity and different integral time scales. The wake recovery rate, and by extension the behaviour of the turbine wake in high-integral time scale flows, is seen to be a linear function of the free stream turbulence intensity for flows with Kolmogorov-like turbulence spectrum, in accordance with literature. This relation is seen not to hold for flows with different free stream turbulence spectral distribution; however, this trend is recovered if the contributions of low frequency velocity components to the turbulence intensity are ignored or filtered out from the computation.

Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet

During the first half of their main-sequence lifetimes, stars rapidly lose angular momentum to their magnetized winds, a process known as magnetic braking. Recent observations suggest a substantial decrease in the magnetic braking efficiency when stars reach a critical value of the Rossby number, the stellar rotation period normalized by the convective overturn timescale. Cooler stars have deeper convection zones with longer overturn times, reaching this critical Rossby number at slower rotation rates. The nature and timing of the transition to weakened magnetic braking have previously been constrained by several solar analogs and two slightly hotter stars. In this Letter, we derive the first direct constraints from stars cooler than the Sun. We present new spectropolarimetry of the old G8 dwarf τ Cet from the Large Binocular Telescope, and we reanalyze a published Zeeman Doppler image of the younger G8 star 61 UMa, yielding the large-scale magnetic field strengths and morphologies. We estimate mass-loss rates using archival X-ray observations and inferences from Lyα measurements, and we adopt other stellar properties from asteroseismology and spectral energy distribution fitting. The resulting calculations of the wind braking torque demonstrate that the rate of angular momentum loss drops by a factor of 300 between the ages of these two stars (1.4–9 Gyr), well above theoretical expectations. We summarize the available data to help constrain the value of the critical Rossby number, and we identify a new signature of the long-period detection edge in recent measurements from the Kepler mission.

The effect of pressure on lean premixed hydrogen-air flames

The effect of pressure on the propagation of lean premixed hydrogen-air flames is investigated numerically with a hierarchy of canonical configurations including direct numerical simulations of turbulent flames in homogeneous isotropic turbulence. Thermo-diffusive instability and the ratio of turbulent to laminar burning velocity are found to be clearly amplified for increasing pressure. The observed amplification results from the combined effects of multi-dimensional geometrical features of the reaction front induced by stretch, chemical kinetics and flame speed / thickness sensitivity to preferential diffusion induced by the flame geometry. High-pressure flames exhibit stronger sensitivity to fast molecular diffusion of hydrogen into the reaction front of a reference freely-propagating flame that is nominally weaker at high pressure due to the greater relative importance of chain-termination. In this context, two-dimensional flames subjected to monochromatic velocity perturbations demonstrate locally enhanced flame speeds and reduced flame thickness at high pressure in regions of curvature that are convex towards the reactants. Furthermore, it is found that a Peclet number definition, based on the ratio of diffusive to convective time scales, provides a satisfactory global representation of pressure effects upon thermo-diffusive instabilities of freely-propagating flames. Finally, employing a series of carefully designed direct numerical simulations, it is empirically demonstrated that very similar flame responses can be obtained at atmospheric and pressurized conditions by approximately matching a selection of four key parameters (Leeff, Ze, Ma, Pe). This key finding demonstrates that the flame speed enhancement often observed at elevated pressure is not a pressure effect per se, but rather determined by the sensitivity of the flame to preferential diffusion (Pe) versus its own reactivity (Ze), with nominally ‘weaker’ flames showing stronger sensitivity.

A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations

ABSTRACT We perform two-dimensional (2D) numerical simulations of core convection for zero-age main-sequence stars covering a mass range from 3 to 20 M⊙. The simulations are performed with the fully compressible time-implicit code music. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 M⊙ models. The simulations cover hundreds to thousands of convective turnover time-scales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance (dov) scales with the stellar luminosity (L) and the convective core radius (rconv). We derive a scaling law $d_{\rm ov} \propto L^{1/3} r_{\rm conv}^{1/2}$, which is implemented in a one-dimensional stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses ≳10 M⊙. Our 2D simulations show the formation of a nearly adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent three-dimensional simulations of convection. The most luminous models show a growth in size with time of the nearly adiabatic layer. This growth seems to slow down as the upper edge of the nearly adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive time-scale in the overshooting layer.