Convective Scale Research Articles

The Vertical Structure of Tropical Temperature Change in Global Storm‐Resolving Model Simulations of Climate Change

AbstractGlobal storm‐resolving model (GSRM) simulations (kilometer‐scale horizontal resolution) of the atmosphere can capture the interaction between the scales of deep cumulus convection and the large‐scale dynamics and thermodynamic properties of the atmosphere. Here, we assess the vertical structure of tropical temperature change in Geophysical Fluid Dynamics Laboratory's GSRM X‐SHiELD, perturbed by a uniform sea surface temperature (SST) warming and/or increased concentration. The simulated warming from an SST increase is weakly amplified relative to the surface through the mid‐troposphere before increasing to a factor of about 2.5 in the upper troposphere. This combination of muted warming in the mid‐troposphere and amplified warming aloft is within the range of CMIP6 models at individual pressure levels but, taken together, is distinctive behavior. The response to increase with unchanged SST is an approximately vertically uniform warming, comparable to CMIP6 models, and is linearly additive with the SST‐induced warming in X‐SHiELD.

Characteristics of the Mediterranean Cyclone IANOS in Convection‐Permitting Simulations: Unraveling Model Sensitivity to Microphysics and Cumulus Parameterization

AbstractThis study quantified the relative impact of microphysics parameterization (MP) and cumulus parameterization (CP) schemes on storm prediction using a non‐hydrostatic weather research and forecasting model for an intense Medicane: IANOS. All the simulations agreed with the main observed characteristics of this storm, with some discrepancies in magnitude and location, which vary with CP and MP schemes. These discrepancies were larger during the mature phase of the storm. In the CP‐on simulations, the non‐scale aware Kain–Fritsch (KF) scheme typically resulted in higher precipitation, while the Betts‐Miller‐Janjic (BMJ) scheme led to lower precipitation compared to the CP‐off simulations (C0). The tendency of the KF scheme to consume available convective potential energy at a relatively high rate (i.e., short time scale) resulted in high mass fluxes and latent heat release, leading to strengthened convective activity and, hence, precipitation. The multi‐scale aware (MSKF) substantially reduces the precipitation compared to KF due to the reduced contribution of convective scale precipitation. It also modulates the spatial structure precipitation compared to KF, especially light precipitation over the outer bands, and the contribution of grid‐scale precipitation to total precipitation. KF shows the lowest contribution, around 50%, whereas BMJ exhibits a slightly higher contribution, and MSKF versions nearly reach 100%, making it closer to CP‐off. The improved performance in MSKF compared to KF highlights the importance of MSKF convection parameterization for gray zone (~1–4 km) simulation. The persistent discrepancy in landfall location in CP‐on and CP‐off simulation underscored the need of further investigating other physics parameterizations and dynamical mechanisms.

Moist convective scaling: Insights from an idealised model

AbstractThe response of clouds and moist‐convective processes to heat loss to space by long‐wave radiative cooling is an important feedback in the Earth's atmosphere. It is known that moist convection increases roughly in equilibrium with radiative cooling, an assumption often made in simplified models of the tropical atmosphere. In this study, we use an idealised two‐dimensional model of the atmosphere introduced by Vallis et. al. and incorporate a bulk‐cooling term, which is an idealisation of radiative cooling in the atmosphere. We comment briefly on the static stability of the system to dry and moist convection and characteris its moist convective response to changes in the bulk cooling. We find that, while the clear‐sky regions of the model respond directly to the change in the cooling term, the regions dominated by moist convective plumes are insensitive to changes in cooling. Similar to previous findings from cloud‐resolving models, we too find in our idealised setting that the majority of the increase in convection occurs via an increase in the areal coverage of convection, rather than its intensity. We argue that these small‐scale convective processes are an upper bound on how quickly convective intensity can change to stay in equilibrium with radiative cooling.

A pore-scale resolved direct numerical simulation study for scaling analysis of the solutal convection in porous media

Understanding the solutal convection is a crucial step towards accurate prediction of CO $_2$ sequestration in deep saline aquifers. In this study, pore-scale resolved direct numerical simulations (DNS) are performed to analyse the scaling laws of the solutal convection in porous media. The porous media studied are composed of uniformly distributed square or circular elements. The Rayleigh numbers in the range $426 \le Ra \le 80\,000$ , the Darcy numbers in the range $1.7\times 10^{-8} \le Da \le 8.8\times 10^{-6}$ and the Schmidt numbers in the range $250 \le Sc \le 10^4$ are considered in the DNS. The main time, length and velocity scales affecting the solutal convection are classified as the diffusive scales ( $t_I$ , $l_I$ and $u_I$ ), the convective scales ( $t_{II}$ , $l_{II}$ and $u_{II}$ ) and the shut-down scales ( $t_{III}$ , $l_{III}$ and $u_{III}$ ). These scales determine the pore-scale Rayleigh number $Ra_K$ and the Rayleigh number $Ra$ . Based on the DNS results, the scaling laws for the transient dissolution flux are proposed in the different regimes of convection. It is found that the onset time of convection ( $t_{oc}$ ) and the period of the flux-growth regime ( $\Delta t_{fg}$ ) vary linearly with the convective time scale $t_{II}$ . The merging of the original plumes and the re-initiation of the new plumes start in the same period, resulting in the merging re-initiation regime. Horizontal dispersion plays an important role in plume merging. The dissolution flux $F$ and the time since the onset of convection $t^{\ast }$ have an $F / u_{II} \sim (t^{\ast }/ t_{II})^{-0.2}$ scaling in the later stage of the merging re-initiation regime. This scaling is caused by the merging of the low-wavenumber plumes. It becomes more pronounced with decreasing porosity and leads to the nonlinear relationship between the Sherwood number $Sh$ and $Ra$ when the domain is not high enough for the plumes to fully develop. According to the DNS results, a regime is expected that is independent of both $Ra$ and $Ra_K$ , while the dimensionless constant flux $F_{cf}/u_{II}$ in this regime decreases with decreasing porosity. When the mean solute concentration reaches approximately 30 %, convection enters the shut-down regime. For large $Ra$ , the dimensionless flux in the shut-down regime follows the scaling law $F/u_{III}\sim (t/t_{III})^{-1.2}$ at large porosity ( $\phi =0.56$ ) and $F/u_{III}\sim (t/t_{III})^{-1.5}$ at small porosity ( $\phi =0.36$ or $0.32$ ). The study shows the significant pore-scale effect on the convection. The DNS cases in this study are mainly for simplified geometries and large $Ra_K$ . This can lead to uncertainties of the obtained scaling coefficients. It is important to determine the scaling coefficients for real geological formations to predict a real CO $_2$ sequestration process.

Dynamic topography and the planform of mantle convection since the Jurassic inferred from global continental hiatus maps

The planform is a defining feature of mantle convection. It can be gleaned from the stratigraphic record by mapping the continent-scale distribution of hiatus and no hiatus surfaces serving as a proxy for high and low dynamic topography. We carry this out for all continents apart from Antarctica for eight geological series since the Upper Jurassic, showing that: (i) the planform as indicated by our maps contains wavelengths of the order of 1000 km, smaller than the convective scales implied by the geoid. (ii) The planform changes on timescales of geological series (10–20 Myrs), smaller than the mantle transit time. (iii) Flood basalt eruptions are frequently preceded by hiatus surfaces. (iv) Some hiatus surfaces are not linked to any known plume, potentially reflecting the lateral transport of material in the asthenosphere. Our results reveal the importance of mantle viscosity stratification in shaping the convective planform and the resulting dynamic topography. Geodynamic Earth models should aim to reproduce the global characteristics of our maps, as well as specific regional events identified in this work. Finally, we separate the effects of sea-level variation from regional changes in base level induced by dynamic topography by contrasting the stratigraphic evolution of different regions.

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.

Separating urban heat island circulation and convective cells through dynamic mode decomposition

AbstractThis study applies dynamic mode decomposition (DMD) to three‐dimensional simulation results of urban heat island circulation (UHIC, which is horizontal circulation) and thermals (vertical convections). The aim of this study is to revisit how these phenomena coexist based on the characteristics of temporal changes in the flow field. We used DMD to obtain the dominant spatial patterns and information on temporal changes. One of the modes of horizontal wind, which does not change temporally (no oscillation or amplification), exhibits a spatial UHIC pattern. The unique feature of this UHIC mode is that there are small‐scale striated structures (150–200 m) and large‐scale convergence. The other modes are time‐varying (oscillating and decaying) and represent smaller spatial‐scale phenomena (150–250 m), such as thermals. The frequency of each mode takes various values, some of which are lower than the lifetime of thermals in accordance with the Deardorff convective scale (~10 min). These low‐frequency modes showed striated structures similar to that observed in the UHIC modes. These results suggest that UHIC and thermals deform each other through components that vary in long temporal scales.

Ensemble versus deterministic lightning forecast performance at a convective scale over Indian region

The present study quantifies the improvement achieved in lightning forecast skill of the NCMRWF regional ensemble prediction system (NEPS-R) compared to its deterministic counterpart (CNTL). The lightning forecasts over study regions of East and Northeast India (ENEI) and Peninsular India (PI) during the pre-monsoon season and Central-East and Northeast India (CENEI) during the monsoon season have been verified using lightning observations from the Indian Institute of Tropical Meteorology (IITM) Lightning Detection Network (LDN). The persisting systematic negative bias in deterministic and EPS-based forecasts of the ensemble mean (EnsMean) and ensemble maximum (EnsMax) indicate the lack of spread among the members, supported by the low values of ensemble spread over all the study regions. EnsMean has the lowest RMSE, with a decrease in error ranging from 0.8 % to 2.18 % compared to CNTL. Categorical skill scores indicate that the EPS-based forecasts (EnsMean and EnsMax) are more skillful than the deterministic forecast at all thresholds and lead times. Further, Fractions Skill Score (FSS) establishes the superiority of the ensemble forecasts over the deterministic forecasts, where for threshold >1, EnsMean is skillful at comparatively smaller neighborhood sizes (ENEI and PI ∼68 km; CENEI ∼36 km for day-1) than CNTL (ENEI-116 km; PI-196 km; CENEI-68 km). EnsMax at higher thresholds (>5 and >10) is skillful at lesser neighborhood sizes ranging from 116 to 276 km compared to CNTL (>401 km) for day-1. Hence, skillful re-scaled EPS forecasts based on FSS could provide better guidance for the forecasters. The Continuous Ranked Probability Score of EPS forecasts is lower by around 9 % than the Mean Absolute Error of CNTL forecasts, and the ROC of EPS shows better discrimination of events and non-events compared to CNTL. These highlight the merits of using an EPS over a deterministic system for forecasting a field of high spatial variability, like lightning, and thereby, the use of vast computational resources to run a convective scale EPS is justified.

Towards a 2DEnVar surface data assimilation approach within the convective scale numerical weather prediction model AROME‐France

AbstractSurface data assimilation (DA) plays a key role in the initialisation of soil variables in coupled surface–atmosphere numerical weather prediction (NWP) models. Météo‐France, as many other NWP centres, uses an operational surface DA method based on an optimal interpolation (OI), implemented more than 30 years ago. The current surface DA system implemented at Météo‐France in the operational limited‐area AROME‐France model operates in two steps. First, a two‐dimensional OI method analyses the diagnostic screen‐level parameters, which are then used to initialise the prognostic soil variables according to a one‐dimensional OI method. This article presents the implementation and the results of a new two‐dimensional ensemble‐based variational (2DEnVar) system, using the object‐oriented prediction system framework, for the diagnostic screen‐level variable analyses (2‐m temperature and 2‐m relative humidity) within the AROME‐France model. These analysed variables are then used to initialise the soil temperature and soil moisture of the first and second soil layers. A two‐dimensional variational system is initially implemented and compared with an equivalent system that uses an OI surface analysis. The comparison of 2‐m temperature increments shows that the two systems behave in a similar way. From this two‐dimensional variational approach, a 2DEnVar scheme is developed and compared with the OI screen‐level analysis used operationally (reference system). The results are encouraging even though a degradation in forecast quality is noticed at short ranges for 2‐m temperature and 2‐m relative humidity. This is mainly due to a low spread near the surface in the ensemble‐based data assimilation that is used to compute background‐error covariances in 2DEnVar. Sensitivity tests have been performed to improve the initial version of the 2DEnVar scheme. A positive and significant impact is noticed when a multiplicative inflation is applied to the background perturbations coming from the ensemble‐based data assimilation for the computation of 2‐m temperature and 2‐m relative humidity background‐error covariances. Finally, when comparing the inflated 2DEnVar system with the reference, the two systems behave similarly. This suggests that the 2DEnVar scheme, based on ensemble statistics, is capable of properly reconstructing background‐error structures derived from the empirical correlations described in OI.

Satellite based analysis of rapid intensification of Super Cyclone Amphan

Tropical Cyclones (TCs) are formidable natural hazards with destructive impacts on life and property along the tropical belt. TCs are responsible for multiple hazards such as riverine and urban floods, extreme winds, and lightning, storm surge significantly amplifying the threats they pose. Rapid Intensification (RI), defined as a sudden increase in Maximum Sustained Winds (MSWs) by 30 kt or more in 24 h, has been a growing concern. These events, characterized by a swift escalation in MSW are challenging to the forecasters and remain a considerable operational challenge, amplifying risks for coastal communities. Numerical modeling also struggles to predict RI, with limitations in describing inner core convective scale processes cited as a major limitation. Monitoring and assessing TCs heavily rely on satellite-based observations due to the absence of adequate in-situ measurements over the ocean. In the present study, we examine Super Cyclonic Storm (SuCS) Amphan, the first Super Cyclone of this century, that formed over the Bay of Bengal in 2020 using satellite imagery and derived products available in near-real time to monitor and identify the early signatures for the RI. It is observed that the intensification is intricately tied to substantial expansions in both the outer and inner core sizes along with its symmetricity before the RI. Notably, no significant alterations in size are observed between the very severe cyclonic storm (VSCS) and SuCS stages. The convection characteristics of TCs are found to provide crucial markers of their intensification, with a particular emphasis on polar satellite-based passive microwave imagery for analyzing embedded convection and early eye detection. Key observations indicate that inner convective ring patterns, identified through 37Ghz microwave imagery in lower-level convection, act as precursors to rapid intensification. Concurrently, the outer ring pattern observed during the mid-life course is found to permit further intensification of the system.

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.

Near‐surface wind profiles from numerical model predictions. Part II: Verifications against Australia‐wide surface wind observations

AbstractThe new scheme for deriving the near‐surface wind profiles discussed in Ma (in review) is applied to an Australian Bureau of Meteorology operational convective scale model over various domains. Both the new and conventional schemes' diagnostic 10‐m winds are then verified against Australia‐wide automatic weather station observations. Analyses of bulk statistics reveal that the new scheme's 10‐m wind forecasts have generally better accuracy than the current conventional scheme with a consistent reduction of biases over all domains. A widely recognised diurnal bias pattern of surface wind speed over the land is substantially reduced, and the inclusion of Ekman spiral effect on the 10‐m wind marginally improves statistics of the wind direction during the nighttime. The new scheme introduces no systemic bias, given the histogram of a bulk mean bias is analogiased to a Gaussian distribution, and moves the distribution of diagnostic wind speed closer to that observed.

НАУКАСТИНГ ПАРАМЕТРОВ И ЯВЛЕНИЙ ПОГОДЫ: ИНСТРУМЕНТЫ, ВОЗМОЖНОСТИ И ОГРАНИЧЕНИЯ

Specific features of nowcasting as a forecast of current weather, its needs for observational data, and main approaches to solving a forecast problem are discussed: from simple extrapolation to hydrodynamic models with assimilation of an extended set of high-resolution observations. Prospects of machine learning applications are assessed. Some peculiarities of the nowcasting of precipitation and wind, which are the parameters of particular interest for most of users, are considered. The methodological complexity of the seamless approach to the nowcasting problems, extremely limited deterministic predictability on convective spatiotemporal scales, and importance of using a probabilistic approach are noted. Some illustrations from the national nowcasting developments are presented.

Effect of Hot Air Drying Temperature on Drying Kinetics, Physico-Chemical Properties, and Energy Consumption of Culture Asparagus (Asparagus officinalis L.)

Influences of drying air temperatures on drying time, specific energy consumption as well as product quality of culture asparagus were investigated in hot-air drying. The drying properties of asparagus samples were performed in a laboratory scale convection dryer at three different temperatures. The drying times of asparagus samples were found as 1200, 630 and 510 min for 50, 60 and 70 °C, respectively. In regard to the data obtained, Midilli et al. model is superior to other models to describe drying behavior of asparagus samples. The effective moisture diffusivity values of asparagus samples were calculated between 6.32 ∙ 10−9−1.62 ∙ 10−8 m2/s and the activation energy was estimated as 43.59 kJ/mol. The highest rehydration content and the least total color change were found in asparagus slices dried at 50 °C. Energy consumption values for asparagus samples dried at 50, 60 and 70 °C temperatures were obtained as 10.14, 5.32 and 4.31 kWh, respectively. In terms of energy consumption values, the best efficiency among all drying temperatures was obtained at 70 °C. It has been determined that the specific energy consumption decreased with increasing temperature.

Diagnostics for Imbalance on the Convective Scale

Abstract The analyses produced by a data assimilation system may be unbalanced, that is dynamically inconsistent with the forecasting model, leading to noisy forecasts and reduced skill. While there are effective procedures to reduce synoptic-scale imbalance, the situation on the convective scale is less clear because the flowon this scale is strongly divergent and non-hydrostatic. In this studywe compare three measures of imbalance relevant to convective-scale data assimilation: (i) surface pressure tendencies, (ii) vertical velocity variance in the vicinity of convective clouds, and (iii) departures from the vertical velocity prescribed by the weak temperature gradient (WTG) approximation. These are applied in a numerical weather prediction system, with three different data assimilation algorithms: 1. Latent Heat Nudging (LHN), 2. Local Ensemble Transform Kalman Filter (LETKF), and 3. LETKF in combination with incremental analysis updates (IAU). Results indicate that surface pressure tendency diagnoses a different type of imbalance than the vertical velocity variance and theWTG departure. The LETKF induces a spike in surface pressure tendencies, with a large-scale spatial pattern that is not clearly related to the precipitation pattern. This anomaly is notably reduced by the IAU. LHN does not generate a pronounced signal in the surface pressure, but produces the most imbalance in the other two measures. The imbalances measured by the partitioned vertical velocity variance andWTG departures are similar, and closely coupled to the convective precipitation. Between these two measures, the WTG departure has the advantage of being simpler and more economical to compute.

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.

High resolution Tibetan Plateau regional reanalysis 1961-present

With the rapid global warming in recent decades, the Tibetan Plateau (TP) has suffered severe impacts, such as glacier retreat, glacial lake expansion, and permafrost degradation, which threaten the lives and properties of the local and downstream populations. Regional Reanalysis (RR) is vital for TP due to the limitations of observations. In this work, a 62-year (1961–2022) long atmospheric regional reanalysis with spatial resolution of 9 km (convective gray-zone scale) and temporal resolution of 1 hour over the TP (TPRR) was developed using the Weather Research and Forecasting (WRF) model, combined with re-initialization method, spectral nudging (SN), and several optimizations. TPRR is forced by ERA5 at hourly intervals. TPRR outperforms ERA5, realistically capturing climatological characteristics and seasonal variations of precipitation and T2m (air temperature at 2m above ground level). Moreover, TPRR better reproduces the frequency and intensity of precipitation, as well as the diurnal cycle of precipitation. This study also quantifies the wetting trend of 0.0071 mm/year over the TP amid global warming using TPRR.

Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers

The geostrophic turbulence in rapidly rotating thermal convection exhibits characteristics shared by many highly turbulent geophysical and astrophysical flows. In this regime, the convective length and velocity scales and heat flux are all diffusion-free, i.e. independent of the viscosity and thermal diffusivity. Our direct numerical simulations (DNS) of rotating Rayleigh–Bénard convection in domains with no-slip top and bottom and periodic lateral boundary conditions for a fluid with the Prandtl number $Pr=1$ and extreme buoyancy and rotation parameters (the Rayleigh number up to $Ra=3\times 10^{13}$ and the Ekman number down to $Ek=5\times 10^{-9}$ ) indeed demonstrate all these diffusion-free scaling relations, in particular, that the dimensionless convective heat transport scales with the supercriticality parameter $\widetilde {Ra}\equiv Ra\, Ek^{4/3}$ as $Nu-1\propto \widetilde {Ra}^{3/2}$ , where $Nu$ is the Nusselt number. We further derive and verify in the DNS that with the decreasing $\widetilde {Ra}$ , the geostrophic turbulence regime undergoes a transition into another geostrophic regime, the convective heat transport in this regime is characterized by a very steep $\widetilde {Ra}$ -dependence, $Nu-1\propto \widetilde {Ra}^{3}$ .

Simulating small-scale dynamo action in cool main-sequence stars

Context. The origin of the ubiquitous small-scale magnetic field observed on the solar surface can be attributed to the presence of a small-scale dynamo (SSD) operating in the sub-surface layers of the Sun. It is expected that a similar process could self-sustain a considerable amount of magnetic energy also in the near-surface layers of cool main-sequence stars other than the Sun. Aims. In this paper the properties of the magnetic field resulting from SSD action operating in the near-surface layers of four cool main-sequence stars and its self-organization into magnetic flux concentrations are investigated numerically. Methods. Three-dimensional radiative magnetohydrodynamic simulations of SSD action in the near-surface layers of four cool main-sequence stars of spectral types K8V, K2V, G2V, and F5V are carried out with the CO5BOLD code. The simulations are set up to have approximately the same Reynolds and magnetic Reynolds numbers, and to disentangle the impact of the effective temperature and the surface gravity on the SSD action from numerical effects. Results. It is found that the SSD growth rates in SI units differ for the four stellar models; the highest and lowest growth rate is for the K2V and F5V model, respectively. This is due to the different turnover times in the four simulations. Even so, the SSD field strengths reached in the saturation phases are similar in all models, with the same amount of kinetic energy converted into magnetic energy. If the magnetic energy that is pumped out from the computational domain across the bottom boundary is partially replenished from outside of the computational domain, we find that the SSD action leads to a sufficient reduction in the convective velocities to reduce the convective horizontal length scales in the convection zone by 5–10%, vanishing towards the optical depth unity level. In this case, strong kilogauss magnetic flux concentrations emerge at the surface, leading to magnetic bright features, which are more numerous and conspicuous for the K2V and G2V models than for the K8V and F5V models. Their vertical magnetic field component on the surface of optical depth unity increases from 1 kG to 1.6 kG with decreasing effective temperature from F5V to K8V. However, more than 90% of the magnetic flux through any of these stellar surfaces has a field strength of less than 1 kG.

Convective scale and subadiabatic layers in simulations of rotating compressible convection

Context. Rotation is thought to influence the size of convective eddies and the efficiency of convective energy transport in the deep convection zones of stars. Rotationally constrained convection has been invoked to explain the lack of large-scale power in observations of solar flows. Aims. Our main aims are to quantify the effects of rotation on the scale of convective eddies and velocity as well as the depths of convective overshoot and subadiabatic Deardorff layers. Methods. We ran moderately turbulent three-dimensional hydrodynamic simulations of rotating convection in local Cartesian domains. The rotation rate and luminosity of the simulations were varied in order to probe the dependency of the results on Coriolis, Mach, and Richardson numbers measuring the influences of rotation, compressibility, and stiffness of the radiative layer. The results were compared with theoretical scaling results that assume a balance between Coriolis, inertial, and buoyancy (Archimedean) forces, also referred to as the CIA balance. Results. The horizontal scale of convective eddies decreases as rotation increases, and it ultimately reaches a rotationally constrained regime consistent with the CIA balance. Using a new measure of the rotational influence on the system, we found that even the deep parts of the solar convection zone are not in the rotationally constrained regime. The simulations captured the slowly and rapidly rotating scaling laws predicted by theory, and the Sun appears to be in between these two regimes. Both the overshooting depth and the extent of the Deardorff layer decrease as rotation becomes more rapid. For sufficiently rapid rotation, the Deardorff layer is absent due to the symmetrisation of upflows and downflows. However, for the most rapidly rotating cases, the overshooting increases again due to unrealistically large Richardson numbers that allow convective columns to penetrate deep into the radiative layer. Conclusions. Relating the simulations with the Sun suggests that the convective scale, even in the deep parts of the Sun, is only mildly affected by rotation and that some other mechanism is needed to explain the lack of strong large-scale flows in the Sun. Taking the current results at face value, the overshoot and Deardorff layers are estimated to span roughly 5% of the pressure scale height at the base of the convection zone in the Sun.