Convection Velocity Research Articles

Variation of vortical structures across shock-wave/turbulent boundary-layer interaction region in a compression ramp flow

This paper describes direct numerical simulations of a shock-wave/turbulent boundary-layer interaction (STBLI) process in a compression-ramp flow with a ramp angle of 24° and a free-stream Mach number of Ma∞=2.9. Spectral analysis, two-point cross correlation, convection velocity statistics, and individual vortex identification are used to elucidate the streamwise variation of multiscale turbulent structures in the STBLI process. Typical Lagrangian coherent structures in the turbulent boundary layer before the STBLI region are characterized as hairpin-like vortical structures, with heads that rise together with the separated mean flow in the STBLI region. In the downstream region, the reattached turbulent boundary layer has a two-layer structure. The outer layer is characterized as an intensification of large-scale velocity structures, which is attributed to the shock-wave-induced compression effect on vortical structures. A viscous-dominated layer develops independently in the vicinity of the wall, leading to a gradual restoration of the wall-shear effect that accumulates the inner-layer dynamics of small-to-moderate-scale turbulent motions.

Debris-induced consequences on turbulence and vorticity in solar photovoltaic module-generated array wakes

Particle-laden flows in solar photovoltaic (PV) systems are inevitable, where wind-swept debris in open environments are carried by high winds and turbulence, coating panel surfaces or damaging structures. Particle deposition, or soiling, is a well-known issue for large-scale plants which rely on uninhibited solar rays for optimal production. But understanding the mechanisms leading to soiling requires a physical and fluid dynamics-centered focus, since turbulence dominates PV panel wakes and is also known to alter particle concentration and trajectories. This study presents an experimental campaign toward consequences of particle-laden flow between two model PV panels using time-resolved particle image velocimetry. The model array was subjected to varied particle volume fractions, including a tracer particle case and a water droplet case. Characterization of mean velocity, turbulence statistics, and mean kinetic energy within the single phase and, separately, particle phase flows showed modified features due to particle inertia. Images captured at a frequency of 1 kHz in the near wake of the upstream panel allow for a first experimental look at vorticity and convective velocity of vortex structures for single-phase and particle-phase flows which are crucial to debris transport and soiling in PV environments.

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, $Nu-1\propto \widetilde {Ra}^{3}$ .

Direct numerical simulations of supersonic flat-plate turbulent boundary layers with uniform blowing

The effect of uniform blowing on a spatially developing flat-plate turbulent boundary layer at Mach 2.25 is investigated using direct numerical simulations. Two values of the wall blowing ratio are considered, corresponding to low and high blowing rates. Uniform blowing is found to significantly reduce the near-wall turbulence anisotropy, although the turbulent kinetic energy still exhibits near-wall asymptotic behavior and the Reynolds analogy is relatively insensitive to changes in the blowing ratio. The pre-multiplied spectra of turbulent kinetic energy production demonstrate that increasing the blowing ratio significantly energizes the large-scale structures in the outer region, while suppressing the inner small-scale structures. An increase in the blowing ratio also has a strong influence on the behavior of the fluctuating wall pressure, amplifying the fluctuation intensity and reducing the dominant frequencies in the power spectrum. Two-point space–time correlations indicate that the characteristic length scale of the pressure fluctuations increases with increasing blowing ratio, whereas the convection velocity exhibits the opposite trend. Analysis of the reduced mean wall heat flux reveals that it is dominated by the relative balance between the work of the Reynolds stress and the turbulent transport of heat, but is insensitive to uniform blowing. Importantly, bidimensional empirical mode decomposition of the turbulent structures highlights the increasingly dominant contributions related to the significantly energized outer large-scale structures in the blowing region.

Generalized eddy‐diffusivity mass‐flux formulation for the parametrization of atmospheric convection and turbulence

AbstractThe atmospheric convection is a phenomenon that has a length scale smaller than the resolution at which the state‐of‐the‐art general circulation numerical models are running, and thus the convection needs to be parametrized. In this work, a theoretical formulation for the parametrization of subgrid‐scale convection based on subgrid averaging that represents a generalized eddy‐diffusivity mass‐flux formulation is presented. The subgrid fluxes are derived by considering a decomposition of subgrid variables into convective and turbulent variables, and by assuming that the convection is modeled by round convective plumes with generic radial profiles. The main difference between our formulation and the mass‐flux formulations is that the condition of a very small fractional area occupied by the convection is replaced with the condition that the convective vertical velocity goes to the mean state far from the updraft region of the plume. The plume model can also be generalized by considering that the convective elements are energy‐consistent plumes, governed by the conservation of mass, momentum, kinetic energy, and buoyancy, which provides a physical‐based closure for the entrainment. Therefore, the closing problem of our formulation consists of the specification of the convective radial profiles and the boundary conditions at the initial vertical level. Furthermore, our formulation allows one to consider more realistic profiles for the convective variables, making the formulation suitable for the parametrization of atmospheric convection at the convective gray zone. This aspect is discussed in the last part of this work, where it is showed how the formulation can be implemented at any resolution. Moreover, in the present framework, no distinct assumptions are required for each convective type, thus facilitating the parametrization of convection in a unified way.

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.

Asphaltene Adsorption on Solid Surfaces Investigated Using Quartz Crystal Microbalance with Dissipation under Flow Conditions.

Asphaltenes can cause operational challenges in petroleum production facilities and adversely affect production by adsorption on mineral surfaces and alteration of the oil wettability of reservoirs. Therefore, understanding asphaltene adsorption mechanisms and their effects is crucial to improving the efficiency of oil production and reducing costs. In this study, we focus on understanding the impact of asphaltene concentration and the depositing environment of asphaltene adsorption on solid surfaces using the quartz crystal microbalance with dissipation (QCM-D) technique. The initial and long-term kinetics of adsorption at different concentrations were examined on three different solid surfaces including silicon dioxide to represent quartz mineral, stainless steel, and gold. The frequency-dissipation data showed evidence of monolayer adsorption initially, followed by multilayer formation. At short times, the adsorbed mass increased linearly with time, suggesting that the process was kinetically controlled rather than diffusion-controlled. The results were reproducible and did not depend on convection velocity but did depend on the surface material. At later stages, the monolayer development appeared to follow the random sequential adsorption (RSA) theory. Once multilayer adsorption commenced, the rates agreed well with the two-layer model of Zhu and Gu, 1990. The impact of asphaltene adsorption on the wettability of the surface was examined using contact angle studies, which showed decreasing water wettability with an increase in the adsorbed mass. The contact angle of water after 12 h of adsorption leveled off at around 100° on all three surfaces. Contact angle measurements were also used to evaluate if brine salinity causes the wettability alteration of surfaces with the adsorbed asphaltene. The results indicate that at 3% NaCl solution, the contact angle decreased only slightly by less than 2°.

Marangoni Convection Velocity in Nonlinear Hanging-Droplet Vibration Phenomena

The Marangoni effect involves a mass transfer along an interface between two phases owing to the gradient of the interfacial tension. The flow caused by this phenomenon is called Marangoni convection, a complex phenomenon that involves mass transfer processes, such as surfactant adsorption/desorption processes, solvent dissolution phenomena, and viscous dissipation processes. Therefore, the strength of the convection depends on the various thermodynamic and physical properties of the fluids. In this study, we experimentally investigated the relationship between the Marangoni convection generated inside a hanging oil droplet and the interfacial tension of the oil droplet in an aqueous phase by the particle image velocimetry method. This convection velocity depended on the initial value of the interfacial tension in the oil–water interfacial tension oscillation phenomenon accompanied by the expansion and contraction of the hanging drop. Additionally, the droplet oscillation frequency decreased as the Marangoni convection velocity increased. Furthermore, continuous convection, which is unlike Marangoni convection, was observed within this spontaneously expanding and contracting hanging-droplet system. This buoyant convection was caused by the mutual dissolution of the hanging-droplet oil phase and the surrounding aqueous phase.

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.

Fluid–acoustic interactions around an expanding pipe with orifice plates

Expanding pipes with orifice plates are often utilized as silencers for fluid machinery. However, intense tonal sounds can be generated from a flow through such expanding pipes. To clarify the mechanism of tonal sound from a flow through a circular expanding pipe with two orifice plates and the conditions for intense acoustic radiation, the flow and acoustic fields are directly solved based on the compressible Navier–Stokes equations. Phase-averaged flow fields indicate the occurrence of periodic vortex shedding in the free shear layers of the expanding pipe, resulting in acoustic radiation. The effects of the orifice radius and freestream Mach number on the acoustic radiation are focused on. The computational results demonstrate that vortex rings or spiral vortices are generated in the cavities formed by the orifice plates, where the primary vortical shape changes, depending on the freestream Mach number and orifice radius. The collision of the vortex ring and spiral vortex with the orifice plate or downstream edge of the expanding pipe leads to the occurrence of circumferentially in-phase and one-wavelength-mode pressure fluctuations, respectively. The orifice radius also affects the convective velocity of vortices and the position of the acoustic source, varying the frequency of the acoustic radiation. The findings of this research provide the first clarifications of fluid–acoustic interactions in an expanding pipe with orifice plates.

A Short Intense Dynamo at the Onset of Crystallization in White Dwarfs

The origin of large magnetic fields (≳106 G) in isolated white dwarfs is not clear. One possible explanation is that crystallization of the star’s core drives compositional convection, which when combined with the star’s rotation, can drive a dynamo. However, whether convection is efficient enough to explain the large intensity of the observed magnetic fields is still under debate. Recent work has shown that convection in cooling white dwarfs spans two regimes: efficient convection at the onset of crystallization, and thermohaline convection during most of the star’s cooling history. Here, we calculate the properties of crystallization-driven convection for cooling models of several white dwarfs of different masses. We combine mixing-length theory with scalings from magnetorotational convection to estimate the typical magnitude of the convective velocity and induced magnetic field for both scenarios. In the thermohaline regime, we find velocities ∼10−6–10−5 cm s−1, with fields restricted to ≲ 100 G. However, when convection is efficient, the flow velocity can reach magnitudes of ∼102–103 cm s−1, with fields of ∼106–108 G, independent of the star’s rotation rate. Thus, dynamos driven at the onset of crystallization could explain the large intensity magnetic fields measured for single white dwarfs.

The Robin boundary condition for modelling heat transfer

The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature and the flux continuity) using rigorous mathematical analysis. Our main results are the following. We first show that a generalized version of the Robin boundary condition can be justified. Second, we prove that replacing the generalized by the standard Robin condition can be justified for high convection velocity if the conductivity of the surrounding liquid is much lower than that of the body. On the other hand, if the fluid conducts much better than the body, then the effective boundary condition is shown not to be the Robin one, but it involves second-order derivatives. We strongly believe that those findings bring new insights to the physics of the heat exchange processes and, thus, could prove useful in engineering practice.

Small-scale Anisotropies of Cosmic Rays from Turbulent Flow

Within the classical convection–diffusion approximation, we show that the angular distribution of cosmic rays (CRs) in a highly turbulent flow may exhibit significant small-scale anisotropies. The CR intensity angular power spectrum C ℓ is then a direct reflection of interstellar turbulence, from which one expects C ℓ ∝ ℓ −γ−1 for ℓ ≫ 1, where γ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law γ = 5/3 with a convection velocity dispersion of 20 km s−1 on the scale of 10 pc.

Asymptotic scaling relations for rotating spherical convection with strong zonal flows

We analyse the results of direct numerical simulations of rotating convection in spherical shell geometries with stress-free boundary conditions, which develop strong zonal flows. Both the Ekman number and the Rayleigh number are varied. We find that the asymptotic theory for rapidly rotating convection can be used to predict the Ekman number dependence of each term in the governing equations, along with the convective flow speeds and the dominant length scales. Using a balance between the Reynolds stress and the viscous stress, together with the asymptotic scaling for the convective velocity, we derive an asymptotic prediction for the scaling behaviour of the zonal flow with respect to the Ekman number, which is supported by the numerical simulations. We do not find evidence of distinct asymptotic scalings for the buoyancy and viscous forces and, in agreement with previous results from asymptotic plane layer models, we find that the ratio of the viscous force to the buoyancy force increases with Rayleigh number. Thus, viscosity remains non-negligible and we do not observe a trend towards a diffusion-free scaling behaviour within the rapidly rotating regime.

Composite control of airfoil broadband noise based on the combination of porous material and serrated trailing edges

Improving the noise reduction capability of airfoil broadband noise through serrated trailing edge design is a challenging task. To address this, we propose a novel porous-serrated trailing edge design where the gaps between the serrations are filled with porous media. Implicit large eddy simulations were conducted at Mach number Ma=0.1631 and Reynolds number Re=96 000 under a zero incidence angle. In addition to straight trailing edges and conventional serrated trailing edges, cutting-type porous-serrated (CPS) and insert-type porous-serrated (IPS) trailing edges with different porosities were designed. The flow in the porous media is described by Darcy's law, which is related to the pressure and velocity. The results indicate that the CPS trailing edges offer limited noise reduction compared to conventional serrated trailing edges, while IPS trailing edges achieve a significant noise reduction of approximately 5.21 dB. However, the drag force increases by 8.0% in the IPS case with maximum noise reduction. The composite control mainly affects flow structures near the trailing edges, especially inducing the flow penetration across the porous surface. To investigate the noise reduction mechanism, dynamic mode decomposition was conducted to show that both the CPS and IPS designs promote energy transferring significantly from the energetic mode to the modes at other frequencies, which would partly explain the difference in the noise reduction performance to some extent. Furthermore, the analysis of the wall pressure fluctuations reveals that the reduced convection velocity on the porous surface and enhanced destructive interference between the porous and the solid surfaces in IPS cases could be identified as the key factors contributing to lower noise radiation efficiency.

Measurement of the Convection Velocities in a Hypersonic Turbulent Boundary Layer Using Two-Point Cylindrical-Focused Laser Differential Interferometer

A two-point cylindrical-focused laser differential interferometer (2P-CFLDI) system and a conventional Z-type Schlieren were used to measure the hypersonic turbulent boundary layer on a flat plate at Mach number Ma = 6 and Reynolds number Re = 1.08 × 106 m−1. The boundary layer thickness at the measurement location and the noise radiation angle were obtained by post-processing the Schlieren image. The 2P-CFLDI data underwent cross-correlation analysis to calculate the mean convective velocities at different heights and compared with previous experimental and numerical results. The experimentally measured mean convective velocities agree with the trend of available DNS and experimental results. The mean convective velocity near the wall is significantly larger than the local mean velocity and is the main noise source region. Further filtering treatment shows that the convective velocity of the disturbed structure decreases gradually with the increase in the disturbance scale. The differences between convective velocities at different scales are significantly larger outside the boundary layer than inside the boundary layer, which is in agreement with the findings of the previous hot wire experiments. Near the wall, large-scale disturbances mainly determine the localized mean convective velocity, which are the main source of noise radiation for the hypersonic turbulent boundary layer.

Intensifying the particle deposition from a colloidal solution for the purpose of liquid purification: Comparison of deposition mechanisms and rates

The deposition of particles from a layer of colloidal solution (water and microparticles) has been experimentally studied in the presence of laser heating. Instantaneous temperature and velocity fields are measured using a thermal imager and the Particle Image Velocimetry and the Particle Tracking Velocimetry methods. The unstable behavior of the velocity field in the presence of heating and a free liquid surface are assumed to be determined by the Bond number (Bo). Of interest is also an additional mechanism for the instability formation when the Peclet number (Pe) exceeds the critical value and when the ratio of characteristic velocities VT/Vavr > 1, where VT is the heat front velocity at the initial moment of laser heating, and Vavr is the average convection velocity. A new mechanism of particle deposition due to the use of local laser heating is proposed for the first time. The control over local heating and local deposition increases the particle deposition rate by 2–3 orders compared with that without convection. The particle deposition rate and the deposit area increase with increasing height of the liquid layer, reach maximum values at a critical height, and then decrease sharply with increasing height. The dependence for determining the area and mass of the deposit is proposed to take into account the deposition time, the height of the liquid layer and the rate of convection. The resulting particle deposition method and calculation method may be used in technologies related to the purification of liquid from solid impurities in small volumes, as well as in problems where deposition in a given direction is required to form an ordered nanocoating.

Convection velocities in droplets before and after their collisions

High-speed video recording was used together with particle image velocimetry with tracer particles of titanium dioxide to study the characteristics of shifting and mixing of liquid layers in the coalescence, disruption, and separation of droplets. Convection velocities (Uc) were determined in droplets before and after their collisions. Vortex contours of different sizes and in different cross sections of droplets were derived. The average values of Uc were calculated. The effect of a group of factors on Uc was investigated. These factors include the relative velocity before the collision Urel, the ratio of droplet sizes Δ, the Weber number, the impact angle, and the rheological properties of liquid. Uc changed most significantly (more than threefold) from variations in Δ, Urel, and We. When varying the dimensionless linear interaction parameter B, Uc changed by 20%–40%. In disruption, Uc increased more than eightfold. In separation and coalescence, they increased by a factor of 10 and 11, respectively. The convection velocity was maximum after the collision. Then, 0.29–0.37 s after the collision, it fell to the values corresponding to a free-falling droplet. An increase in the convection velocity was compared for different droplet sizes and velocities before and after their interaction. Mathematical equations were obtained to predict the convection velocities affected by several investigated factors, taken separately or in combination. For the first time, the ranges of Uc were found, and the effect of a wide group of parameters (geometric sizes and velocities of droplets, rheological characteristics) on the velocities of convective flows was identified.

Modeling of temperature convection in microtubes under point heating: dependence of convection velocity on tilt angle

This paper presents the results of a study of the dependence of the convection velocity of a liquid in a microtube on the angle of inclination during point heating. This study utilizes a previously prepared finite-volume mesh of a cone-shaped microtube for use within the OpenFOAM software package. A detailed analysis and description of the mathematical model and a series of computational experiments using the built-in buoyantBoussinesqPimpleFoam solver are performed. An important step in this paper is the post-processing of the results obtained from a series of computational experiments. The paper provides a detailed description of the features of the data processing carried out for direct quantitative comparison of the results obtained in the individual experiments of the series. In the conducted computational experiments, quantitative data were obtained to reveal the dependence of the liquid convection velocity in a microtube on the angle of inclination during spot heating. From the obtained results, a significant influence of the inclination angle on the convection velocity was revealed, which can serve as a solution for the problems of optimization of mixing processes in microscale systems in the future.

Small-scale dynamo in cool stars

Context. Some of the quiet solar magnetic flux could be attributed to a small-scale dynamo (SSD) operating in the convection zone. An SSD operating in cool main-sequence stars is expected to affect the atmospheric structure, in particular, the convection, and should have observational signatures. Aims. We investigate the distribution of SSD magnetic fields and their effect on bolometric intensity characteristics, vertical velocity, and spatial distribution of the kinetic energy (KE) and magnetic energy (ME) in the lower photosphere of different spectral types. Methods. We analyzed the SSD and purely hydrodynamic simulations of the near surface layers of F3V, G2V, K0V, and M0V stars. We compared the time-averaged distributions and power spectra in SSD setups relative to the hydrodynamic setup. The properties of the individual magnetic fields are also considered. Results. The probability density functions with a field strength at the τ = 1 surface are quite similar for all cases. The M0V star displays the strongest fields, but relative to the gas pressure, the fields on the F3V star reach the highest values. In all stars, the horizontal field is stronger than the vertical field in the middle photosphere, and this excess becomes increasingly prominent toward later spectral types. These fields result in a decrease in the upflow velocities and a slight decrease in granule size, and also lead to formation of bright points in intergranular lanes. The spatial distribution of the KE and ME is also similar for all cases, implying that important scales are proportional to the pressure scale height. Conclusions. The SSD fields have rather similar effects on the photospheres of cool main-sequence stars: a significant reduction in convective velocities, as well as a slight reduction in granule size and a concentration of the field to kilogauss levels in intergranular lanes that is associated with the formation of bright points. The distribution of the field strengths and energies is also rather similar.