arXiv subjects

M. J. Korpi

Publications and source records attributed to M. J. Korpi.

At least 19 recordsLinked to original sources

arXiv2011

Open and closed boundaries in large-scale convective dynamos

Context. Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. Aims. Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Methods. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos. Open (vertical-field) and closed (perfect-conductor) boundary conditions are used for the magnetic field. The shear flow is such that the contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. Results. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate of the field in this regime increases as Rm^(1/2). Regarding the nonlinear regime, the saturation level of the energy of the total magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

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arXiv2011

From convective to stellar dynamos

Convectively driven dynamos with rotation generating magnetic fields on scales large compared with the scale of the turbulent eddies are being reviewed. It is argued that such fields can be understood as the result of an alpha effect. Simulations in Cartesian domains show that such large-scale magnetic fields saturate on a time scale compatible with the resistive one, suggesting that the magnitude of the alpha effect is here still constrained by approximate magnetic helicity conservation. It is argued that, in the absence of shear and/or any other known large-scale dynamo effects, these simulations prove the existence of turbulent alpha^2-type dynamos. Finally, recent results are discussed in the context of solar and stellar dynamos.

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arXiv2010

Convective dynamos in spherical wedge geometry

Self-consistent convective dynamo simulations in wedge-shaped spherical shells are presented. Differential rotation is generated by the interaction of convection with rotation. Equatorward acceleration and dynamo action are obtained only for sufficiently rapid rotation. The angular velocity tends to be constant along cylinders. Oscillatory large-scale fields are found to migrate in the poleward direction. Comparison with earlier simulations in full spherical shells and Cartesian domains is made.

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arXiv2010

The alpha effect in rotating convection with sinusoidal shear

Using three-dimensional convection simulations it is shown that a sinusoidal variation of horizontal shear leads to a kinematic αeffect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the streamwise direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of αusing an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the αeffect.

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arXiv2009

Reynolds stresses from hydrodynamic turbulence with shear and rotation

To study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation. Three-dimensional numerical simulations are used to study turbulent transport under the influences of large-scale shear and rotation in homogeneous, isotropically forced turbulence. We study three cases: one with only shear, and two others where in addition to shear, rotation is present. These cases differ by the angle (0 or 90\degr) the rotation vector makes with respect to the z-direction. Two subsets of runs are performed with both values of θwhere either rotation or shear is kept constant. When only shear is present, the off-diagonal stress can be described by turbulent viscosity whereas if the system also rotates, nondiffusive contributions (Λ-effect) to the stress can arise. Comparison of the direct simulations are made with analytical results from a simple closure model. We find that the turbulent viscosity is of the order of the first order smoothing result in the parameter regime studied and that for sufficiently large Reynolds numbers the Strouhal number, describing the ratio of correlation to turnover times, is roughly 1.5. This is consistent with the closure model based on the minimal tau-approximation which produces a reasonable fit to the simulation data for similar Strouhal numbers. In the cases where rotation is present, separating the diffusive and nondiffusive components of the stress turns out to be challenging but taking the results at face value, we can obtain nondiffusive contributions of the order of 0.1 times the turbulent viscosity. We also find that the simple closure model is able to reproduce most of the qualitative features of the numerical results provided that the Strouhal number is of the order of unity.

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arXiv2009

Surface temperature maps for II Peg during 1999-2002

The active RS CVn star II Peg has been spectroscopically monitored for almost 18 years with the SOFIN spectrograph at NOT, La Palma, Spain. In this paper we present five new surface temperature maps of the object for the years 1999 (two maps), 2001 (one map) and 2002 (two maps).

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arXiv2009

Solar active regions: a nonparametric statistical analysis

The sunspots and other solar activity indicators tend to cluster on the surface of the Sun.These clusters very often occur at certain longitudes that persist in time.It is of general interest to find new and simple ways to characterize the observed distributions of different indicators and their behaviour in time. In the present work we use Greenwich sunspot data to evaluate statistical but not totally coherent stability of sunspot distribution along latitudes as well as longitudes. The aim was to obtain information on the longitudinal distribution of the underlying spot-generating mechanism rather than on the distribution and migration of sunspots or sunspot groups on the solar surface. Therefore only sunspot groups were included in the analysis, and only the time of their first appearance was used. We use simple nonparametric approach to reveal sunspot migration patterns and their persistency. Our analysis shows that regions where spots are generated tend to rotate differentially as the spots and spot groups themselves do. The activity areas, however, tend to break down relatively fast, during 7-15 solar rotations. This study provides a challenge for solar dynamo models, as our results are consistent with the presence of a non-axisymmetric spot-generating mechanism experiencing differential rotation (known as phase mixing in dynamo theory). The new nonparametric method introduced here, completely independent of the choice of the longitudinal distribution of sunspots, was found to be a very powerful tool for spatio-temporal analysis of surface features.

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arXiv2009

Alpha effect and turbulent diffusion from convection

(abridged) Aims: To study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods: We use the test field method together with 3D numerical simulations of turbulent convection with shear and rotation to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. 1D mean-field models are used with the derived turbulent transport coefficients to compare with direct simulations. Results: The alpha-effect increases monotonically as rotation increases. Turbulent diffusivity, eta_t, is proportional to the square of the turbulent vertical velocity. Whereas eta_t decreases approximately inversely proportional to the wavenumber of the field, the alpha-effect and turbulent pumping show a more complex behaviour. In the presence of shear and no rotation a small alpha-effect is induced which does not seem to show any consistent trend as a function of shear. If the shear is large enough, this small alpha is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are well below those in direct simulations suggesting that an incoherent alpha-shear dynamo may also act in them. If both rotation and shear are present, the alpha-effect is more pronounced. The combination of the shear-current and Omega x J-effects is also stronger than in the case of shear only, but subdominant to the alpha-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

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arXiv2009

Large-scale dynamos in rigidly rotating turbulent convection

The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the alpha-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent alpha-effect. This result demonstrates the existence of an alpha-effect and an alpha^2-dynamo with natural forcing.

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arXiv2008

Turbulent stresses as a function of shear rate in a local disk model

We present local numerical models of accretion disk turbulence driven by the magnetorotational instability with varying shear rate. The resulting turbulent stresses are compared with predictions of a closure model in which triple correlations are modelled in terms of quadratic correlations. This local model uses five nondimensional parameters to describe the properties of the flow. We attempt to determine these closure parameters for our simulations and find that the model does produce qualitatively correct behaviour. In addition, we present results concerning the shear rate dependency of the magnetic to kinetic energy ratio. We find both the turbulent stress ratio and the total stress to be strongly dependent on the shear rate.

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arXiv2008

Large-scale dynamos in turbulent convection with shear

(abridged) Aims: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. Methods: We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results: Without shear no large-scale dynamos are found even if the ingredients necessary for the alpha-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.

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arXiv2006

Effects of Rotation and Input Energy Flux on Convective Overshooting

We study convective overshooting by means of local 3D convection calculations. Using a mixing length model of the solar convection zone (CZ) as a guide, we determine the Coriolis number (Co), which is the inverse of the Rossby number, to be of the order of ten or larger at the base of the solar CZ. Therefore we perform convection calculations in the range Co = 0...10 and interpret the value of Co realised in the calculation to represent a depth in the solar CZ. In order to study the dependence on rotation, we compute the mixing length parameters alpha_T and alpha_u relating the temperature and velocity fluctuations, respectively, to the mean thermal stratification. We find that the mixing length parameters for the rapid rotation case, corresponding to the base of the solar CZ, are 3-5 times smaller than in the nonrotating case. Introducing such depth-dependent alpha into a solar structure model employing a non-local mixing length formalism results in overshooting which is approximately proportional to alpha at the base of the CZ. Although overshooting is reduced due to the reduced alpha, a discrepancy with helioseismology remains due to the steep transition to the radiative temperature gradient. In comparison to the mixing length models the transition at the base of the CZ is much gentler in the 3D models. It was suggested recently (Rempel 2004) that this discrepancy is due to the significantly larger (up to seven orders of magnitude) input energy flux in the 3D models in comparison to the Sun and solar models, and that the 3D calculations should be able to approach the mixing length regime if the input energy flux is decreased by a moderate amount. We present results from local convection calculations which support this conjecture.

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arXiv2006

Kinematic frames and "active longitudes": does the Sun have a face?

It has recently been claimed that analysis of Greenwich sunspot data over 120 years reveals that sunspot activity clusters around two longitudes separated by 180 degrees (``active longitudes'') with clearly defined differential rotation during activity cycles.In the present work we extend this critical examination of methodology to the actual Greenwich sunspot data and also consider newly proposed methods of analysis claiming to confirm the original identification of active longitudes. Our analysis revealed that values obtained for the parameters of differential rotation are not stable across different methods of analysis proposed to track persistent active longitudes. Also, despite a very thorough search in parameter space, we were unable to reproduce results claiming to reveal the century-persistent active longitudes. We can therefore say that strong and well substantiated evidence for an essential and century-scale persistent nonaxisymmetry in the sunspot distribution does not exist.

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arXiv2006

Solar dynamo models with alpha-effect and turbulent pumping from local 3D convection calculations

(abridged) Results from kinematic solar dynamo models employing alpha-effect and turbulent pumping from local convection calculations are presented. We estimate the magnitude of these effects to be around 2-3 m/s. The rotation profile of the Sun as obtained from helioseismology is applied. We obtain an estimate of the ratio of the two induction effects, C_alpha/C_Omega \approx 10^-3, which we keep fixed in all models. We also include a one-cell meridional circulation pattern having a magnitude of 10-20 m/s near the surface and 1-2 m/s at the bottom of the convection zone. The model essentially represents a distributed turbulent dynamo, as the alpha-effect is nonzero throughout the convection zone, although it concentrates near the bottom of the convection zone obtaining a maximum around 30 degrees of latitude. Turbulent pumping of the mean fields is predominantly down- and equatorward. We find that, when all these effects are included in the model, it is possible to correctly reproduce many features of the solar activity cycle, namely the correct equatorward migration at low latitudes and the polar branch at high latitudes, and the observed negative sign of B_r B_phi. Although the activity clearly shifts towards the equator in comparison to previous models due to the combined action of the alpha-effect peaking at midlatitudes, meridional circulation and latitudinal pumping, most of the activity still occurs at too high latitudes (between 5-60 degrees). Other problems include the relatively narrow parameter space within which the preferred solution is dipolar (A0), and the somewhat too short cycle lengths of the solar-type solutions. The role of the surface shear layer is found to be important only in the case where the alpha-effect has an appreciable magnitude near the surface.

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arXiv2006

Local models of stellar convection III: The Strouhal number

Aims: The Strouhal number (St), which is a nondimensional measure of the correlation time, is determined from numerical models of convection. The Strouhal number arises in the mean-field theories of angular momentum transport and magnetic field generation, where its value determines the validity of certain widely used approximations, such as the first order smoothing (hereafter FOSA). More specifically, the relevant transport coefficients can be calculated by means of a cumulative series expansion if St < St_crit \approx 1. Methods: We define the Strouhal number as the ratio of the correlation and turnover times, which we determine separately, the former from the autocorrelation of velocity, and the latter by following test particles embedded in the flow. Results: We find that the Strouhal numbers are, generally, of the order of 0.1 to 0.4 which is close to the critical value above which deviations from FOSA become significant. Increasing the rotational influence tends to shorten both timescales in such a manner that St decreases. However, we do not find a clear trend as function of the Rayleigh number for the parameter range explored in the present study.

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arXiv2006

Magnetoconvection and dynamo coefficients III: alpha-effect and magnetic pumping in the rapid rotation regime

Aims. The alpha- and gamma-effects, which are responsible for the generation and turbulent pumping of large scale magnetic fields, respectively, due to passive advection by convection are determined in the rapid rotation regime corresponding to the deep layers of the solar convection zone. Methods. A 3D rectangular local model is used for solving the full set of MHD equations in order to compute the electromotive force (emf), E = , generated by the interaction of imposed weak gradient-free magnetic fields and turbulent convection with varying rotational influence and latitude. By expanding the emf in terms of the mean magnetic field, E_i = a_ij , all nine components of a_ij are computed. The diagonal elements of a_ij describe the alpha-effect, whereas the off-diagonals represent magnetic pumping. The latter is essentially the advection of magnetic fields by means other than the underlying large-scale velocity field. Comparisons are made to analytical expressions of the coefficients derived under the first-order smoothing approximation (FOSA). Results. In the rapid rotation regime the latitudinal dependence of the alpha-components responsible for the generation of the azimuthal and radial fields does not exhibit a peak at the poles, as is the case for slow rotation, but at a latitude of about 30 degrees. The magnetic pumping is predominantly radially down- and latitudinally equatorward as in earlier studies. The numerical results compare surprisingly well with analytical expressions derived under first-order smoothing, although the present calculations are expected to lie near the limits of the validity range of FOSA.

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arXiv2005

Local models of stellar convection II: Rotation dependence of the mixing length relations

We study the mixing length concept in comparison to three-dimensional numerical calculations of convection with rotation. In a limited range, the velocity and temperature fluctuations are linearly proportional to the superadiabaticity, as predicted by the mixing length concept and in accordance with published results. The effects of rotation are investigated by varying the Coriolis number, Co = 2 Omega tau, from zero to roughly ten, and by calculating models at different latitudes. We find that αdecreases monotonically as a function of the Coriolis number. This can be explained by the decreased spatial scale of convection and the diminished efficiency of the convective energy transport, the latter of which leads to a large increase of the superadibaticity, δ= \nabla - \nabla_ad as function of Co. Applying a decreased mixing length parameter in a solar model yields very small differences in comparison to the standard model within the convection zone. The main difference is the reduction of the overshooting depth, and thus the depth of the convection zone, when a non-local version of the mixing length concept is used. Reduction of αby a factor of roughly 2.5 is sufficient to reconcile the difference between the model and helioseismic results. The numerical results indicate reduction of αby this order of magnitude.

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arXiv2004

Estimates of the Strouhal number from numerical models of convection

We determine the Strouhal number (hereafter St), which is essentially a nondimensional measure of the correlation time, from numerical calculations of convection. We use two independent methods to estimate St. Firstly, we apply the minimal tau-approximation (MTA) on the equation of the time derivative of the Reynolds stress. A relaxation time is obtained from which St can be estimated by normalising with a typical turnover time. Secondly, we calculate the correlation and turnover times separately, the former from the autocorrelation of velocity and the latter by following test particles embedded in the flow. We find that the Strouhal number is in general of the order of 0.1 to 1, i.e. rather large in comparison to the typical assumption in the mean-field theories that St << 1. However, there is a clear decreasing trend as function of the Rayleigh number and increasing rotation. Furthermore, for the present range of parameters the decrease of St does not show signs of saturation, indicating that in stellar convection zones, where the Rayleigh numbers are much larger, the Strouhal number may indeed be significantly smaller.

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