Vortices in Simulations of Solar Surface Convection Rainer Moll with Robert Cameron and Manfred Schüssler Solar Group Seminar March 22, 2011 Fig.: Intensity and velocity streamlines ( 1400 350 km)
Simulations of solar surface convection MURaM code (A. Vögler) solves the MHD equations in a Cartesian grid Includes radiative transfer Equation of state incorporates effects of partial ionization Bottom boundary: in- and outflow with inflows vertical, pressure & entropy total mass constant radiative energy loss solar luminosity Top boundary closed Horizontal boundaries periodic Introduction 1 / 19
Simulations of solar surface convection: typical result hot upflows cool downflows vertical velocity (at z optical surface) Introduction 2 / 19
Simulations of solar surface convection: typical result hot upflows cool downflows bolometric intensity Introduction 2 / 19
A bright vertical vortex Cuts at the average height of the optical surface: vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 25 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 50 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 76 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 101 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 126 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 101 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 76 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 50 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 25 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex Cuts at the average height of the optical surface: t = 0 s vortical streamlines in downflow lane, diameter 80 km decreased gas pressure and density locally bright Introduction 3 / 19
A bright vertical vortex 3D visualization of streamlines and the optical surface: Central depression of the optical surface: 110 km below the average height Introduction 4 / 19
Detection of vortices High vorticity v is not a good indicator for vortices, because it can be high also in non-rotating shear flows (!) x v x y v x z v x Eigenanalysis of the velocity gradient tensor x v y y v y z v y x v z y v z z v z All eigenvalues real no swirl One real, two complex conjugate eigenvalues swirling flow Imaginary part λ ci = swirling strength : 2π/λ ci = rotation period in case of rigid rotation Eigenvector corresponding to real eigenvalue λ r = vortex inclination Signs of eigenvalues contain additional information about the vortex, e.g. spiraling inward & diverging: Galilean invariant (unlike streamlines!) Haimes & Kenwright 1999 Methods 5 / 19
Swirling regions: an unsteady, tangled network of filaments τ =1 surface size of the box: 4.8 4.8 1.4 Mm Occurrence of Vortices 6 / 19
Strong swirls near the optical surface Vertical swirls: at the center of downflow lanes Horizontal swirls: at the edge of granules (swirling period < 2 minutes) Occurrence of Vortices 7 / 19
Strong swirls near the optical surface Vertical swirls: at the center of downflow lanes Horizontal swirls: at the edge of granules Occurrence of Vortices 7 / 19
Vortex coverage as f (height) Strong swirls mostly at a few 100 km below the optical surface Deep swirls are slow (but same filamentary structure) Isotropy horizontal swirls (dotted lines) more numerous than vertical ones (dashed lines) Occurrence of Vortices 8 / 19
Histograms: swirling period and inclination swirling period < 2 minutes Deep: isotropy High: preferentially horizontal and vertical orientations Fraction with period < 2 minutes: 5 24% Statistical Properties 9 / 19
Histograms: gas pressure and mass density Depressed and rarefied (with respect to mean in downflows) Not much dependence on height and orientation Statistical Properties 10 / 19
Histograms: temperature and vertical velocity Mean T / T 1 at all heights, distribution broader at low depth Vertical swirls: stronger downflow and lower median temperature Statistical Properties 11 / 19
2D histograms: B and intensity vs swirling strength Rarely strong magnetic fields in strong swirls No clear trend towards higher intensity brightness differences between different lanes dominate Statistical Properties 12 / 19
Contiguous vortex features Above the τ = 1 surface, swirling period < 60 s, volume 100 grid cells (5.6 10 4 km 3 ): Vortex orientations are in alignment with the features. Statistical properties agree with point-by-point statistics Contiguous Features 13 / 19
Examples Formation of a strong vertical vortex, box size: 1.1 1.1 0.8 Mm Rise and fall of a vortex arc, box size: 1.5 1.5 0.8 Mm Some Examples 14 / 19
Examples Visual inspection of several features, mean lifetime 3:30 minutes (standard deviation 1:40 minutes) Formation of a strong vertical vortex, box size: 1.1 1.1 0.8 Mm where lifetime visible as distinct entity above the τ = 1 surface Rise and fall of a vortex arc, box size: 1.5 1.5 0.8 Mm Some Examples 14 / 19
Vortex arcs Big arc: length 1.4 Mm, peak height 330 km above τ = 1 Small arc: length 310 km, peak height 210 km above τ = 1, rapidly moving, not visible in streamlines Some Examples 15 / 19
Vortex arcs Big arc: length 1.4 Mm, peak height 330 km above τ = 1 Small arc: length 310 km, peak height 210 km above τ = 1, rapidly moving, not visible in streamlines Some Examples 15 / 19
Evolution of the small vortex arc Moving 2.7 km s 1 horizontally and 1.3 km s 1 vertically Underdense (ϱ is 87% of mean) buoyant? Not clear, probably not. Some Examples 16 / 19
Large-scale vortex motion in observations Bonet et al. 2008 tracked magnetic bright points and found a logarithmic spiral: Observations 17 / 19
Large-scale vortex motion in observations Maximum of the swirling strength in a 3 minute time frame and pseudo pathlines (apparent fluid trajectories from horizontal v): Curved cork trajectories can indicate a strong central vortex, but may also be misleading in some cases. Observations 18 / 19
Summary By doing an eigenanalysis of the velocity gradient tensor we detect small-scale vortices in solar convection simulations: Vortical flows form a tangled, filamentary network in downflow lanes Vertically oriented vortices in the center of the intergranules Horizontally oriented vortices at the edges of the granules Most vortices are spiraling inward and diverging in vortex direction Highly unsteady, lifetimes of several minutes Depression of the optical surface potentially observable as bright points Cork animations with curved trajectories at granular scale can indicate a strong central vortex, but one must be careful Summary 19 / 19