155. Hydrodynamic Properties of the Sun’s Giant Polar Vortices

Contributed by David H. Hathaway. Posted on April 6, 2021

Contributed by David H. Hathaway1 and Lisa A. Upton2

1. W. W. Hansen Experimental Physics Laboratory, Stanford University, Stanford, CA 94305
2. Space Systems Research Corporation, Alexandria, VA 22314

Solar convection is driven by radiative cooling at the Sun’s photosphere. Granules are the dominant manifestation of the process with typical dimensions of about 1 Mm. Radiative-hydrodynamical simulations show how the downdrafts at the corners of these cells plunge inward and join with other downdrafts to form larger and larger structures in deeper and deeper layers. The fact that the Sun is adiabatically stratified to a depth of 200 Mm indicates that convective mixing must extend to these depths. The existence of cells wide enough and deep enough to extend to depths of 200 Mm was proposed by George Simon and the recently departed Nigel Weiss[1].

The velocity spectrum of the convective structures observed in the photosphere[2] exhibits a decrease in velocity amplitude with increasing convection cell size from 3000 m/s at the peak representing granules (1 Mm wavelength), to 500 m/s at the bump representing supergranules (35 Mm wavelength), to velocities of only a few m/s for cells with wavelengths of 400 Mm. These values indicate turnover times/lifetimes of minutes for granules, about a day for supergranules, and months for the largest cells. Since the Sun rotates about once a month, the flows in the largest cells must be highly influenced by the Coriolis force.

In a recent ApJ paper[3] we improved the data analysis techniques we had previously used to discover giant cellular flows on the Sun[4]. It’s now apparent that there are two flow regimes for the giant cell flow structures – low latitude Rossby waves and high latitude vortices. The polar vortices (shown in Figure 1) have properties which are particularly important for the Sun’s convection zone dynamics and its magnetic dynamo, so we focus on the polar vortices in this science nugget.

Figure 1| Velocity streak-lines superimposed over a synchronic map of the vorticity field – blue for clockwise flow and red for counter-clockwise flow. The polar vortices organize themselves into chains of like vorticity that spiral into the poles. [ a 400 Mb movie covering 10 years is available for download at: http://solarcyclescience.com/bin/SolarVortices.mp4 ]

We track the motions of the Doppler patterns associated with supergranules as seen in the 720s averaged full-disk Dopplergrams obtained by the HMI instrument on the SDO mission. This gives us good high-latitude coverage. We begin by removing the Doppler signals due to solar rotation, differential rotation, meridional circulation, convective blue shift, and spacecraft motion to isolate the supergranules. We then map the hourly Dopplergrams to heliographic longitude and latitude and cross-correlate circular patches 90 Mm in diameter from pairs of maps separated by 4 hours to find the displacement (and thus horizontal velocity) that maximizes the correlation between the two patches. We made these measurements hourly from the start of the SDO mission in May of 2010 through March of 2020. Following the local correlation tracking step, we remove the velocity signals that are fixed relative to the observed disk (primarily differential rotation and meridional flow) in order to isolate the non-axisymmetric giant cellular flows of interest here.

Synchronic maps of these non-axisymmetric flow velocities are constructed by averaging the hourly measurements over the 34 days it takes for the cellular pattern to rotate back into view at the highest latitudes. An example of the north polar region is shown in Figure 1.

We find that the flows are toroidal in the sense that the curl of the horizontal velocity is much stronger than the divergence. We can use the divergence of the velocity as a proxy for the radial flow and take its dot product with the radial vorticity to determine the kinetic helicity of the flow. These measurements, averaged over longitudes and 6-month intervals, are shown in Figure 2 as a function of latitude. The kinetic helicity is negative (left-handed) in the north and positive (right-handed) in the south. The dominance of toroidal flow and the hemispheric difference in the sign of kinetic helicity, are expected from the effects of the Sun’s rotation on these large, slow flows.

Figure 2| (Left) Kinetic helicity (normalized) as a function of latitude from daily synchronic maps of the giant cell flows. The kinetic helicity is left-handed in the north and right-handed in the south. (Right) Reynolds stress given by the correlation between prograde and southward flows. Positive values in the north and negative values in the south indicate an equatorward (up gradient) transport of angular momentum.

We can readily measure the latitudinal transport of angular momentum – a component of the Reynolds stress tensor given by the longitudinal average of the product of the latitudinal velocity and the longitudinal velocity (see Figure 2). Positive values in the north indicate a correlation between prograde and southward flows and/or retrograde and northward flows – a stress that is needed to maintain the Sun’s differential rotation with a rapidly rotating equator and more slowly rotating poles.

Finally, we measure how the giant cell pattern itself drifts in longitude with differential rotation and in latitude with the meridional circulation by cross-correlating the vorticity features in the daily synchronic maps (see Figure 3). The high latitude polar vortices rotate faster than the magnetic network – an indication that these cells are carried by the differential rotation near the base of the convection zone. For the meridional drift, the polar vortices drift poleward with a velocity of a couple m/s.

Figure 3| (Left) Differential rotation relative to the Carrington rate for the giant cellular structures (black) and for the magnetic network elements (red). The polar vortices rotate at a rate that matches that at the base of the convection zone. (Right) Meridional motion of the giant cellular structures. The Polar vortices drift poleward with peak velocities of about 2 m/s.

We find that the Sun’s polar vortices are highly constrained by the Sun’s rotation. The flows are dominated by vorticity. They form chains of connected cells that drift in longitude at rates like those seen near the base of the convection zone and drift poleward as well. They have left-handed helicity in the north and right-handed helicity in the south. They transport angular momentum toward the equator (up gradient) and thus represent a key process for maintaining the Sun’s differential rotation which drives the Sun’s magnetic dynamo.


[1] Simon, G. W., Weiss, N. O. 1968 ZA, 69, 435
[2] Hathaway, D. H., Teil, T., Norton, A. A., Kitiashvili, I. 2015 ApJ, 811, 105
[3] Hathaway, D. H., Upton, L. A. ApJ, 908, 160
[4] Hathaway, D. H., Upton, L., Colegrove, O. 2013 Science, 342, 1217

Leave a comment

Your email address will not be published. Required fields are marked *