Differential rotation of the sun
The rotation of the sun
The sun's surface rotates at different speeds depending on geographical latitude,
with the duration of rotation increasing according to a mathematical curve from the equator to the poles.
The visible surface of the sun is covered with over 2 million convection cells,
the granules. In the meteorological sense, these are low-pressure areas.
At the lower limit*(a) of the convection zone there is violent eddy formation and a pressure of several tens of thousands of bar, with a correspondingly higher density than at the surface.
Turbulence and frictional forces to the neighboring cells are of crucial importance here.
Coming from the edges of the cells, the heated plasma flows into the central regions of rise of the granules and thus, under the influence of the Coriolis force*(b), causes the cells in the northern hemisphere to rotate to the left and those in the southern hemisphere to rotate to the right.
For example, in the northern hemisphere, the neighboring cells to the north counteract the rotational movement through friction and turbulence,
and thus cause the centers to drift to the east.
The neighboring cells to the south, on the other hand, cause the centers to drift west.
Both influences do not cancel each other out, because they are unequally strong.*(c) I.e. the neighboring cell to the north rotates faster and has a greater tangential speed than the cell to the south.
Therefore, an easterly drift predominates overall. And because the sun rotates from west to east,
the peripheral speed increases by the drift speed.
Image: Schematic representation of the processes
at the bottom of the convection cells of middle
northern latitudes, using the example of 3 cells.
(Werren)
The Coriolis force increases with the angle of the vortex rotation plane to the solar axis.
(On a spinning sphere of unit radius 1, an offset from 80th to 70th latitude causes a circumference difference of 1.057, but from 20th to 10th only 0.283.)
Consequently, from the north pole to the equator, the statistical probability for a left rotation decreases steadily, to only 50%.*(d)
The relative motion between two neighboring cells on a meridian is only a few meters per second, but after one revolution of the sun and at the distance of 10 degrees of latitude,
the distance in the middle latitudes adds up to over 600000 km
The schematic drawing shows a group of convection cells, which are shifted in an easterly direction by tangential friction. Conditions in the southern hemisphere are mirrored. (with the equator as mirror axis)
Drift speeds accumulate from the poles to the equator.
However, this effect is reduced or negated with increasing geographical latitude,
because the neighboring cells on the pole side, which are responsible for the easterly drift, decrease in percentage compared to the equator side, towards the poles. In this way,
a flow pattern is generated that roughly resembles a sine curve from +90° to -90°.
Source: Werren
The granules are not lined up, as in the schematic drawing, but chaotically disordered,
but that doesn't change anything about the basic processes.
The extremely short lifespan of the granules, compared to their size,
is a further indication of rotating thermal vortices at depth, which,
as a result of the processes described above, are running away from the ascent tubes and constantly allowing new regions of hot plasma to rise.
The actual drive of the differential rotation lies in the lower convection layer,
which pulls the plasma above it with it.
The calculation in 5-degree increments from the poles to the equator shows what the curve of the velocity distribution looks like after the processes described above.
Source: Werren
The operations are shown in the schematic drawing.
The correspondence with reality is striking.
If you equate the maximum numerical values of the diagrams (calculated and real),
then there are only minimal differences in the intermediate values.
The calculation scheme also shows a maximum change in angular velocity in the middle latitudes (green curve), just as it is observed in reality.
(Differentiated speed curve, (diagram with gray background))
There is a report on the online site "Welt der Physik", funded by the Federal Ministry of Education and Research, which is based on the original work:
"Giant Convection Cells Found on the Sun", D.H. Hathaway; Science, 2013 based.
It describes huge flow cells on the sun and their physical formation mechanisms.
Based on the findings of the Helioseismic and Magnetic Imager on board NASA's Solar Dynamics Observatory probe, it is reported how different flow cells are superimposed on the large-scale flow distribution.
According to the observations, the differential rotation, as I described it with the help of the individual granules, is superimposed on large-scale flow cells that appear to be randomly distributed over the sun's surface.
What is striking, however, is the accumulation of easterly drift cells in the middle latitudes.
The flow pattern shows the differential flows in relation to the environment and corresponds on average to curve 2 of the differentiated speed profile.
I avoided inserting the flow diagram because the copyright for this belongs to Dr. David Hathaway (NASA) and refer to the web link instead:
I consider the summary in the text to be decisive, which confirms my explanation in principle, but in less detail.
Sources:
* Störing: ''Knaurs moderne Astronomie.'' S. 34 (Diameter of the granules), Droemersche Verlagsanstalt, Kanuer Nachf., München, 1985, ISBN 3-426-26236-3<br />
* Becker und Sauermost: ''Erforschter Weltraum.'' S. 84 (Rotation duration numbers), Herder-Verlag, Freiburg Brsg. 1976, ISBN 3-451-17393-X<br />
* Hans-Ulrich Keller: ''Astrowissen.'' S. 166 (Pressure curve in the convection layer), Kosmos, Stuttgart, 2003, 3. Auflg., ISBN 3-440-09713-7<br />
* Heribert Stroppe: Physik, 14. Auflg., S. 55 , (Coriolis force depends on latitude), Fachbuchverl. Leipzig im Carl-Hanser-Verl., München, 2008, ISBN 978-3-446-41502-7