The overturning flow at the edges of granules produces horizontal vortex tubes at the interface between
the granule and the intergranular lane. The equation for vorticity is obtained by taking the
curl of the equation for the velocity (the equation for the momentum, Equation 6, divided by the density),

The result is (for the case of constant viscosity)

From this equation we see that vorticity is generated where the density and pressure gradients are not
parallel, which occurs where radiation transport effects are important, that is near the surface. At the
mushroom heads of downdrafts, where there is a change in entropy, so that the density and pressure
gradients are not parallel, ring vortices form (Figure 17). These are connected back up to the surface by
typically two, but sometimes more, trailing vortices (similar to those from the tips of airplane wings)
(Figure 18). The equation for the vorticity also shows that existing vorticity is enhanced by stretching and
compression, which occurs primarily in turbulent downflows, and it is diminished by expansion in
upflows.

Figure 18: mov-Movie (29987 KB)
Magnitude of the vorticity (entrophy) in a single downdraft. Top of the image is the
visible solar surface, bottom is 2.5 Mm below the surface. The vertical scale is stretched. Horizontal
tickmarks are 237 km apart.

Figure 19: Maximum horizontal and vertical flow Mach numbers as a function of depth.

Figure 20: Mach numbers in horizontal planes (contours at Mach number = 1, 1.2, 1.4, 1.6) for
vertical (top) and horizontal flow (bottom) superimposed on images of the vertical velocity at the
surface (left) and 1 Mm below the surface (right) (velocity scale on right in km s^{–1}).