where d[??] is a microsegment in vortex line and vector l is the distance between d[??] and the specific point.
The angle between the vortex line and the x-axis is [theta] and [beta] indicates the angle between [l.sub.0] and x-axis.
From the physical point of view such a factorization seems natural because far enough from the sphere surface, the abstract surfaces containing vortex lines
follow the magnetic field stream lines, but these are exactly the dipole magnetic field lines.
Quickly after vortex lines
snap away from each other, they could jerk and wiggle and form what are called "Kelvin waves." If these wiggly lines loop up, they can cascade into even tinier rings.
The contours of v = constant are known as the vortex lines
of the flow.
When the magnetic fields are strong enough, they create an array of vortex lines
around which electric currents swirl (SN: 11/27/93, p.
"The interesting thing is that people saw masses of vortex lines
in liquid helium for years and wanted to get rid of them," says Zurek.
In this case, the defects materialize as vortex lines
-- tiny, invisible whirlpools of fluid that penetrate the liquid helium.
"The trouble [with helium] is that you have to work at low temperatures, and you have a fairly hard time finding these vortex lines
because you can't see them directly" says Zurek.