A vector field of constant unit magnitude and directed away from the origin.

VectorPlot[  {x/Sqrt[x^2+y^2],y/Sqrt[x^2+y^2]}, {x,-2,2}, {y,-2,2}]

Some ideas for a “whirlpool” vector field in 3 dimensions, i.e., a field that rotates and moves down, with the downward pull increasing as you get lower.

whirl = { y, -x, -1/z}
VectorPlot3D[ whirl, {x,-2,2},{y,-2,2}, {z,0,2}]