According to Wikipedia ‘Wingtip vortices’
are tubes of circulating air which are left behind a wing as it generates lift. One wingtip vortex trails from the tip of each wing. The cores of vortices spin at very high speed and are regions of very low pressure.
Vortex-lines cannot end in fluid (Milne-Thomson  1973, p. 168); in three dimensions, the starting vortex shed by the trailing edge on take-off remains joined to the wing by counterrotating wingtip vortices, which are associated with the escape of air from the underside to above via the wingtips, following the negative pressure difference from below to above which must be present if the wing is generating lift.
This vortex-line consisting of the starting vortex and pair of wingtip vortices is notionally continued and closed by the ‘bound vortex’ inside the wing, associated with the circulation around the wing, and proportional to its lift in accordance with the Kutta–Joukowsky theorem.
As the flow over the wing evolves from start-up to steady-state, the starting vortex recedes and the wing-tip vortices extend back to infinity. For sketches of this ‘horseshoe vortex’ system (Glauert  p. 130; Milne-Thompson  p. 172), see, e.g. Glauert ( Figure 80, p. 131), Hanson  (1970, Figure 2, p. 268) or Milne-Thomson  (1973, Figure 10-41, p. 186).