  A visualization of three-dimensional incompressible flows by divergence-free
quasi-two-dimensional projections of velocity field on three coordinate planes
is proposed. It is argued that such divergence-free projections satisfying all
the velocity boundary conditions are unique for a given velocity field. It is
shown that the projected fields and their vector potentials can be calculated
using divergence-free Galerkin bases. Using natural convection flow in a
laterally heated cube as an example, it is shown that the projection proposed
allow for a better understanding of similarities and differences of
three-dimensional flows and their two-dimensional likenesses. An arbitrary
choice of projection planes is further illustrated by a lid-driven flow in a
cube, where the lid moves parallel either to a sidewall or a diagonal plane.
