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

Visualization of three-dimensional incompressible flows by quasi-two-dimensional divergence-free projections