Why normal component of particle velocity must be continuous at boundary? I have problems for understanding the following:

Source: https://mycourses.aalto.fi/pluginfile.php/393850/mod_resource/content/1/Lecture7.pdf 
Why there would be a vacuum at the boundary? I dont see the concept that fluids can overlap each other.If someone could explain me this in layman terms I would appreciate it so much.
 A: This refers to a boundary where two fluids meet (say, the surface of the ocean where it meets the atmosphere). First, note that flow parallel to the boundary does not move the boundary (neither fluid expands or shrinks). Next, if fluid 1 at its edge has a normal (perpendicular to the boundary) velocity component that is "outward" (toward fluid 2), then the volume occupied by fluid 1 is expanding. To avoid a vacuum or overlap, then, the shared boundary must move "into" the fluid 2 space, and fluid 2's velocity at its edge must have the same normal component ("inward" from its perspective), such that the volume occupied by fluid 2 shrinks.
Think of a combat front between two armies that never leave a gap or penetrate each other. The velocity of the front equals the velocity at which one army's front line is advancing and also equals the velocity at which the other army's front line is retreating.
EDIT: "Flow" means motion of fluid particles. In the army analogy, the soldiers are fluid particles. If they march left and right along the front, the front does not move. The front moves due to forward or backward motions (which are normal to the front). If one army's soldiers march backward, they are retreating; then if the other army does not advance, this would leave a gap between their front lines (a vacuum). Or if one army marches forward (advances) but the other army does not retreat, this is only possible if the armies can occupy the same space at the same time (overlap). The rule is just saying "advancing velocity equals retreating velocity".
