means To move, twist, or stir in a curving, spiraling motion — or the curling shape such motion leaves behind.

from A Middle English word, swirl, that started life describing an eddy or whirlpool in water. It likely came north — from Scots and the Low German/Dutch side of the family — where words like Dutch zwirrelen (to whirl) swirl in the same current. Whatever the exact source, it's almost certainly imitative at heart: the kind of word your mouth makes when it tries to sound like water turning back on itself.