Why does stirring a liquid in a cup create a vortex?

When you stir liquid in a tumbler, you are forcing it to spin in circles. For anything to move in a circle, it needs an inward pull. In a liquid, this inward pull comes from pressure differences: the pressure is higher near the walls, where the liquid moves faster, and lower at the centre. Gravity still pulls the liquid down while the spinning motion pushes it outward. The liquid’s surface finds a balance between these forces by forming a curved shape: it rises at the edges and dips in the middle. In fact, the dip is not random but adopts a parabolic shape. The depth at the centre deepens in proportion to the square of the distance from the middle.

Friction also matters. The liquid close to the tumbler’s sides and bottom slows down because it rubs against the solid surface, while the liquid near the top moves more freely. This uneven speed makes the liquid spiral inward along the surface and downward at the centre. The result is the funnel-shaped vortex you see. It is the liquid’s way of balancing rotation, pressure, and gravity all at once.