Why do gyres flow in giant circular patterns instead of straight lines?

Answer 1

Because of the rotation of the earth.

A gyre is any manner of swirling vortex. "Gyre" is often used to describe wind or ocean currents such as the North Pacific Gyre. Gyres are caused by the Coriolis effect.

The Coriolis effect is the apparent deflection of a moving object in a rotating frame of reference.

The Coriolis effect you are asking about is caused by the rotation of the Earth, which is responsible for deflecting objects moving along the surface of the Earth to the right of the direction of travel in the Northern hemisphere and to the left of the direction of travel in the Southern hemisphere. ( As a consequence, winds around the center of a cyclone rotate counterclockwise on the northern hemisphere and clockwise on the southern hemisphere.)

Answer 2

Patterns With Straight Lines

Answer 3

The Coriolis effect. This is the rotation caused by the rotation of the planet about its axis. It gives a rotation of one revolution per day. Anything moving over the face of the Earth is affected by Coriolis which turns things to the left in the southern hemisphere and to the right in the northern hemisphere.