industrial chimney

Why do industrial chimneys / flues have swirls at the top?

They create a distubance in the airflow around the chimney and thus carry the smoke/fumes further, and hence more diluted, before they touchdown.

Yup. I think the disturbance also has the effect of drawing fumes up the chimey more effectively. Industrial chimneys tend to be fairly long and, as gases rise, they lose heat and so tend to rise less vigorously. The disturbance creates an updraft which helps draw the fumes up.

The spiral devices are to reduce wind induced vibration. Dispersal is primarily a function of the stack height and plume velocity.

This article explains the history of the smokestack, including a description of the role of the spiral in reducing vibration.