Which term best describes the operation where a welder or welding operator has control of a molten weld pool and the weld pool has a side to side motion that is transverse to the travel direction?

The term that best describes this operation is "oscillation." In this context, oscillation refers to the side-to-side motion of the molten weld pool, which is transverse to the direction of travel. This technique can help achieve better penetration and bead shape in the weld. Oscillation is often used in processes like TIG or MIG welding to improve the quality of the weld joint.