How does the Kuiper belt supply Jupiter-family comets?

The Kuiper belt serves as the primary reservoir for Jupiter-family comets, which are characterized by their relatively low-inclination orbits and orbital periods of less than 20 years.123

The process by which these objects transition from the Kuiper belt to the inner solar system involves several stages:

• Scattered Disk: A specific population of Kuiper belt objects, known as the scattered disk, consists of bodies in more eccentric and inclined orbits with perihelia near Neptune.1
• Gravitational Perturbation: Neptune exerts a strong gravitational influence on these objects. It can scatter them inward toward the giant planets or outward toward the Oort cloud.14
• Transition via Centaurs: Objects scattered inward often become Centaur objects, which orbit among the giant planets. These bodies are in unstable orbits and represent a transitional phase as they slowly diffuse into the planetary region.253
• Capture by Jupiter: Through successive gravitational interactions with the giant planets, these comets are eventually "handed down" until they are captured by Jupiter, which places them into their final, short-period orbits.3