Since your supervisor is aware that you have periods of free time, perhaps you can ask your supervisor what career paths are available to you from your present position; and how you could make use of the free time you have available to acquire new skills or knowledge that could help you move yourself along your chosen career path.
Taking the initiative to better yourself at work makes an EXCELLENT impression on the powers that be
Are you taking any classes? Having free time at work is an excellent situation for people who work full-time but are also furthering their education.
Good luck to you!!