Q:

Is there a special name in Korean for adverbs like '반짝반짝', '흔들흔들', '빙글빙글'?

There seems to be a group of 'doubled' words in Korean that often describe how something looks or moves, e.g. : 
반짝반짝  - 'twinkle' or 'sparkle'
흔들흔들  - 'shake' or 'wobble'
빙글빙글  - to go round and round
Is there a special name in Korean for these kind of words?
(Further examples more than welcome - I really like these words!)

A:

They are mimetic words. They're called 음성상징어, and can be further classified into two categories:

의성어 are words that reflect the sound of something (phonomimes / onomatopoeia):

후루룩 (the sound of slurping)
쨍그랑 (the sound of a metal dish falling)

의태어 are words that reflect the "shape" of something (for example it's movement or feeling) (phenomimes).  Your examples (반짝반짝, 흔들흔들, 빙글빙글) all belong to this category.  Some others:

성큼성큼 ("shape" of walking with large steps)
데굴데굴 (rolling "shape")
깡총깡총 (hopping "shape", especially rabbits)

More examples here.  And a comedy program spoofing 의성어 words.
All these words are adverbs (부사), but usually these words can be used as verbs by "halving" them and adding the ending -거리다 (or sometimes -대다):

빙글거리다, 흔들거리다, 흔들대다

