Q. Is there a source for throwing the arovos after being used on top of the aron hakodesh?

A. Malbushei Yom Tov (on Levush 664: 1), Maharsham (4: 53), Netzotzei Zohar (Parshas Tzav), Bikurei Yaakov (664: 16) and others quote this minhag.
Nitei Gavriel (Sukkos 79: 7) understands that they mean to throw them on top of the aron hakodesh. He also quotes Darkei Chaim Veshalom that on the contrary averts not to place them there. He mentions that the Chabad tradition is to place them on a chair. However, he also mentions that many of the Chassidic groups do place them on top of the aron hakodesh.
Moadim Uzmanim (2: 131) writes as a support to this tradition, the fact that in the Beis Hamikdosh the arovos were placed vertically leaning on the mizbeach and the aron hakodesh represents symbolically the altar.
Horav Shlomo Miller’s Shlit’a opinion is that one should follow the minhogim of his family and congregation.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a