What do you do with your hoshanos

There is no mention anywhere

to throw הושענות on top of ארון הקודש. Placing the הושענות (after use) on top of the ארון הקודש  has no מקור. (source) The מלבושי יו"ט (Tosfos Y.T.) writes to throw the הושענות on the  ledges in the Shul. (not necessarily the ledge of ארון הקודש,  can be window ledges, etc.) By throwing them we remove the ניצוצי הדין    (sparks of Din) at the end of Din. (Throwing away the last remnants of Din on the last day of Din) Perhaps the simple reason is that הושענות are placed  (or thrown if too high to place) on ledges so that they won't remain דרך בזיון on the floor. (Shuls had no tables)  אמבצי