Whirlpool is a move in the games, but it doesn't actually clear whirlpools in the environment. The way to clear whirlpools in Pokémon Shiny Gold is to use the following:
* Surf: This move will allow you to navigate through whirlpools.
* Strength: This move can be used to push boulders that block the entrance to some whirlpools.
There is no in-game item or ability that can directly clear whirlpools.