Mutoryu is a related fighting style that Zoro was forced to come up with during the game Groggy Ring event in the Davy Back Fight.
This is an unorthodox form of his fighting style that uses no swords. As he has not been forced to use it since the Davy Back Fight with the Foxy Pirates, he has only one technique in this fighting style:
Tatsu Maki (龍巻き,Tatsu Maki?, literally meaning "Dragon Twister"): The motions of this technique are the same as Santoryu's Tatsu Maki, only this version is performed without swords, only with the arms. Zoro's lack of swords means the technique has no cutting power, and is more used only to send the opponent flying. As with the sword version, the rotating motion of Zoro spinning himself creates a spinning vortex, which sends the opponent several feet skyward. However, getting hit by one of Zoro's arms as he performs this move could also send the shockwaves into the unlucky victim's body, causing great blunt trauma and harm, as a sort of substitute in place of the cutting power of the original version. This was first seen being used against Pickles. In the VIZ manga, this is called Dragon Twister. Like the Santoryu version, there appears to be a dragon image beside him in this technique.