Kappa-ryu is a swordsmanship style used by the samurai Kawamatsu. As noted by Raizo and Kikunojo, this style is Kawamatsu signature fighting style, despite the latter being a sumo wrestler.
According to Kawamatsu, fighting against the Kappa-ryu is like trying to swim against raging waters. When wielding his Soto Muso, Kawamatsu was able to blow away several men charging against him, taking them down with a single blow.
Menamugawa (,Menamugawa?): Kawamatsu lunges toward his opponents, holding the blade's tip toward them and overwhelming them. It was first used against several Beasts Pirates guards in the Prisoner Mine.