Abstract: Water purification may occur by introducing sufficient heat into a standing fluid wave produced by supplying impure water into a supersonic gas stream. At least partially purified water may be recovered in the form of steam and undergo condensation into liquid water thereafter. Such water purification methods may comprise: generating a supersonic gas stream by feeding a gas through a shockwave nozzle under conditions sufficient to achieve a supersonic velocity, supplying impure water into the supersonic gas stream to produce a standing fluid wave comprising atomized water droplets downstream from an exit end of the shockwave nozzle, introducing sufficient heat into the standing fluid wave to cause at least a portion of the atomized water droplets to phase change into steam, and obtaining the steam as an overhead stream separated from an effluent stream containing one or more contaminants.