Zero absolute vorticity plane Couette flow as an hydrodynamic representation of quantum energy states under perpendicular magnetic field

Here we extend the Madelung transformation of Schr\"{o}dinger equation into a fluid-like form to include influence an external electromagnetic field on charged particle. The vorticity fluid is then in opposite direction imposed magnetic and equal magnitude cyclotron angular frequency. When particle motion confined plane, perpendicular field, equivalent flow dynamics that zero absolute obtained quasi 2D rotating frame, where frequency plays role Coriolis frame. We show how Landau levels extended modes integer quantum Hall effect are all mapped such vorticity-like plane Couette flows, latter exhibit geostrophic-like balance between force gradients (Bohm) potential electric force.