Superfluids in rotation: Landau–Lifshitz vortex sheets vs Onsager–Feynman vortices

Landau's and Lifshitz's 1955 paper on vortex sheets in a rotating superfluid came out almost simultaneously with Feynman's paper on quantized vortices in superfluid $^4$He and was long considered incorrect. Forty years later, in what was a triumph for the authors' theory, experiments at the Olli Lounasmaa Low Temperature Laboratory (Otaniemi, Finland) detected vortex sheets in chiral superfluid $^3$He-A in a rotating cryostat, validating Landau's and Lifshitz's equation relating the vortex sheet separation and the angular velocity of rotation. This paper discusses vortex sheet configurations that have been or can be observed in superfluid $^3$He.