ABSTRACT
This chapter, based substantially on Reference [1], is written in coauthorship with Evgeny Kozik.
A plethora of striking phenomena exhibited by superfluids is based on the quantization of velocity circulation. It is quite remarkable that quantized circulation is perfectly consistent with the hydrodynamics of ideal classical incompressible fluid (ICIF). Indeed, vortex filaments with arbitrary velocity circulation around them introduced in an ideal fluid are preserved under evolution governed by the Euler equation. In this respect, very instructive is the example of Kelvin waves (KWs)—waves of precessing distortions on a single vortex line-which were predicted by Thompson (Lord Kelvin) in the context of classical hydrodynamics well before the discovery of superfluidity. However, such vortex lines in realistic classical fluids are rather artificial; only in a superfluid at T → 0 does any form of rotational motion necessarily involve quantized vortex lines.
