Vortex wake patterns in superfluid $^{4}He$

Abstract

Excitations in the form of quantized vortex rings are known to exist in superfluid $^{4}He$ at energies and momenta exceeding those of the Landau phonon-roton spectrum. They form a vortex branch of elementary excitations spectrum which is disconnected from the Landau spectrum. Interference of vortex ring excitations determines wake patterns due to uniformly traveling sources in bulk superfluid at low speeds and pressures. The dispersion law of these excitations resembles that of gravity waves on deep water with infrared wave number cutoff. As a result, vortex wake patterns featuring elements of the Kelvin ship wake are predicted. Specifically, at lowest speeds the pattern with fully developed transverse and diverging wavefronts is present. At intermediate speeds transverse wavefronts are absent within a cone whose opening angle increases with the source velocity. At largest speeds only diverging wavefronts confined within a cone whose opening angle decreases with the source velocity are found. When experimentally observed, these changes in appearance of wake patterns serve as indicators of the beginning part of the vortex branch of elementary excitations.