Negative group velocity and Kelvin-like wake pattern

Abstract

Wake patterns due to a uniformly traveling source are a result of the resonant emission of the medium's collective excitations. When there exists a frequency range where such excitations possess a negative group velocity, their interference leads to a wake pattern resembling the Kelvin ship wake: while there are "transverse" and "divergent" wavefronts trailing the source, they are oriented oppositely to Kelvin's. This is illustrated by an explicit calculation of "roton" wake patterns in superfluid $^{4}He$ where a Kelvin-like wake emerges when the speed of the source marginally exceeds the Landau critical roton velocity.