Negative group velocity and Kelvin-like wake pattern

TL;DR

This paper explores how negative group velocity in medium excitations causes wake patterns similar to Kelvin wakes, demonstrated through superfluid helium's roton excitations and their interference effects.

Contribution

It introduces the concept of Kelvin-like wake patterns arising from negative group velocity excitations, with explicit calculations in superfluid helium showing this phenomenon.

Findings

Kelvin-like wake patterns occur with negative group velocity excitations.

Superfluid helium roton wake patterns are explicitly calculated.

Wake pattern orientation is opposite to classical Kelvin wakes.

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.