Density pattern in supercritical flow of liquid He-4

TL;DR

This paper uses density functional theory to analyze the emergence of a periodic density pattern in superfluid helium-4 flowing above the critical velocity, confirming earlier predictions and exploring effects in bulk and nanoconfined environments.

Contribution

It provides a theoretical confirmation of the density modulation phenomenon in supercritical helium-4 flow, detailing its amplitude and wave vector dependence.

Findings

Density modulation amplitude scales as (u - v_c)^{1/2}.

Density pattern occurs at the roton wave vector.

Pattern observed in both bulk and nanoconfined helium.

Abstract

A density functional theory is used to investigate the instability arising in superfluid $^4$He as it flows at velocity u just above the Landau critical velocity of rotons v_c. Confirming an early theoretical prediction by one of us [JETP Lett. 39, 511 (1984)], we find that a stationary periodic modulation of the density occurs, with amplitude proportional to (u-v_c)^{1/2} and wave vector equal to the roton wave vector. This density pattern is studied for supercritical flow both in bulk helium and in a channel of nanometer cross-section.