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Soviet Journal of Low Temperature Physics

Superfluid vortex formation at rough boundaries

Yu. K. Krasnov

Published Oct 1, 1980• 1 citation
Publisher

Abstract

It is shown that roughness of a superfluid boundary lowers the surface energy barrier, which prevents the detachment of quantized vortices from the boundary under the action of the Magnus force exerted by the external flow past the roughness.
DOI
10.1063/10.0030150

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The dynamics of a superfluid over a surface exhibits significant differences from compressible flow in ordinary fluids. In ordinary fluids, when the local speed exceeds the sound speed, intrinsic dissipation due to viscosity can enable a shock wave. However, in superfluids, lack of dissipation prevents shock waves. Instead, spatial modulation of a wave train of solitons, as in the figure, allows for a smooth transonic transition. This wave train has been observed to eventually become unstable, leading to quantized vortices and an effective drag on a rough surface. The wave train occurs beneath a lambda-shaped structure with a fore and back-front, reminiscent of ordinary compressible fluids.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
We discuss the hydrodynamic boundary condition for a superfluid moving tangentially to a rough surface. Specifically, we argue that the scattering of quantum fluctuations off surface roughness affects the nature of the boundary condition, and that this has important consequences including a theorized critical speed and the presence of normal fluid at any nonzero speed, even if the boundary is held at zero temperature (i.e., a moving superfluid flow creates a sustained temperature difference between the superfluid and the boundary). This hydrodynamic boundary condition is relevant not only for superfluid helium experiments but also for experiments with trapped dilute Bose--Einstein condensates, in particular, those involving atomic waveguides near surfaces.
The energy and momentum associated with vortex formation in an imperfect Bose gas have been computed quantum mechanically. In the computation, explicit account is taken of the boundary condition to be satisfied by the wave function at the walls surrounding the fluid. Numerical estimates of the critical velocity obtained thereby throw considerable light on the question of the most favorable location (relative to the walls) for the formation of the vortex. It is concluded that the optimum location for this formation could be well within the fluid---significantly away from the walls.
An object can move through a superfluid without resistance provided that its speed is below a critical value; higher speeds result in the formation of vortices, which are small volumes of normal fluid and superfluid that rotate and dissipate energy. Although the dynamics of these vortices are considered to be crucial in understanding superfluidity, the strong and complex interactions of the superfluid, dissipative forces, and surface effects in most superfluids (such as liquid helium) all combine to obscure observations.