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Drag on a penetrable two-dimensional disk in a superfluid

Published online by Cambridge University Press:  22 April 2026

John Elie Sader Open the ORCID record for John Elie Sader [Opens in a new window] ,
Alex Nunn  and
D.I. Pullin Open the ORCID record for D.I. Pullin [Opens in a new window]
John Elie Sader*
Affiliation:
Lynn Booth & Kent Kresa Department of Aerospace, California Institute of Technology, Pasadena, CA 91125, USA Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA 91125, USA
Alex Nunn
Affiliation:
Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, CA 91125, USA
D.I. Pullin
Affiliation:
Lynn Booth & Kent Kresa Department of Aerospace, California Institute of Technology, Pasadena, CA 91125, USA
*
Corresponding author: John Elie Sader, jsader@caltech.edu
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Abstract

The motion of a body through a superfluid can generate phenomena distinct from a normal viscous fluid. This includes the absence of drag below a critical body speed with the shedding of quantised vortices and non-zero drag above this speed. These phenomena are often modelled using the Gross–Pitaevskii (GP) equation, which describes the wavefunction of a weakly interacting Bose–Einstein condensate and its superfluid dynamics. We study the drag experienced by a penetrable circular disk of radius, $a$, in the form of a two-dimensional potential barrier of height, $V_0$, that is moving in a superfluid of bulk density, $n_\infty$, by solving the GP equation. The drag is found to exhibit a unimodal dependence on the disk speed for a fixed value of its barrier height. This behaviour is quantified analytically and confirmed using direct numerical solution. The maximum drag per unit length of $F_{\textit{drag}}^{\textit{max}} \approx 5 a n_\infty V_0$ occurs when the barrier height coincides with the relative kinetic energy of the fluid particles. Flow excitations are diminished at a high particle kinetic energy with a commensurate reduction in the drag. This generates a saddle-node bifurcation in the dynamics of a moving disk under an applied force. These results advance understanding of the motion of bodies with finite penetrability, which is relevant to laser experiments probing the superfluidity of Bose–Einstein condensates.

JFM classification

Aerodynamics: Flow-structure interactions Compressible Flows: Compressible Flows Vortex Flows: Vortex Flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1033 , 25 April 2026 , A34
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Copyright
© The Author(s), 2026. Published by Cambridge University Press

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Supplementary material: File

Sader et al. supplementary material 1

Sader et al. supplementary material
Download Sader et al. supplementary material 1(File)
File 6.4 MB
Supplementary material: File

Sader et al. supplementary movie 2

Synchronised animations of DNS data for the number density distribution (upper) and the instantaneous drag (lower), as a function of the instantaneous position of the disk centre, xdisk. The moving open circle in the lower animation aligns with this instantaneous disk position in the upper animation. Disk radius, R = 3, barrier height, V0 = 30 and disk speed, Udisk = 0.5. Computational parameters as for Fig. 3.
Download Sader et al. supplementary movie 2(File)
File 1.7 MB
Supplementary material: File

Sader et al. supplementary movie 3

As for Movie 1, but with a disk speed of Udisk = 0.7.
Download Sader et al. supplementary movie 3(File)
File 2.2 MB
Supplementary material: File

Sader et al. supplementary movie 4

As for Movie 1, but with a disk speed of Udisk = 1.
Download Sader et al. supplementary movie 4(File)
File 2.3 MB
Supplementary material: File

Sader et al. supplementary movie 5

As for Movie 1, but with a disk speed of Udisk = 3.
Download Sader et al. supplementary movie 5(File)
File 5.6 MB