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Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow

Shah, R; Van Gorder, RA; (2016) Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow. Physical Review E , 93 (3) , Article 032218. 10.1103/physreve.93.032218. Green open access

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Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow by Rehan Shah and Robert Van Gorder Final.pdf - Published Version

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Abstract

We demonstrate the existence of localized structures along quantized vortex filaments in superfluid helium under the quantum form of the local induction approximation (LIA), which includes mutual friction and normal fluid effects. For small magnitude normal fluid velocities, the dynamics are dissipative under mutual friction. On the other hand, when normal fluid velocities are sufficiently large, we observe parametric amplification of the localized disturbances along quantized vortex filaments, akin to the Donnelly-Glaberson instability for regular Kelvin waves. As the waves amplify they will eventually cause breakdown of the LIA assumption (and perhaps the vortex filament itself), and we derive a characteristic time for which this breakdown occurs under our model. More complicated localized waves are shown to occur, and we study these asymptotically and through numerical simulations. Such solutions still exhibit parametric amplification for large enough normal fluid velocities, although this amplification may be less uniform than would be seen for more regular filaments such as those corresponding to helical curves. We find that large rotational velocities or large wave speeds of nonlinear waves along the filaments will result in more regular and stable structures, while small rotational velocities and wave speeds will permit far less regular dynamics.

Type: Article
Title: Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/physreve.93.032218
Publisher version: https://doi.org/10.1103/physreve.93.032218
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10132392
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