eprintid: 10132392 rev_number: 14 eprint_status: archive userid: 608 dir: disk0/10/13/23/92 datestamp: 2021-08-17 10:12:36 lastmod: 2021-10-20 23:50:28 status_changed: 2021-08-17 10:12:36 type: article metadata_visibility: show creators_name: Shah, R creators_name: Van Gorder, RA title: Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow ispublished: pub divisions: UCL divisions: B04 divisions: C05 divisions: F46 note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. 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. date: 2016-03 publisher: American Physical Society (APS) official_url: https://doi.org/10.1103/physreve.93.032218 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 1880385 doi: 10.1103/physreve.93.032218 lyricists_name: Shah, Rehan lyricists_id: RSHAH54 actors_name: Shah, Rehan actors_id: RSHAH54 actors_role: owner full_text_status: public publication: Physical Review E volume: 93 number: 3 article_number: 032218 citation: 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 <https://doi.org/10.1103/physreve.93.032218>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10132392/1/Localized%20nonlinear%20waves%20on%20quantized%20superfluid%20vortex%20filaments%20in%20the%20presence%20of%20mutual%20friction%20and%20a%20driving%20normal%20fluid%20flow%20by%20Rehan%20Shah%20and%20Robert%20Van%20Gorder%20Final.pdf