Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2001-06-26
Physics
Condensed Matter
Soft Condensed Matter
Submitted to J. Phys. A: Math. Gen.; Corrected references
Scientific paper
10.1088/0305-4470/34/47/311
The Gross-Pitaevskii (GP) equation admits a two-dimensional solitary wave solution representing two mutually self-propelled, anti-parallel straight line vortices. The complete sequence of such solitary wave solutions has been computed by Jones and Roberts (J. Phys. A, 15, 2599, 1982). These solutions are unstable with respect to three-dimensional perturbations (the Crow instability). The most unstable mode has a wavelength along the direction of the vortices of the same order as their separation. The growth rate associated with this mode is evaluated here, and it is found to increase very rapidly with decreasing separation. It is shown, through numerical integrations of the GP equation that, as the perturbations grow to finite amplitude, the lines reconnect to produce a sequence of almost circular vortex rings.
Berloff Natalia G.
Roberts Paul H.
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