Summary
the 2014 International Symposium on Nonlinear Theory and its Applications
2014
Session Number:B1L-A
Session:
Number:B1L-A5
Cylindrical Korteweg-de Vries solitons on a ferrofluid jet
Andreas Engel,
pp.217-219
Publication Date:2014/9/14
Online ISSN:2188-5079
Summary:
Dilute ferrofluids combine the hydrodynamic properties of Newtonian liquids with superparamagnetic response to external magnetic fields. For a cylindrical ferrofluid jet with a current-carrying wire along its axis the Rayleigh-Plateau instability may be suppressed due to the magnetic body force. The resulting axissymmetric surface deformations show a linear dispersion relation similar to shallow water waves. Accordingly, the weakly non-linear regime is characterized by a Kortewegde Vries (KdV) equation which can be derived using multiple scale perturbation theory. With the coefficients of this KdV-equation depending on the magnetic field strength both dark (depression) and bright (elevation) solitons are possible. These predictions have recently been verified in experiments, and also in a fully nonlinear numerical analysis.