6533b824fe1ef96bd12801c6

RESEARCH PRODUCT

Waves on a vortex filament: exact solutions of dynamical equations

Michele SciaccaTommaso BrugarinoMaria Stella Mongiovì

subject

PhysicsVortex tubeApplied MathematicsGeneral MathematicsGeneral Physics and Astronomysuperfluid helium.MechanicsVortexKelvin wavesymbols.namesakeClassical mechanicsDispersion relationCompressibilitysymbolsvortex filamentSeries expansionSettore MAT/07 - Fisica MatematicaKelvin waveEquations for a falling bodySuperfluid helium-4

description

In this paper we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.

yearjournalcountryeditionlanguage
2014-09-10Zeitschrift für angewandte Mathematik und Physik
https://doi.org/10.1007/s00033-014-0450-5