TY - JOUR
T1 - Dynamics of helical vortices and helical-vortex rings
AU - Sonin, E. B.
PY - 2012/2
Y1 - 2012/2
N2 - The letter considers dynamics of helical vortices and helical-vortex rings either solving directly the equations of motions of a vortex line or using canonical relations following from the Hamiltonian equations of motion. An analytical solution in elliptical integrals was found for helical-vortex rings in the local-induction approximation. The analysis based on the canonical Hamilton relation provides a clear physical explanation for anomalous velocities of helical-vortex rings, i.e., for suppression of the velocity and even inversion of its direction at sufficiently large amplitude of the helical distortion. The extended local-induction approximation is suggested, which provides an exact solution for the equations of motion of helical vortices and helical-vortex rings in the limit when the small-pitch helical vortex reduces to a cylindric sheet of uniform vorticity.
AB - The letter considers dynamics of helical vortices and helical-vortex rings either solving directly the equations of motions of a vortex line or using canonical relations following from the Hamiltonian equations of motion. An analytical solution in elliptical integrals was found for helical-vortex rings in the local-induction approximation. The analysis based on the canonical Hamilton relation provides a clear physical explanation for anomalous velocities of helical-vortex rings, i.e., for suppression of the velocity and even inversion of its direction at sufficiently large amplitude of the helical distortion. The extended local-induction approximation is suggested, which provides an exact solution for the equations of motion of helical vortices and helical-vortex rings in the limit when the small-pitch helical vortex reduces to a cylindric sheet of uniform vorticity.
UR - http://www.scopus.com/inward/record.url?scp=84857550038&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/97/46002
DO - 10.1209/0295-5075/97/46002
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AN - SCOPUS:84857550038
SN - 0295-5075
VL - 97
JO - Lettere Al Nuovo Cimento
JF - Lettere Al Nuovo Cimento
IS - 4
M1 - 46002
ER -