The contributions of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics

1996 ◽  
Vol 18 (5) ◽  
pp. 245-268 ◽  
Author(s):  
Renzo L Ricca
Keyword(s):  
Potential Theory ◽  
Vortex Filament ◽  
Filament Dynamics ◽  
Asymptotic Potential

scholarly journals About the non-standard viewpoint on the dynamics of closed vortex filament

2018 ◽  
Vol 32 (33) ◽  
pp. 1850410 ◽  
Author(s):  
S. V. Talalov
Keyword(s):  
Phase Space ◽  
Effective Mass ◽  
Explicit Formula ◽  
Vortex Filament ◽  
Hamiltonian Description ◽  
Suggested Approach ◽  
Galilei Group ◽  
Filament Dynamics

In this paper, we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of the considered system as a structured particle that possesses certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the structured particle “closed vortex filament” is suggested.

Erratum: Vortex filament dynamics in plasmas and superconductors

1996 ◽  
Vol 53 (4) ◽  
pp. 4246-4246
Author(s):  
Lars Uby ◽  
Michael B. Isichenko ◽  
Vladimir V. Yankov
Keyword(s):  
Vortex Filament ◽  
Filament Dynamics

Regularity of Desingularized Models for Vortex Filaments in Incompressible Viscous Flows: A Geometrical Approach

2020 ◽  
Vol 73 (3) ◽  
pp. 217-230
Author(s):  
Siran Li
Keyword(s):  
Sobolev Spaces ◽  
Weak Solutions ◽  
Classical Model ◽  
Viscous Flows ◽  
Vortex Filament ◽  
Vorticity Equation ◽  
Geometrical Approach ◽  
Filament Dynamics ◽  
Incompressible Viscous Flows ◽  
Regularity Of Weak Solutions

Summary We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularized models for vortex filament dynamics in 3D incompressible viscous flows. These generalize the classical model ‘of an allowance for the thickness of the vortices’ due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.

scholarly journals Geometry and dynamics of vortex sheets in 3 dimension

2002 ◽  
pp. 55-76 ◽  
Author(s):  
D.A. Burton ◽  
R.W. Tucker
Keyword(s):  
Fluid Velocity ◽  
Normal Component ◽  
Vortex Sheet ◽  
The Self ◽  
Vortex Filament ◽  
Vortex Sheets ◽  
Filament Dynamics ◽  
De Rham ◽  
Induced Velocity

We consider the properties and dynamics of vortex sheets from a geometrical, coordinate-free, perspective. Distribution-valued forms (de Rham currents) are used to represent the fluid velocity and vorticity due to the vortex sheets. The smooth velocities on either side of the sheets are solved in terms of the sheet strengths using the language of double forms. The classical results regarding the continuity of the sheet normal component of the velocity and the conservation of vorticity are exposed in this setting. The formalism is then applied to the case of the self-induced velocity of an isolated vortex sheet. We develop a simplified expression for the sheet velocity in terms of representative curves. Its relevance to the classical Localized Induction Approximation (LIA) to vortex filament dynamics is discussed. .

Vortex filament dynamics in plasmas and superconductors

1995 ◽  
Vol 52 (1) ◽  
pp. 932-939 ◽  
Author(s):  
Lars Uby ◽  
Michael B. Isichenko ◽  
Vladimir V. Yankov
Keyword(s):  
Vortex Filament ◽  
Filament Dynamics
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