Geometric and topological aspects associated with integrability of vortex filament motion in the Localized Induction Approximation (LIA) context (which includes a family of local dynamical laws) are discussed. We show how to interpret integrability in relation to the Biot-Savart law and how soliton invariants can be interpreted in terms of global geometric functionals of knotted solutions. Under the basic (zeroth-order) LIA, we prove that vortex filaments in the shape of torus knots T p, q (p, q co-prime) with (q/p)>1 are stable, whereas those with (q/p)<1 are unstable.

Ricca, R. (1995). Geometric and topological aspects of vortex filament dynamics under LIA. In M. Meneguzzi, A. Pouquet, P.L. Sulem (a cura di), Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence (pp. 99). Springer Berlin Heidelberg [10.1007/BFb0102404].

Geometric and topological aspects of vortex filament dynamics under LIA

RICCA, RENZO
Primo
1995

Abstract

Geometric and topological aspects associated with integrability of vortex filament motion in the Localized Induction Approximation (LIA) context (which includes a family of local dynamical laws) are discussed. We show how to interpret integrability in relation to the Biot-Savart law and how soliton invariants can be interpreted in terms of global geometric functionals of knotted solutions. Under the basic (zeroth-order) LIA, we prove that vortex filaments in the shape of torus knots T p, q (p, q co-prime) with (q/p)>1 are stable, whereas those with (q/p)<1 are unstable.
Capitolo o saggio
Vortex knots, LIA, vortex dynamics
English
Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence
Ricca, R. (1995). Geometric and topological aspects of vortex filament dynamics under LIA. In M. Meneguzzi, A. Pouquet, P.L. Sulem (a cura di), Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence (pp. 99). Springer Berlin Heidelberg [10.1007/BFb0102404].
Ricca, R
File in questo prodotto:
File Dimensione Formato  
procconf95.pdf

accesso aperto

Dimensione 948.67 kB
Formato Adobe PDF
948.67 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/100211
Citazioni
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
Social impact