Europhys. Lett.
Volume 66, Number 1, April 2004
Page(s) 69 - 75
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 March 2004
Europhys. Lett., 66 (1) , pp. 69-75 (2004)
DOI: 10.1209/epl/i2003-10137-8

Geometrical physics of the many vortex filament problem

D. Kivotides and A. Leonard

Graduate Aeronautical Laboratories, California Institute of Technology Pasadena, CA 91125, USA

(Received 4 August 2003; accepted in final form 13 January 2004)

We employ a model of fully structured decaying turbulence consisting of unconstrained, reconnecting vortex filaments with dynamic finite cores of uniform circulation, interacting via inertial and viscous forces. We show that the fractal dimension and the length of the vortex tangle approach constant values. The former is observed in the same range of scales as Kolmogorov's -5/3 inertial range scaling. The curvature and torsion spectra show evidence of non-flat scalings corresponding to the inertial range. The vorticity along the core centerlines tends to align mostly with the intermediate eigenvector of the rate of strain tensor and to be normal to the expansive one.

47.27.Ak - Fundamentals.
47.27.Gs - Isotropic turbulence; homogeneous turbulence.
47.32.Cc - Vortex dynamics.

© EDP Sciences 2004