article · Nonlinearity · 2014
Vortex filament equation for a regular polygon
Francisco de la Hoz, Luis Vega
Cited by 45Open access
Abstract
In this paper, we study the evolution of the localized induction approximation (LIA), also known as vortex filament equation, Xt = Xs ∧Xss, for X(s, 0) a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give strong evidence that X(s, t) is also a polygon at any rational time; moreover, it can be fully characterized, up to a rigid movement, by a generalized quadratic Gauß sum. We also study the fractal behavior of X(0, t), relating it with the so-called Riemann’s non-differentiable function, that, as proved by S. Jaffard, fits with the multifractal model of U. Frisch and G. Parisi, for fully developed turbulence. Keywords: vortex filament equation, Schrödinger map, generalized quadratic Gauß sums, pseudo-spectral methods, fractals
Cite this paper
de la Hoz, F., & Vega, L. (2014). Vortex filament equation for a regular polygon. Nonlinearity, 27(12), 3031–3057. https://doi.org/10.1088/0951-7715/27/12/3031
de la Hoz, Francisco, and Luis Vega. “Vortex filament equation for a regular polygon.” Nonlinearity, vol. 27, no. 12, 2014, pp. 3031–57, https://doi.org/10.1088/0951-7715/27/12/3031.
de la Hoz, Francisco, and Luis Vega. 2014. “Vortex filament equation for a regular polygon.” Nonlinearity 27 (12): 3031–57. https://doi.org/10.1088/0951-7715/27/12/3031.
de la Hoz, F. and Vega, L. (2014) ‘Vortex filament equation for a regular polygon’, Nonlinearity, 27(12), pp. 3031–3057. Available at: https://doi.org/10.1088/0951-7715/27/12/3031.
@article{delahoz2014vortex,
title = {{Vortex filament equation for a regular polygon}},
author = {de la Hoz, Francisco and Vega, Luis},
journal = {Nonlinearity},
volume = {27},
number = {12},
pages = {3031--3057},
year = {2014},
doi = {10.1088/0951-7715/27/12/3031}
}Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.