The universal structure of high-curvature regions of material lines in chaotic flows
Regions of high curvature of a material line as they evolve in a chaotic flow are considered. In such a region, the curvature as a function of arclength along the line is found to have a universal form with the peak curvature the only parameter involved. The alignment of the principal axes of the strain tensor with respect to the local tangent vector of the curve and the ratio of the two largest finite-time Lyapunov exponents play a key role. Numerical experiments with ABC flow demonstrate the result.
Copyright © Cambridge University Press 2009. (Received 11 July 2008 and in revised form 2 October 2008). Published online by Cambridge University Press 23 February 2009.
Published - Leonard2009p5489J_Fluid_Mech.pdf