Stretching and Curvature of Material Lines in Chaotic Flows

Details Stretching and Curvature of Material Lines in Chaotic Flows Stretching and Curvature of Material Lines in Chaotic Flows

2002-04-29

arxiv.org/abs/nlin/0204069v3

Physica D 198 (3-4), 169-181 (2004)

Nonlinear Sciences

Chaotic Dynamics

14 pages, 9 figures. RevTeX4 with psfrag macros

Scientific paper

10.1016/j.physd.2004.04.009

As a streak of dye is advected by a chaotic flow, it stretches and folds and becomes indistinguishable from a one-dimensional idealized material line. The variation along a material line of the total stretching experienced by fluid elements is examined, and it is found that it can be decomposed into an overall time-dependent factor, constant along the line, and a smooth time-independent deviation. The stretching is related by a power law to the curvature of the line near sharp bends. This is confirmed numerically and motivated by a simple model. A conservation law for Lyapunov exponents explains deviations from a power-law.

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