Stretching and curvature of material lines in chaotic flows

[摘要] 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. (C) 2004 Elsevier B.V. All rights reserved.

[发布日期] 2004-11-15

[关键词] stretching in fluids;Lyapunov exponents;curvature