A multiplicative process of material line stretching by turbulence

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Abstract
Statistics of material lines passively advected in stationary homogeneous isotropic turbulence of an incompressible fluid are investigated from the viewpoint that material line stretching is a multiplicative process. It is shown by a simple argument based upon this perspective that material line elements cannot be treated equivalently in the line statistics. In other words, a frequently used assumption (Batchelor G K 1952 Proc. R. Soc. A 213 349–66) of their equivalence is not valid in general. The invalidity of this assumption is further confirmed by numerically estimating the correct stretching rate of material lines as 0.17/(Kolmogorov time) which would be 0.13/(Kolmogorov time) if the Batchelor assumption were valid. This substantial difference is a manifestation of the fact that turbulence has spatial inhomogeneity of order of the Kolmogorov length and none-zero finite correlation time of order of the Kolmogorov time, reflecting the existence of small-scale coherent structures. This article was chose...

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