On the convergence of multiplicative branching processes in dynamics of fluid flows

Details On the convergence of multiplicative branching processes in dynamics of fluid flows On the convergence of multiplicative branching processes in dynamics of fluid flows

2006-06-14

arxiv.org/abs/cond-mat/0606364v1

Physics

Condensed Matter

Soft Condensed Matter

22 pages, LaTeX

Scientific paper

The Brownian motion over the space of fluid velocity configurations driven by the hydrodynamical equations is considered. The Green function is computed in the form of an asymptotic series close to the standard diffusion kernel. The high order asymptotic coefficients are studied. Similarly to the models of quantum field theory, the asymptotic contributions demonstrate the factorial growth and are summated by means of Borel's procedure. The resulting corrected diffusion spectrum has a closed analytical form. The approach provides a possible ground for the optimization of existing numerical simulation algorithms and can be used in purpose of analysis of other asymptotic series in turbulence.

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