Statistical conservation laws in turbulent transport

Details Statistical conservation laws in turbulent transport Statistical conservation laws in turbulent transport

2001-04-10

arxiv.org/abs/nlin/0104027v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevLett.87.164502

We address the statistical theory of fields that are transported by a turbulent velocity field, both in forced and in unforced (decaying) experiments. We propose that with very few provisos on the transporting velocity field, correlation functions of the transported field in the forced case are dominated by statistically preserved structures. In decaying experiments (without forcing the transported fields) we identify infinitely many statistical constants of the motion, which are obtained by projecting the decaying correlation functions on the statistically preserved functions. We exemplify these ideas and provide numerical evidence using a simple model of turbulent transport. This example is chosen for its lack of Lagrangian structure, to stress the generality of the ideas.

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