Binary tree models of high-Reynolds-number turbulence
Erik Aurell (1,2),
Emmanuel Dormy (3,4)
and Peter Frick (2,3,5)
(1) Mathematics Dept., Stockholm University, SWEDEN
(2) PDC/KTH, Stockholm, SWEDEN
(3) LMD/ENS, Paris, FRANCE
(4) IPGP, Paris, FRANCE
(5) ICMM, Perm, RUSSIA
Physical Review E, Vol. 56, No. 2,
pp. 1692-1698.
Abstract. We consider hierarchical models for
turbulence, that are simple generalizations
of the standard Gledzer-Ohkitani-Yamada shell models (E.B. Gledzer,
Dokl, Akad. Nauk SSSR 209, 5 (1973)
[Sov. Phys. Dokl. 18, 216 (1973)]; M. Yamada and K. Ohkitani,
J. Phys. Soc. Jpn. 56, 4210 (1987)).
The density of degrees of freedom is constant in wave-number space.
Looking only at this behaviour and at the quadratic invariants in the inviscid
unforced limit, the models can be thought of
as systems living naturally in one spatial dimension, but being
qualitatively similar to hydrodynamics in two (2D) and three dimensions.
We investigated cascade phenomena and intermittency in the different cases.
We observed and studied a forward cascade of enstrophy in the 2D case.