3 research outputs found
Self-truncation and scaling in Euler-Voigt- and related fluid models
A generalization of the Euler-Voigt- model is obtained by
introducing derivatives of arbitrary order (instead of ) in the
Helmholtz operator. The limit is shown to correspond to
Galerkin truncation of the Euler equation. Direct numerical simulations (DNS)
of the model are performed with resolutions up to and Taylor-Green
initial data. DNS performed at large demonstrate that this simple
classical hydrodynamical model presents a self-truncation behavior, similar to
that previously observed for the Gross-Pitaeveskii equation in Krstulovic and
Brachet [Phys. Rev. Lett. 106, 115303 (2011)]. The self-truncation regime of
the generalized model is shown to reproduce the behavior of the truncated Euler
equation demonstrated in Cichowlas et al. [Phys. Rev. Lett. 95, 264502 (2005)].
The long-time growth of the self-truncation wavenumber appears to
be self-similar.
Two related -Voigt versions of the EDQNM model and the Leith model
are introduced. These simplified theoretical models are shown to reasonably
reproduce intermediate time DNS results. The values of the self-similar
exponents of these models are found analytically.Comment: 14 figure