Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg–Landau equation

E. Floriani (1) , Thierry Dudok de Wit (2) , P. Le Gal (3)

1 CPT - Centre de Physique Théorique - UMR 7332
2 LPC2E - Laboratoire de Physique et Chimie de l'Environnement et de l'Espace
3 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre

The physical system under consideration is the flow above a rotating disk and its cross-flow instability, which is a typical route to turbulence in three-dimensional boundary layers. Our aim is to study the nonlinear properties of the wavefield through a Volterra series equation. The kernels of the Volterra expansion, which contain relevant physical information about the system, are estimated by fitting two-point measurements via a nonlinear parametric model. We then consider describing the wavefield with the complex Ginzburg–Landau equation, and derive analytical relations which express the coefficients of the Ginzburg–Landau equation in terms of the kernels of the Volterra expansion. These relations must hold for a large class of weakly nonlinear systems, in fluid as well as in plasma physics.

Domains: Sciences of the Universe [physics]

E. Floriani, Thierry Dudok de Wit, P. Le Gal. Nonlinear interactions in a rotating disk flow: From a Volterra model to the Ginzburg–Landau equation. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2000, 10 (4), pp.834. ⟨10.1063/1.1285863⟩. ⟨insu-02928474⟩