NSC Seminar Soft-mode turbulence as a new type of spatiotemporal chaos at onset

2007-02-02 15:30 - 2007-02-02 17:00
M. Tribelsky (Moscow State Institute of Radioengineering, Electronics and Automation (Technical University))
The main goal of the talk is to call attention of the mathematicalcommunity to a new an appealing physical phenomenon related topattern formation in dissipative systems and to theory ofturbulence. We name the phenomenon \textit{Soft-mode turbulence}(SMT). Up to now it does not have any rigorous description beingdescribed by application of perturbation theory, computer simulationand alike. SMT is exhibited by solutions of a (set) of nonlinear PDEwith the Turing-type instability of a spatially uniformtime-independent solution. It is important for the PDE to beinvariant under transformations of a continuous group of symmetry,so that application of the transformation to the spatially uniformsolution generates a continuous family of such solutions. Because ofthat the stability spectrum of the spatially uniform solutionsagainst spatially periodic perturbations possesses aneutrally-stable in the long wavelength limit (Goldstone) branch,whose interaction with the Turing branch affects the dynamics ofweakly nonlinear patterns dramatically. As a result the entirefamily of time-independent spatially periodic patterns may bedestabilized and SMT comes into being. SMT reveals itself as chaoticlong wavelength spatiotemporal modulations of such patterns whichbasically is not accompanied by defect generation of any kind. Thephenomenon is associated with a single supercritical bifurcation ofthe spatially uniform steady solution. Nevertheless it presentsinterplay of different spatiotemporal scales, Kolmogorov cascadesand other features typical to developed turbulence. The simplest PDEwhose solutions exhibit SMT is introduced and discussed along withthe experimental evidence of the phenomenon.