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Local models of spatio-temporally complex fields. (English) Zbl 0885.35115

Summary: We investigate the ability of local models of the one-dimensional Kuramoto-Sivashinsky partial differential equation with periodic boundary conditions, obtained by projection on a small set of Fourier modes on a short subinterval, to reproduce coherent events typical of solutions of the same equation on a much longer interval. We find that systems containing as few as two linearly unstable modes can produce realistic local events in the short term, but that for more reliable short time tracking and long term statistics, three or four interacting modes are required, and that the length of the short interval plays a subtle role, certain “resonant” lengths giving superior results.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
76F05 Isotropic turbulence; homogeneous turbulence
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