Statistical Model with Localized Structures Describing the Spatio-Temporal Chaos of Kuramoto-Sivashinsky Equation

Statistical properties of the chaos of the Kuramoto-Sivashinsky equation are investigated numerically and theoretically. It is found that the chaos consists of spatially localized structures (pulses) and the distances between adjacent pulses have the distribution which is localized around a single peak through fate mechanism of creation and annihilation of pulses. The energy spectrum is calculated by a statistical model in which the pulses with a fixed shape are lined up in the way that each distance is independent of others. This model reproduces a peak near the wavenumber \(k=1/√2\) as well as the flat part near k =0 in the energy spectrum. The linear dependence of the amount of chaos on the system parameter is discussed with this model.