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arXiv · 1505.02254

Scaling properties of generalized two-dimensional Kuramoto-Sivashinsky equations

Vaidas Juknevicius
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Abstract

This paper presents numerical results for the two-dimensional isotropic Kuramoto-Sivashinsky equation (KSE) with an additional nonlinear term and a single independent parameter. Surfaces generated by this equation exhibit a certain dependence of the average saturated roughness on the system size that indicates power-law shape of the surface spectrum for small wave numbers. This leads to a conclusion that although cellular surface patterns of definite scale dominate in the range of short distances, there are also scale-free long-range height variations present in the large systems. The dependence of the spectral exponent on the equation parameter gives some insight into the scaling behavior for large systems.

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Vaidas Juknevicius. 2015-05-09. Scaling properties of generalized two-dimensional Kuramoto-Sivashinsky equations. https://doi.org/10.1140/epjb%2Fe2016-60830-3

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