Dynamic Scaling Behaviour in (2+1)-Dimensional Kuramoto-Sivashinsky Model

We study the evolution of (2+1)-dimensional surface morphology in the Kuramoto-Sivashinsky (K-S) model by using the numerical simulation approach. The results show that the surface morphology has the self-affine fractal properties and exhibits cellular structure after long time growth. With numerical correlation analysis, we explicitly observe the dynamic scaling characteristics and obtain the roughness exponent to be 0.77±0.07, the growth exponent to be 0.28 and 0.43, and the dynamic exponents 0.31 and 0.46, for the early times and later times. The simulating results are consistent with the theoretical values in the K-S model.