A Chaotic Wave Interaction Model for 2D Fluid Flow

Charles Y. Li, Mathematics, UCLA

We introduce a chaotic wave interaction model for 2D fluid flow, by taking a group of ``resonant five wave interactions'' as basic elements and all other modes as noises for chaotic fluid flow. First, we study in detail the chaotic resonant five wave interaction, by constructing homoclinic orbits and Smale horseshoes and symbolic dynamics. Then, we construct homoclinic orbits and Smale horseshoes and symbolic dynamics for the model when the noises are small.