Low mode interactions in water wave model in triangular domain

Abstract

We study gravity water waves in a domain with inclined lateral boundaries that make a $45$°angle with the horizontal axis. We consider free surface potential flow and a simplified model that contains quadratic nonlinear interactions among the normal modes. The particular geometry leads to classical semi-explicit expressions for the normal modes and frequencies, and we use this information to compute the mode interaction coefficients. We further use a partial normal form to compute the amplitude dependence of nonlinear frequency correction of the lowest frequency mode. We indicate the general computation and present numerical results for a truncations to a system for the two lowest modes.