The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $219,997 Project Grant to the University of Delaware to conduct research in Hamiltonian formalism applied to wave turbulence problems. The research aims to develop new mathematical models to better understand nonlinear phenomena related to ocean waves, specifically wave-current interactions and wave-structure interactions. Key areas of focus include rogue wave generation, contaminant transport, sediment transport/coastal erosion, and optimization of wave energy converter array configurations. This research will contribute to advancing the theory of weak wave turbulence in complex media. The project provides opportunities for graduate student participation and training. The research is funded through the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which supports the progress of mathematical and physical sciences to strengthen the nation's scientific enterprise.