Nonlinear Resonant Wave Interactions in Density-Stratified Flows

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Nonlinear internal waves and their interaction with surface waves have been frequently observed in density-stratified oceans, where the temperature and salinity vary with depth. In particular, nonlinear resonant interactions have been known to play a crucial role in the long-term evolution of surface and internal wave spectra. In addition, recent observations from remote sensing have shown that internal waves can substantially change the surface expression of the ocean. Therefore, a better understanding of the dynamics of nonlinear surface and internal waves and their interactions is crucial in many disciplines, including physical oceanography, environmental science, and ocean and coastal engineering. Ultimately this information would help researchers working on climate change as the transfer of energy and momentum across the air-sea boundary and in the interior of the ocean is fundamental to their work. This project will address several aspects of the dynamical interaction of internal and surface waves through a combination of modeling, numerical simulations, and experiments at the newly developed wave research laboratory at NJIT. The project will also provide opportunities for the involvement of undergraduate and graduate students in the research.This project will study numerically the recently developed explicit Hamiltonian system for multi-directional waves in two-layered flows and will derive reduced models for near-resonant interactions between narrow-banded 2D surface waves and a large amplitude long internal wave. With keeping realistic oceanic conditions in mind, the project will study the effects of wave direction, bandwidth, and high-order nonlinearity on the modulation of surface waves induced by internal waves and the subsequent energy transfer between the two wave modes. The focus is on the evolution of a packet of short surface waves satisfying the so-called group resonance condition, which requires the group velocity of the packet to match approximately the phase speed of a long internal wave. This condition can be easily met under realistic oceanic conditions. The mathematical models will be then validated for one dimensional waves with fully nonlinear numerical solutions of the Euler equations obtained via an unsteady conformal mapping technique and previous laboratory observations. The theoretical approach for two-layered flows will be extended to three-layered flows, and the conditions for resonant interactions between the first two internal wave modes and their dynamics will be studied. In addition to time-periodic resonant interactions, a special resonant interaction with no energy exchange will be examined to find traveling wave and steady-state solutions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.