Generation of mode-2 internal waves in a two-dimensional stratification by a mode-1 internal wave

The generation of mode-2 nonlinear internal waves (IWs) by the evolution of a mode-1 IW in a two-dimensional stratification is investigated. A generation model accounting for intermodal interaction is derived based on a multi-modal approach in a weakly nonlinear and non-hydrostatic configuration. The generation model is numerically solved to simulate the evolution of mode-1 and mode-2 IWs in an inhomogeneous pycnocline. The numerical experiments confirm that a mode-2 IW is generated due to linear and nonlinear intermodal interaction. The mode-2 IW continues growing and gradually separates with the mode-1 IW during the generation process. A non-dimensional quantity quantifying the energy of mode-2 IWs is used to investigate the favorable conditions for the formation of mode-2 IWs. The numerical results suggest that the pycnocline strength or depth prominently affects the formation of mode-2 IWs, followed by pycnocline thickness. A weakening or shoaling pycnocline favors the formation of mode-2 IWs by evidently enhancing linear and nonlinear intermodal interaction, whereas a thinning pycnocline favors the process mainly by enhancing nonlinear intermodal interaction. Shortening the front length inhibits nonlinear intermodal interaction while equivalently strengthens the linear intermodal interaction. Increasing the initial mode-1 IW amplitude can noticeably increase the produced mode-2 IW amplitude.