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The generation of mode-2 nonlinear internal waves (IWs) by the evolution of amode-1 IW in a two-dimensional stratification is investigated. A generationmodel accounting for intermodal interaction is derived based on a multi-modalapproach in a weakly nonlinear and non-hydrostatic configuration. Thegeneration model is numerically solved to simulate the evolution of mode-1 andmode-2 IWs in an inhomogeneous pycnocline. The numerical experiments confirmthat a mode-2 IW is generated due to linear and nonlinear intermodalinteraction. The mode-2 IW continues growing and gradually separates with themode-1 IW during the generation process. A non-dimensional quantity quantifyingthe energy of mode-2 IWs is used to investigate the favorable conditions forthe formation of mode-2 IWs. The numerical results suggest that the pycnoclinestrength or depth prominently affects the formation of mode-2 IWs, followed bypycnocline thickness. A weakening or shoaling pycnocline favors the formationof mode-2 IWs by evidently enhancing linear and nonlinear intermodalinteraction, whereas a thinning pycnocline favors the process mainly byenhancing nonlinear intermodal interaction. Shortening the front lengthinhibits nonlinear intermodal interaction while equivalently strengthens thelinear intermodal interaction. Increasing the initial mode-1 IW amplitude cannoticeably increase the produced mode-2 IW amplitude.

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