Nonlinear generation of harmonics by an internal wave beam incident on a model oceanic pycnocline: numerical study

The interaction of an internal wave beam with an idealized oceanic pycnocline is examined using 2-D fully nonlinear direct numerical simulation. These simulations vary the normalized pycnocline thickness and the ratio of peak pycnocline buoyancy frequency to that of the stratified lower layer. The angle of the beam with respect to the horizontal is held fixed at 45 degrees. Harmonics at the point of beam entry into the pycnocline increase in amplitude and number with the maximum gradient of the buoyancy frequency, suggesting refraction as an important factor in harmonic generation. For thin pynoclines, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of a natural pycnocline interfacial wave mode. For thicker pycnoclines, whose thickness is equal to the incident beam thickness, beam refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline. These results are consistent with weakly nonlinear theory and with recent laboratory experiments.