Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline

• Published in: Dynamics of atmospheres and oceans 2014-06, Vol.66, p.110-137
• Main Authors: Diamessis, P.J., Wunsch, S., Delwiche, I., Richter, M.P.
• Format: Article
• Language: English
• Subjects: Dynamics of the ocean (upper and deep oceans); Earth, ocean, space; Exact sciences and technology; External geophysics; Interfacial waves; Internal waves; Nonlinear wave interactions; Physics of the oceans; Simulation; Stratified flows
• ISSN: 0377-0265; 1872-6879
• DOI: 10.1016/j.dynatmoce.2014.02.003

•Numerical method enables unprecedented high resolution/accuracy of the pycnocline.•Harmonic amplitude and number increase with the max. gradient of the buoyancy frequency.•Beam refraction is driving factor in harmonic generation in pycnocline entry region.•Thin pycnoclines: harmonic amp. max. during resonance with interfacial wave mode.•Thick pycnoclines: complex structure in pycnocline due to multiple refractions of beam. The interaction of an internal wave beam (IWB) with an idealized oceanic pycnocline is examined using two-dimensional fully nonlinear direct numerical simulations based on a spectral multidomain penalty method in the vertical direction. The phenomenon of focus is the nonlinear generation of harmonics. A total of 24 simulations have been performed, varying the normalized pycnocline thickness and the ratio of peak pycnocline Brunt-Väisälä frequency to that of the stratified lower layer. Harmonics at the point of IWB entry into the pycnocline increase in amplitude and number with a measure of the maximum gradient of the Brunt-Väisälä frequency, suggesting refraction as an important factor in harmonic generation. Among the simulations performed, two distinct limits of pycnocline thickness are identified. For thin pynoclines, whose thickness is 10% of the incident IWB's horizontal wavelength, harmonics trapped within the pycnocline have maximum amplitude when their frequency and wavenumber match those of the natural pycnocline interfacial wave mode. Results in this case are compared with weakly nonlinear theory for harmonic generation by plane wave refraction. For thicker pycnoclines, whose thickness is equal the incident IWB's horizontal wavelength, IWB refraction results in harmonic generation at multiple locations in addition to pycnocline entry, giving rise to complex flow structure inside the pycnocline.