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Limiting amplitudes of fully nonlinear interfacial tides and solitons
Aguiar-González, B.; Gerkema, T. (2016). Limiting amplitudes of fully nonlinear interfacial tides and solitons. Nonlinear Process Geophys. 23: 285–305. dx.doi.org/10.5194/npg-23-285-2016
In: Nonlinear Processes in Geophysics. Copernicus: Göttingen. ISSN 1023-5809, more
Peer reviewed article  

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  • Aguiar-González, B., more
  • Gerkema, T., more

Abstract
    A new two-fluid layer model consisting of forcedrotation-modified Boussinesq equations is derived for studyingtidally generated fully nonlinear, weakly nonhydrostaticdispersive interfacial waves. This set is a generalization ofthe Choi–Camassa equations, extended here with forcingterms and Coriolis effects. The forcing is represented bya horizontally oscillating sill, mimicking a barotropic tidalflow over topography. Solitons are generated by a disintegrationof the interfacial tide. Because of strong nonlinearity,solitons may attain a limiting table-shaped form, in accordancewith soliton theory. In addition, we use a quasi-linearversion of the model (i.e. including barotropic advection butlinear in the baroclinic fields) to investigate the role of theinitial stages of the internal tide prior to its nonlinear disintegration.Numerical solutions reveal that the internal tidethen reaches a limiting amplitude under increasing barotropicforcing. In the fully nonlinear regime, numerical experimentssuggest that this limiting amplitude in the underlying internaltide extends to the nonlinear case in that internal solitonsformed by a disintegration of the internal tide may not reachtheir table-shaped form with increased forcing, but appearlimited well below that state

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