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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union

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Nonlin. Processes Geophys., 23, 285-305, 2016
http://www.nonlin-processes-geophys.net/23/285/2016/
doi:10.5194/npg-23-285-2016
© Author(s) 2016. This work is distributed
under the Creative Commons Attribution 3.0 License.
Research article
18 Aug 2016
Limiting amplitudes of fully nonlinear interfacial tides and solitons
Borja Aguiar-González1,2 and Theo Gerkema3 1Departamento de Física, Facultad de Ciencias del Mar, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas, Spain
2NIOZ Royal Netherlands Institute for Sea Research, Department of Ocean Systems Sciences, and Utrecht University, P.O. Box 59, 1790 AB Den Burg, Texel, the Netherlands
3NIOZ Royal Netherlands Institute for Sea Research, Department of Estuarine and Delta Systems, and Utrecht University, P.O. Box 140, 4400 AC Yerseke, the Netherlands
Abstract. A new two-fluid layer model consisting of forced rotation-modified Boussinesq equations is derived for studying tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial waves. This set is a generalization of the Choi–Camassa equations, extended here with forcing terms and Coriolis effects. The forcing is represented by a horizontally oscillating sill, mimicking a barotropic tidal flow over topography. Solitons are generated by a disintegration of the interfacial tide. Because of strong nonlinearity, solitons may attain a limiting table-shaped form, in accordance with soliton theory. In addition, we use a quasi-linear version of the model (i.e. including barotropic advection but linear in the baroclinic fields) to investigate the role of the initial stages of the internal tide prior to its nonlinear disintegration. Numerical solutions reveal that the internal tide then reaches a limiting amplitude under increasing barotropic forcing. In the fully nonlinear regime, numerical experiments suggest that this limiting amplitude in the underlying internal tide extends to the nonlinear case in that internal solitons formed by a disintegration of the internal tide may not reach their table-shaped form with increased forcing, but appear limited well below that state.

Citation: Aguiar-González, B. and Gerkema, T.: Limiting amplitudes of fully nonlinear interfacial tides and solitons, Nonlin. Processes Geophys., 23, 285-305, doi:10.5194/npg-23-285-2016, 2016.
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We derive a new two-fluid layer model consisting of forced rotation-modified Boussinesq equations for studying the limiting amplitudes of tidally generated fully nonlinear, weakly nonhydrostatic dispersive interfacial tides and solitons. Numerical solutions show that solitons attain in some cases a limiting table-shaped form, but may also be limited well below that state by saturation of the underlying quasi-linear internal tide under increasing barotropic forcing.
We derive a new two-fluid layer model consisting of forced rotation-modified Boussinesq...
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