Abstract
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.
Highlights
Generated internal solitons are a widespread phenomenon in the oceans and have been observed and studied for decades
They are intrinsically linked to the internal tide, which itself is generated by barotropic tidal flow over topography
For internal solitons as such, an archetypal model has been the Korteweg–de Vries (KdV) equation, which is based on the assumption of weak nonlinearity and weak nonhydrostaticity
Summary
Generated internal solitons are a widespread phenomenon in the oceans and have been observed and studied for decades (see e.g. Apel et al, 2006). As a consequence, when one includes the genuinely nonlinear effects, i.e. products of baroclinic terms, resulting solitons may stay well below their formal limiting amplitude, no matter how strong the forcing To study these effects we derived a set of fully nonlinear, weakly nonhydrostatic model equations, by extending the MCC equations with a barotropic tidal forcing over topography and with Coriolis effects, which have previously been shown to play a key role in soliton generation from internal tides (Gerkema and Zimmerman, 1995). We focus on the novel aspect of studying the wave evolution and limiting amplitudes of fully nonlinear, weakly nonhydrostatic internal tides and solitons when forcing and rotational effects are added. In Appendix C we compare, within the parameter space of this study, the case of an oscillating topography with the case of a tidal flow over a topography at rest
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