Limiting amplitudes of fully nonlinear interfacial tides and solitons

Borja Aguiar-González, Theo Gerkema
2016 Nonlinear Processes in Geophysics Discussions  
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.
more » ... use of strong non-linearity, solitons in some cases attain a limiting table-shaped form, in accordance with soliton theory. More generally, we use the model equations to investigate the role of the initial stages of the internal tide on the limiting amplitudes of solitons under fully nonlinear conditions. Numerical solutions reveal that the tide-generated solitons are primarily limited by the underlying quasi-nonlinear internal tide. We show the decisive factor is the generation of higher harmonics, which already limit the growth of the initial internal tide. As a consequence, and contrary to predictions by classical KdV theory alone, we find that tidally generated solitons are subjected to limiting amplitudes even under weakly nonlinear conditions. This implies that under strongly nonlinear conditions, amplitudes of solitons may be limited before attaining a table-shaped form.
doi:10.5194/npg-2016-1 fatcat:nzu2ld7yjbezpnk2wgd6tsaxfm