The nonlinear response of a Helmholtz oscillator in an interacting, double tidal inlet system

Abstract

Certain field observations indicate irregular tidal oscillations within almost enclosed coastal basins connected to the sea through a narrow channel. Previous studies have explained this using models of Helmholtz resonators which incorporate sloping basin bottoms. These sloping bottoms trigger a nonlinear volume response to external tides coming from the sea. These studies suggest that the nonlinear response of a sloping basin bottom is more pronounced when the basin is near Helmholtz resonance, leading to tides having multiple dynamical equilibria or even exhibit chaotic behaviour within the basin. However, situations where the almost enclosed basin is connected to the sea through multiple channels has not gotten as much exposure in research. This leads, in general, to multiple coupled oscillator equations. This thesis aims to extend the model of the aforementioned articles to a system with two connecting channels and where the coastal basin is, due to a natural barrier, split into two sub-basins that are allowed to interact with each other. It is researched whether similar or new nonlinear effects arise in the extended model. The results imply that the nonlinearities in the extended model still causes, when near Helmholtz resonance, multiple equilibria and chaotic behaviour. In addition, the results suggest that multiple equilibria and chaotic effects may even occur for some basins only if they interact which each other, and not when seperated from each other.