General Spectral Computations of the Nonlinear Shallow Water Tidal Interactions within the Bight of Abaco

Abstract

An iterative frequency?time domain finite element tidal circulation model is applied to the Bight of Abaco in the Bahamas to study the nonlinear interactions that occur between the various astronomical, overtide and compound-tide constituents. The nonlinear origin of the significant shallow water constituents is determined by suppressing the various nonlinear terms in the shallow water equations. Furthermore, the extend to which nonlinear constituents interact with and effect each other is studied in detail by suppressing the interaction of selected tides within the framework of the interative frequency-time domain formulation. It is found that second nonlinear interaction between the astronomical tides and the shallow water tides themselves can significantly affect overtide compound tides and even tides. Some important examples include (i) the M2 interaction with M6 which generates the M8 tide, (ii) the Significant reductions in M6, M8 and M10 responses (respectively by 12%, 15% and 25%) due to the interaction involving the 2MN2 and 2MS2 constituents, and (iii) increased responses in the N2 and S2 constituents (by about 7%) due to interactions with the 2MN2 and 2MS2 tides.