Application of Directional Wave Spectra Method to Numerical Investigations of Internal Tide Reflection

Internal tides can interfere creating complex patterns of standing waves with nodes and antinodes in energy density. The interference picture becomes more complicated for cases when the field is composed of forward and reflected waves. Such phenomena mask important physical process occurring near steep continental slopes, both in observations and in simulations. Here we propose a method of directional wave spectra decomposition for the analysis of tidal interference. The method is based on fitting plane waves to the spectral representation of numerical observations. The cross-spectra and quad-spectra are linearly regressed to a “kernel matrix” describing interactions of elementary directionally different components. Such an approach, in comparison to regular plane wave fits, has advantage of distinctly defining wave propagation and energies involved. However, the interference picture cannot be perfectly reconstructed since the wave phases are not retained. To test the method’s validity idealized simulations with simplified bathymetric features were carried out. In these experiments the scattered waves can be easily identified and compared with the spectral analysis. Further, we present application of the approach to comprehensive numerical simulations: the propagation of internal tides in Tasman Sea and subsequent reflection from the Tasmanian shelf break. The simulations include mesoscale ocean dynamics which complicate the analysis due to interaction of the tidal signal with the background fields as well as complicated bottom bathymetry that scatter low mode internal tides into higher modes. In both cases the method of wave spectra decomposition proves to give satisfactory results and can be used for investigations of large scale internal tide energy pathways.