Theory and model physics development

This research direction relates to advancing the mathematical modelling and physical understanding of linear and nonlinear wave-wave, wave-bottom and wave-current interactions.

Linear and nonlinear shoaling are two of the main mechanisms that change the wave spectrum in the near-shore region. The nonlinear mechanism is still not well understood and no mathematical formulation that can adequately allow its inclusion in stochastic wave action equation models, was derived. This is one of the main discrepancies of using wave forecasting models in the near-shore region. The formulation is currently being improved and plans to be implemented in an operational wave forecasting model.

Infra-gravity (IG) waves are long ocean surface waves with periods of 25-250 sec that are not generated directly from the wind but due to nonlinear interactions mostly in the process of wave shoaling or wave breaking. In the nearshore region they can be dominant in the water motion particularly during storms. They have a significant influence on many nearshore processes such as coastal morphodynamics, coastal flooding, seiches of natural bays and harbour agitations. The main long-term goal of the research is to better understand the underlying nonlinear physics of their generation and to extend wind-wave forecasting models to forecast IG waves in regional and global scales.

Ambient currents have a significant effect on wave propagation. They cause refraction, diffraction, reflection, blocking and Doppler shifts. Vertically shearing currents even change the wave’s vertical structure. The modelling and understanding of wave interactions with vertically shearing currents is limited even for the linear case. Even though wave forecasting models are currently coupled with three-dimensional circulation models, their formulation does not take into account the vertical profile of the ambient currents but only their vertical average or surface values.