In the present study a modified Boussinesq-type model is derived to account for propagation of regular and irregular waves in two horizontal dimensions. An improvement of the linear and nonlinear characteristics of the model is obtained by optimizing the coefficients of each term in the momentum equation, expanding in this way its applicability in very deep waters and thus overcoming a dominant short-coming of most likewise models. The values of the coefficients were obtained by an inverse method in such a way to satisfy exactly the dispersion relation in terms of both first and second order analyse. The modified model was applied to simulate the propagation of regular and irregular waves in one horizontal dimension, in a variety of bottom profiles, such as constant depth, mild slope, submerged obstacles. The simulations are compared with experimental data and analytical results, indicating very good agreement in most cases.
Wind waves are one of the most important phenomena in the marine environment. Understanding wave hydrodynamics and their effects is important for designing marine structures and planning of coastal management. Numerous researchers have contributed to the development of mathematical theories and numerical models aiming at simulating wave propagation and describing wave transformation due to various phenomena such as shoaling, diffraction, refraction, breaking etc. The Boussinesq-type wave models have proven to be quite accurate, especially when applied to relatively shallow water regions. They can incorporate highly non-linear wave characteristics and simulate fully dispersive conditions. Nevertheless these models normally lose some of their efficiency when simulating wave propagation in very deep waters. Thus each of these models has restrictions and specific applicability limits (e.g d/L≤0.5, where d is water depth and L wave length). This is considered a major drawback since wind waves are normally generated and start propagating in deep waters.