Abstract
With the objective of modeling coastal wave dynamics taking into account nonlinear and dispersive effects, an accurate nonlinear potential flow model is studied. The model is based on the time evolution of two surface quantities: the free surface position and the free surface velocity potential (Zakharov, 1968). The spectral approach of Tian and Sato (2008) is used to resolve vertically the velocity potential in the whole domain, by decomposing the potential using the orthogonal basis of Chebyshev polynomials. The model mathematical theory and numerical development are described, and the model is then validated with the application of three 1DH test cases: (1) propagation of nonlinear regular wave over a submerged bar, (2) propagation of nonlinear irregular waves over a barred beach, and (3) wave generation and propagation after an abrupt deformation of the bottom boundary. These three test cases results agree well with the reference solutions, confirming the model's ability to simulate accurately nonlinear and dispersive waves.
Highlights
Coastal and ocean engineers have a growing need for accurate and rapid wave models that are capable of simulating the propagation of waves in the coastal zone, including interactions at the shoreline and with coastal structures
A model based on fully nonlinear potential flow theory is developed as a compromise between computationally expensive CFD (Computational Fluid Dynamics) approaches based on the full Navier-Stokes equations, and Boussinesq, Serre-type or GreenNaghdi models that simplify the vertical structure of the dynamics and are only partially nonlinear and/or dispersive
Assuming irrotational flow of an inviscid and homogeneous fluid with constant density, the velocity potential Φ(x, z, t) (where x = (x, y)) can be defined. This velocity potential must satisfy the Laplace equation in the fluid domain, which is supplemented by boundary conditions at the free surface z = η(x, t)
Summary
Coastal and ocean engineers have a growing need for accurate and rapid wave models that are capable of simulating the propagation of waves in the coastal zone, including interactions at the shoreline and with coastal structures. The model is tested and applied to three nonbreaking wave test cases: the propagation of (1) regular nonlinear waves over submerged bar (Dingemans, 1994) and (2) irregular nonlinear waves over a barred beach (Becq-Girard et al, 1999), and (3) wave generation from an impulsive upthrust of the bottom (Hammack, 1973). These test cases are presented and analyzed in part 3
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
