Session: 12-01-01 Wave theories I

Paper Number: 126146

126146 - New 2d Horizontal Free Surface Flow Models With Applications for Water Waves 

The depth-integrated horizontal momentum (Euler's) equations and continuity equation are the base for a new model development. These depth-integrated equations are exact, satisfying the nonlinear free surface boundary conditions and the no-flux boundary condition on the bottom, and contain only unknown horizontal velocity components, which depend on the vertical coordinate, and free surface elevation. Dividing the water column into several finite elements and approximating the horizontal velocity components using the linear shape function in each element, a set of model equations for horizontal velocities at finite element nodes is derived. These model equations can be applied for transient or steady free surface flows with appropriate lateral boundary conditions and initial conditions. In this paper, we focus on the applications for water wave propagation and scattering problems. A theoretical analysis is conducted to examine the linear wave properties of the new models up to four elements, including wave celerity, group velocity, shoaling gradient, vertical profiles of horizontal and vertical velocities, and non-hydrostatic pressure field. Overall, the new models significantly outperform existing Green-Naghdi-type models in terms of their applicability over the range of water depth to wavelength ratios, and they are also capable of simulating waves interacting with vertically sheared currents, which cannot be treated by Boussinesq-type models. A numerical model based on finite difference method (FDM) is developed for the two-element and three-element models and applied to a wide range of water wave problems.  Numerical validations are performed to study nonlinear Stokes wave propagation in deep water, sideband instability in deep water, shoaling process from deep water to shallow water, regular/irregular wave transformation over a submerged shoal,  and newly-conducted experiments of focusing wave group interacting with linearly sheared currents in deep water, and very good agreements are obtained between the numerical results and laboratory experiments.

Presenting Author: Zhengtong Yang National University of Singapore

Presenting Author Biography: Dr. YANG Zhengtong received his Bachelor’s and Master’s degrees in coastal engineering from Ocean University of China. In 2021, he obtained his Ph.D. degree from the Department of Civil and Environmental Engineering, National University of Singapore. Before joining NUS as a research fellow, he has worked as a scientist at the Technology Centre for Offshore and Marine, Singapore for two years. His research interests are directed toward a better understanding of various coastal processes. He has developed a new set of depth-integrated mathematical and numerical models for simulating wave transformation and wave interacting with vertically sheared current from deep water to nearshore regions. He has published several papers in the Journal of Fluid Mechanics.

Authors:

Zhengtong Yang National University of Singapore
Philip L.-F. Liu Cornell University
Yuzhu Li National University of Singapore