A Numerical Study of Kinematics of Nonlinear Water Waves in Three Dimensions

by Hongbo Xü, Massachusetts Inst of Technology, Cambridge, United States,
Dick K. P. Yue, Massachusetts Inst of Technology, Cambridge, United States,

Document Type: Proceeding Paper

Part of: Civil Engineering in the Oceans V


We present a new method for analyzing the kinematics of nonlinear water waves in a three-dimensional domain. This method is based on our extension and generalization of the mixed-Eulerian-Lagrangian (MEL) approach of Longuet-Higgins & Cokelet (1976) to full three dimensions, which include our development of (i) an efficient and robust high-order Laplace solver based on bi-quadratic curvilinear boundary elements (QBEM); (ii) an effective parametric finite-difference (PFD) scheme for free-surface velocity computations. Extensive convergence tests are formed to validate the accuracy (which is quadratic in the number of unknowns) and effectiveness of the method. This method is first applied to simulate 3D deep-water overturning waves. It is demonstrated that the method is able to describe accurately the evolution of steady and unsteady nonlinear waves including wave overturning. The entire velocity and acceleration fields can be obtained by this method. It is found that the transverse scale of a 3D overturning wave can be much shorter than the longitudinal one.

Subject Headings: Nonlinear waves | Water waves | Numerical analysis | Kinematic waves | Nonlinear analysis | Boundary element method | Three-dimensional models | Free surfaces

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