Control of Three Dimensional Water Waves

Computation of three-dimensional standing water waves

Three-dimensional travelling gravity-capillary water waves

1.1 The hydrodynamic problem The classical water-wave problem concerns the irrotational flow of a perfect fluid of unit density subject to the forces of gravity and surface tension. The fluid motion is described by the Euler equations in a domain bounded below by a rigid horizontal bottom {y = −h} and above by a free surface which is described as a graph {y = η(x, z, t)}, where the function η d...

Three-dimensional Solitary Gravity-capillary Water Waves

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...

Calculation of steady three-dimensional deep-water waves

Boundary Integral Methods for Three-Dimensional Water Waves

We describe a boundary integral method for computing time-dependent, doubly periodic, three-dimensional water waves. This method has been proved to converge to the exact solution. We discuss several analytical issues, including the quadrature of singular integrals, such as single and double layer potentials on surfaces, and stability estimates for discrete versions of operators such as the laye...