Three-dimensional steady nonlinear flexural-gravity waves over bottom topography

In this work, three-dimensional steady nonlinear flexural–gravity waves propagating over localised bottom topography such as bumps and craters are investigated. By re-formulating the problem using a desingularised boundary integral method, we obtain a nonlinear system in surface variables that is solved numerically using a Newton–Krylov approach. The dense Jacobian associated with the nonlocal formulation is treated efficiently through hybrid preconditioning. Solutions for bumps and craters are presented across three regimes, illustrating distinct three-dimensional flexural–gravity wave patterns.