Nonlinear and unsteady waves generated by a traveling pressure distribution and the associated waveless shapes

The wave elevation and flow near a moving pressure distribution of characteristic intensity \(p_0\) and length \(2a\) are investigated using a fully nonlinear and unsteady mixed Eulerian–Lagrangian method. Special attention is paid to the zero-wave-resistance (ZWR) conditions and the associated waveless free-surface profiles. Large-time solutions for free-surface elevation are in good agreement with linear steady-state solutions for small applied pressure parameter \(p_0/(\rho ga)\), with \(\rho g\) being the weight density of the fluid. The ZWR phenomenon predicted by the linear wave theory at certain critical speeds is recovered from these nonlinear solutions. As \(p_0/(\rho ga)\) increases, large-time nonlinear solutions indicate that trailing waves of near-zero amplitude can still be achieved at certain adjusted critical speeds. The time evolution of the trailing waves is presented and discussed.