Nonlinear ship-wave theories by continuous mapping

The exact equations of steady inviscid flow past a ship hull are formulated in a reference domain, onto which the flow domain is mapped. A thin-ship perturbation analysis is performed in the reference domain, and the first- and second-order solutions are derived. The classical thin-ship theory is obtained as the consistent, mapping-independent, perturbation solution in the physical space. Guilloton's method is interpreted as an inconsistent, mapping-dependent, second-order approximation. A new inconsistent approximation is obtained by exploiting the freedom in the mapping of the flow domain onto the reference domain. Further improvements are suggested.