Comparison of nonlinear wave-resistance theories for a two-dimensional pressure distribution

The wave resistance of a two-dimensional pressure distribution which moves steadily over water of finite depth is computed with the aid of four approximate methods: (i) consistent small-amplitude perturbation expansion up to third order; (ii) continuous mapping by Guilloton's displacements; (iii) small-Froude-number Baba & Takekuma's approximation; and (iv) Ursell's theory of wave propagation as applied by Inui & Kajitani (1977). The results are compared, for three fixed Froude numbers, with the numerical computations of von Kerczek & Salvesen for a given smooth pressure patch. Nonlinear effects are quite large and it is found that (i) yields accurate results, that (ii) acts in the right direction, but quantitatively is not entirely satisfactory, that (iii) yields poor results and (iv) is quite accurate. The wave resistance is subsequently computed by (i)-(iv) for a broad range of Froude numbers. The perturbation theory is shown to break down at low Froude numbers for a blunter pressure profile. The Inui-Kajitani method is shown to be equivalent to a continuous mapping with a horizontal displacement roughly twice Guilloton's. The free-surface nonlinear effect results in an apparent shift of the first-order resistance curve, i.e. in a systematic change of the effective Froude number.