Near Field Expression of Ship Wave Resistance by Green’s Theorem

The ship wave resistance can be estimated by two alternative methods after solving the boundary integral equation. One is the far field method e.g. Havelock’s formula based on momentum conservation in fluid domain, and another is the near field method based on direct pressure integration over the wetted body surface. Nakos and Sclavounos (1994) had shown a new near field expression of ship wave resistance from the momentum conservation law in the fluid domain with linearized free surface condition. Their new expression differs slightly from the traditional near field form. This problem of near field expression is reconsidered in terms of Green’s second identity. After linearization of the free suface condition and some transformation of equations, the present paper will agree with the Nakos and Sclavounos’ near field expression for the ship wave resistance. Some numerical calculations of wave resistance from the far field method and from the near field method are shown using the classical Kelvin sources distributed on the centerplane of thin ship but solving the different boundary integral equation. Numerical results suggest that the problematic run-up square integration along the waterline is to be omitted as a higher order small quantity. If this run-up term is omitted in each method except for far field, the traditional direct pressure integrtaion is equal to the Nakos and Sclavounos’ near field expression.