On the waveless statement of the two-dimensional Neumann—Kelvin problem for a surface-piercing body

New supplementary conditions are proposed for the two-dimensional Neumann—Kelvin problem describing the forward motion of a surface-piercing body. They lead to the absence of waves behind the body and, hence, to the wave resistance being equal to zero. Moreover, for the body with symmetry about the vertical axis the total resistance to the forward motion (the sum of wave and spray resistance) also vanishes when these conditions are imposed. The behaviour of spray resistance is investigated numerically for a family of asymmetric contours.