Nonlinear corrections of linear potential-flow theory of ship waves

Abstract

The Neumann–Michell (NM) theory – a practical linear potential flow theory – is applied to four freely-floating ship models (Wigley, S60, DTMB5415, KCS), assumed to advance at a constant speed in calm water of large depth, to investigate nonlinear effects on the wave drag, the sinkage, the trim, and the wave profile along the hull, and to approximately account for these effects via simple corrections of the linear theory. Nonlinear effects are found to be relatively small. However, an important exception to this general finding is that the wave drag of a bulbous ship (DTMB5415, KCS) is greatly reduced due to the nonlinear component of the pressure in the Bernoulli relation. This important nonlinear effect is readily included in the NM theory. The nonlinear component of the pressure in the Bernoulli relation also yields a small increase of the sinkage, likewise readily included in the NM theory. Moreover, free-surface nonlinearities can have appreciable, although not large, effects on the wave profile. These nonlinear effects can also be approximately taken into account via a simple transformation of the linear wave profile. Indeed, the flow computations for the four ship models considered here suggest that simple (post-processing) nonlinear corrections (that require no additional flow computations) of the NM theory yield numerical predictions of the wave drag, the sinkage, the trim and the wave profile that agree well with experimental measurements, and compare favorably with predictions given by more complex computational methods.