Second Order Wave Propagating Along VLFS

Abstract

This paper addresses the nonlinear deflection wave which propagates along a Very Large Floating Structure (VLFS). The whole VLFS is modeled as a one-dimensional beam afloat on the water surface in a vertical two-dimensional plane. It is assumed that the deflection of the wave propagating along the VLFS has a finite amplitude. The nonlinear wave propagating along the VLFS is investigated by extending the propagation theory of the linear wave along the VLFS. The kinetic and kinematic conditions at the boundary surface between the water and VLFS are considered rigorously up to the 2nd order. The 2nd order wave is obtained as a wave associated with the 1st order wave. The characteristics of the nonlinear wave along the VLFS are elucidated by the mathematical solution. The nonlinear wave along the VLFS has characteristics slightly different from the nonlinear free surface wave, known as Stokes wave. The positive peak of the wave along the VLFS is higher than the negative peak due to the nonlinearity in some frequency range while it is the opposite in the other frequency range. The amplitude of the 2nd order wave increases divergently at the frequency range between the two frequency regimes.