HOW NON-LINEAR ARE LINEAR WAVES?

The paper gives an overview on the LAGRANGEian treatment of non-linear water waves. With this approach, which can be seen as an appreciation to the very first wave theory of GERSTNER, it can be shown that the "non-linear higher order terms" arise from linear wave kinematics and can be easily deduced and understood. This also holds true for the mass transport in EULERian or LAGRANGEian version, responsible for wave induced currents, backflow in wave channels, and so important to be understood and distinguished in interpreting sediment moving mean currents in waves, or defining boundary conditions for best physical and numerical modeling. The approach can be seen as exact for deep water, with very good attitude in shallower water. The great advantage of the LAGRANGEian approach is its convincing extensibility to irregular waves with bound long and higher components.