Modeling of the propagation and evolution of nonlinear waves in a wave train - Sulisz, W.; Paprota, M. (Archives of Mechanics, 2011)
A theoretical approach is applied to predict the propagation and evolution of nonlinear water waves in a wave train. A semi-analytical solution was derived by applying an eigenfunction expansion method. The solution is applied to study the evolution of nonlinear waves in a wave train and the formation of freak waves. The analysis focuses on the changes of wave profile and wave spectrum due to the interaction of wave components in a wave train. The results indicate that for waves of very low steepness, the changes of wave profile and wave spectrum are of secondary importance and weakly nonlinear wave theories can be applied to describe wave propagation in a wave train. For waves of low and moderate steepness, the nonlinear terms in the free-surface boundary conditions are becoming more and more important and weakly nonlinear wave theories cannot be applied to describe substantial changes in wave profile. A train of basically sinusoidal waves may drastically change its form within a relatively short distance from its original position and freak waves are often formed. The interaction between waves in a wave train and significant wave evolution has substantial effects on a wave spectrum. A train of initially very narrow-banded spectrum changes its simple one-peak spectrum to a broad-banded and often multi-peak spectrum in a fairly short period of time. The analysis shows that these phenomena cannot be described properly by the nonlinear Schrödinger equation or its modifications. Laboratory experiments were conducted in a wave flume to verify theoretical approaches. The free-surface elevation recorded by a system of wave gauges was compared with the results provided by the semi-analytical solution. Theoretical results are in a fairly good agreement with experimental data. A reasonable agreement between theoretical results and experimental data is observed, even for complex changes of long wave trains.