Laboratory investigations of deep-water wave transformation and stability

The authors performed laboratory investigations and the analysis of the transformation of deep-water waves in the flume of the Institute of Hydro-Engineering. Special wave trains were generated by our piston-type wavemaker. Due to the transformation the wave profiles changed along the path of propagation. At first, the changes appeared at the ends of the wave train. Far from the generator they intruded into the middle interval of initially regular waves. Finally, the whole wave train consisted of a set of irregular groups. To study the instability problem the wave trains were modulated by superposition of wave groups with very small amplitudes. The number of waves in a group was a very important parameter. When the number was proper, even small amplitudes of modulation resulted in strong development of amplitudes of wave groups. In our theoretical analysis the non-linear Schroedinger equation was used. The comparison of laboratory and theoretical results proved that this equation is useful but it does not describe the phenomenon in the best way. There have been many attempts to construct a numerical procedure that describes the propagation of water waves. Very often the numerical algorithm is not stable and the results of calculation diverge from the expected behaviour. The authors believe that in many cases the instability is due to the physical loss of stability of the wave train and thus it is necessary to have a good understanding of the physics of the studied motion.