Modulation instability (MI) is one possible mechanism to explain the formation of extreme waves in uni-directional and narrow-banded seas. It can be triggered, when side-bands around the main frequency are excited and subsequently follow an exponential growth. In physical domain this dynamics translates to periodic pulsations of wave groups that can reach heights up to three times the initial amplitude of the wave train. It is well-known that these periodic wave groups propagate with approximately half the waves phase speed in deep-water. We report an experimental study on modulationally unstable wave groups that propagate with a velocity that is higher than the group velocity since the modulation frequency is complex. It is shown that when this additional velocity to the wave groups is small a good agreement with exact nonlinear Schrödinger (NLS) models, that describe the nonlinear stage of MI, is reached. Otherwise a significant deviation is observed that could be compensated when increasing accuracy of the water wave modeling beyond NLS.

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