In this paper, simulations of freak wave generation and evolution are carried out in a 2-D Numerical Wave Tank (NWT), which is based on the improved Volume of fluid method (VOF). The freak wave can be generated by the individual superposition model or the dual superposition model (a transient wave is embedded into a random wave train). Wavelet analysis method has been adopted to calculate the time-frequency energy spectrums of the wave trains collected during freak wave generation and evolution. In the generation course of the freak wave, the energy is focused gradually and the energy is gradually diffused in the course of evolution. When the most appropriate energy concentration occurs, the freak wave results. The moderately large wave, which occurs during the period around the freak wave and does not satisfy all the qualifications of the adopted definition, has a similar time-frequency energy structure with the freak wave. In its wavelet spectrum, strong energy density surges instantaneously and seemingly carried over to the high frequency components at the instant the large wave occurs. The external characteristic parameter α1 (the ratio of the maximum wave height to the significant wave height) and the internal characteristic parameter αE (energy concentration) appear to correspond.

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