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The nonlinear evolution of waves propagating on a spatially varying opposing current has been observed in a wave–current flume. Regular waves with different initial periods and different initial steepness, s (0.05 < s < 0.19), were generated and observed. Frequency downshift, even with very small initial steepness, was identified. As expected, it was found that opposing currents can have significant interactions with wavetrains. The ultimate frequency downshift increases with the increase in initial steepness. The evolution of frequency modulation was observed via the instantaneous frequency extracted by the Morlet-wavelet transform. The instantaneous frequency showed that often the process of frequency downshift can be local in time and gradual, but abrupt changes of local frequency were also detected. The presence of an opposing current can gradually block the primary wave energy and destroy the conservation of the wave action at downwave locations, thus increasing the asymmetric modulation and accelerating the effective frequency downshift.

A series of physical experiments on the variations of statistics of random waves propagating over a submerged bar were conducted. Random waves were generated by JONWSAP spectra, varying initial spectral width but fixing the wave height and peak frequency. It is found that some freak waves can be formed in the shoaling region close to the top of the bar. And the appearance of these freak waves are mainly caused by the local triad wave-wave interactions. In addition, the probability occurrence of the freak waves has negligible relation with the spectral width. Additionally, the appearance of freak waves is relating to the increasing of wave groupiness in the shoaling region. Furthermore, the relationship between the skewness and kurtosis in the shoaling region can be predicted well with the formula by Mori and Kobayashi (1998).

The main purpose of this article is to decompose the response amplitudes of different resonant modes and to further study the wave energy distributions systematically inside long and narrow rectangular harbors with different bottom slopes when harbor oscillations are induced by normal-incident solitary waves. A series of numerical experiments are carried out using the FUNWAVE 2.0 model. The analysis procedure is mainly based on the improved normal mode decomposition method. Results show that when the incident wave height is small, the resonant wave energy inside harbors is dominated by the lowest few modes, and the higher modes only possess a very small proportion of the resonant energy; when the incident wave height increases, the relative energy distribution becomes uniform, and the proportion of energy in the higher modes increases. In addition, for the same incident wave height, the change of the bottom slope inside the harbor has a negligible effect on the relative energy distribution within the ranges of the variation in bottom slopes and the incident wave heights studied in this article.