The effects of finite water depth (d) on unidirectional wave modulation are examined by considering a deep-water short wave train interacting with an intermediate water-depth long wave. The steady solutions are derived up to third order in wave steepnesses respectively using two different approaches: a conventional one employing linear phase functions to describe both long- and short-wave phases and a modulational one using a modulational phase function to model the short-wave phase. The two results are shown to be identical for e1 coth Kd <> e3. The loss of the convergence in the conventional approach results from the approximation of a modulated short-wave phase by a linear phase formulation. In addition to the increasing modulation of the short-wave phase, amplitude and wavenumber as the water depth is shallower, it is found that the modulation of the short-wave intrinsic frequency and potential amplitude along the long-wave surface becomes significant. The previous results (Zhang et al. 1993a) about virtually non-modulated short-wave intrinsic frequency and potential amplitude are only limited to the case of unidirectional wave modulation in vary deep water. The changes in the short- and long-wave characteristics due to wave-wave interaction are determined. Their implications to coastal wave transformation are demonstrated in a qualitative explanation to the phenomena observed in a laboratory simulation of two distinct shoaling wave trains.
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