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Long period waves are sometimes significantly large and cannot be neglected even for engineering purposes in the nearshore zone. The growth of amplitude of long waves and phase shift between short wave envelope and incoming long waves on sloping bottom have been studied but not clearly understood. We present a theoretical model for the long wave evolution on the basis of the linear long wave equation with forced term and the model of breakpoint forced long waves. The present model shows good agreement with experiment results of random wave field. Then this model was applied to field observation data, and we show that the amplitude of long waves inner surf zone could express with squared of significant wave height.

Modeling and Statistical Properties of Long Period Waves in the Nearshore Zone