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Time dependent forms of the mild-slope wave equation are apphed to the propagation of regular and irregular wave trains over variable bathymetry. The model equation of Smith and Sprinks is found to be a robust predictor of irregular waves, if the frequency spread for a single component calculation is not made too large. The model is extended to include forced, low-frequency components, and some preliminary results for bound and free long wave computation are shown.fatcat:6xfkusdcezdnjpfoklfchq7ccq