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In this work, we analyze the shoaling of linear long water waves generated by a submerged breakwater composed of wavy surfaces. The undulating surfaces are described by sinusoidal profiles. The mathematical model is expressed in its dimensionless version. The effects of two different geometric parameters – the amplitude of the wavy surfaces and the submerged length of the breakwater – on the free surface elevation is analyzed. The wavy surfaces of the breakwater generate larger values of the wave amplitude than those obtained for breakwaters with flat surfaces. The asymptotic solution is compared with a numerical solution and the results are in good agreement. The results are presented for breakwaters with number of undulations of m = n(= 1, 3). The present theory provides basis for comparison with other approximate theories based on shallow water flows and serves as a prelude to characterize submerged breakwaters of undulating surfaces.

Shoaling of long water waves by its interaction with a submerged breakwater of wavy surfaces