Summary
Surface waves trapped over naturally gentle seabed topographies near coasts may decay in time due to energy absorption at the shore. The decay rate is computed in terms of the shore reflection coefficient for round islands and for seabed depth varying only normally to a straight beach, as in laboratory channels. This decay rate is liable to be considerably larger than that due to energy leakage to the open sea, but is still relatively small, since it is proportional to (frequency)-1. The resonant response of such modes may therefore still be important.
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Meyer, R.E., Painter, J.F. Wave trapping with shore absorption. J Eng Math 13, 33–45 (1979). https://doi.org/10.1007/BF00042795
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DOI: https://doi.org/10.1007/BF00042795