Standing waves on beaches

TLDR: In this article, the authors measured run-up spectra and nearshore wave spectra associated with standing waves on a natural beach and found that the cross-spectra phase angles between data records had values near 0 or π at frequencies of high coherence.

Abstract: Simultaneous measurements of run-up spectra and nearshore wave spectra associated with standing waves have been made on a natural beach. Digital wave staffs and bottom-mounted pressure sensors were placed in a line at various distances offshore from a digital run-up meter. The run-up meter, which measured the position of the edge of the water, consisted of a series of electrical contacts suspended above the beach face and spaced 30 cm apart. Because of the possible influence of nonlinear interactions on the spectra, bicoherence was estimated, and the frequency range appropriate to a linearized model was defined. In this low-frequency region of the spectrum the cross-spectra phase angles between data records had values near 0 or π at frequencies of high coherence. The energy spectrum levels and the observed phase differences between records were in good agreement with the linear shallow water wave theory (Lamb, 1932) for standing waves on a plane beach. The general reflection coefficient for the data, estimated from the disagreement between data and standing wave theory, was found to be approximately 0.7. This result indicates that the theory of Miche (1944) for reflection from a plane beach predicts a reflection coefficient that is too high by a factor of approximately 1.5.