Nonlinear Tide and Wave Setup Interactions on Reefs with Observations from Ofu, American Samoa

Setup due to wave breaking on coral reefs creates a cross-reef pressure-driven flow which is modulated by the tide. In addition, the tide-wave setup interaction creates a higher harmonic at twice the tidal frequency forced by nonlinearity in the pressure gradient. Based on a 1D pressure-friction momentum balance over an idealized reef we derive the magnitude of the cross-shore velocity, and examine the behavior on intertidal and subtidal time scales. We show that the higher harmonic is a persistent phenomena and the strength depends on the tidal amplitude squared. We also show that wave conditions modify the phase of cross-shore flows; for large incident waves the currents are in phase with the tide, and for small incident waves the two are out of phase. Our estimates are compared to observations from a reef-pool system in Ofu, American Samoa, based on 7 months of observations with good agreement.