WAVE-DRIVEN FLOW OVER SHALLOW REEFS

Long-term (1 month) observations of waves and currents over a natural reef are presented which show a strong correlation between offshore rm s incident wave height and cross-reef currents at subtidal frequencies . The energy spectrum of the cross-reef currents shows a significant p eak at twice the semidiurnal tidal frequency, while the spectrum;m of sea surface elevation dyer the reef flat shows no corresponding peak. Furthermore, experimental results reported by Gourlay (1993) show setu p over the reef occurs in the absence of a beach, and the cross-reef t ransport decreases with an increase in the sea surface slope across th e reef flat due to an increase in setup at the top of the reef face. A nalytic solutions for flow forced by wave breaking over an idealized r eef explain the above features of cross-reef flows in the absence of a beach. Through the surf zone on the reef face the cross-reef gradient in the radiation stress due to wave breaking is partitioned between b alancing an offshore pressure gradient associated with setup over the reef and forcing a mean flow across the reef. Over the reef flat, wher e the depth is constant, there is no forcing due to wave breaking and the flow is driven by a pressure gradient which results from the setup through the surf zone. The magnitude of the setup through the surf zo ne is such that the transport across the reef flat matches the transpo rt through the surf zone which is forced by the gradient in the radiat ion stress. Solutions are presented for general reef geometry, defined by the reef width and slope of the seaward reef face, and incident wa ve forcing, defined by the depth at the breakpoint and the depth of wa ter over the reef. As the depth over the reef goes to zero, the soluti ons converge to the plane beach solutions described by Longuet-Higgins and Stewart (1964), wave setup is maximized, and the cross-reef trans port is zero. In other cases the relative magnitudes of the setup and the cross-reef transport depend on the geometry of the reef and the in cident wave forcing.