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.