Flow across reefs or between islands, and effects on shelf-sea motions

Oscillatory (e.g., tidal) flow over and around shallow reefs and islands is considered. Overall matching conditions (between sea levels and flows across the reef) are derived, to represent reef effects in models of larger regions.Analyses include various reef forms of uniform cross-section and water depth h(x), both narrow (uniform cross-reef transport) and broad (decoupled motions on either side). Simple island chains, or reefs broken by passages conducting all the flow, are also considered.In all cases, cross-reef transport is “down” the sea-surface slope, phase-shifted by 0 to 1/4 cycle. The transport is sufficient to render broken reefs effectively transparent to tides, unless the reefs are unusually far from the coast (> 100km, say), dense (> 90%) and broad (> 25km).The matching conditions are consistent with (expected) energy losses for unforced trapped waves propagating along a continental shelf with a long-shelf reef. There is a corresponding change of phase speed, if these effects are small, as is generally so for Kelvin waves. Continental shelf waves, particularly near their maximum frequency, may be strongly retarded and damped by a shelf-edge reef.