Observations of combined wave and current interactions with a high relief coral reef bottom

On reefs, interaction between the flow and complex bottom topography results in drag forces on currents, dissipation of wave energy, and generation of turbulence. Here, field observations on a shallow backreef were used to investigate wave and current interactions with the bottom at scales of individual colonies across a coral reef patch. Wave direction was aligned with current direction, and the ratio of wave orbital velocities to current (𝜎𝑤/𝑢̅) was less than 0.5. The time-averaged flow was a network of wakes behind colonies. Wake signatures were also observed for wave orbital velocities associated with longer period (13 - 32 s) waves but were absent for shorter period (3 - 5 s) waves. This pattern was explained by a modified Keulegan-Carpenter number 𝐾𝐶𝑐 = 𝑢̅𝑇/𝐿 representing the ratio of wave period (T) to time scale for advection of water past an obstacle with length scale L by the current (L/𝑢̅). Turbulent dissipation rates were elevated in obstacle wakes. For examples where KCc > 1, time-averaged dissipation varied in proportion to the mean of the cubed total (wave plus current) velocity, consistent with parameterization as work done by a quadratic drag force that varied with incident velocity during the wave cycle. Bulk friction coefficients estimated from volume-integrated dissipation in colony wakes together with topography measurements were similar to previous estimates from the reef-scale momentum budget. These results illustrate that, although uncertainties are large, a quadratic drag law in conjunction with spatial averaging is a reasonable approach for scaling up colony to reef-scale drag and dissipation