Content area
Full text
1. Introduction
A major challenge in modeling flow over coral reefs is parameterization of bottom drag (e.g., Rosman and Hench 2011; Lentz et al. 2017). Bottom drag is a dominant element of the dynamics over most shallow coral reefs (Monismith 2007; Hearn 2011; Lowe and Falter 2015). Surface gravity waves are often an important factor enhancing drag on lower-frequency currents in shallow water (e.g., Grant and Madsen 1986; Feddersen et al. 1998) and are likely to be important over many shallow coral reefs where surface gravity wave orbital velocities can be similar in magnitude to, or larger than, lower-frequency currents (Monismith et al. 2013; Lentz et al. 2017). While there have been numerous studies focusing on low-frequency currents (Roberts et al. 1975; Symonds et al. 1995; Kraines et al. 1998; Callaghan et al. 2006; Coronado et al. 2007; Jago et al. 2007; Hench et al. 2008; Lowe et al. 2009; Vetter et al. 2010; Taebi et al. 2011; Monismith et al. 2013) and on surface gravity wave evolution (Gerritsen 1980; Young 1989; Lugo-Fernandez et al. 1998a,b; Brander et al. 2004; Lowe et al. 2005; Péquignet et al. 2011; Harris and Vila-Concejo 2013; Monismith et al. 2015; Lentz et al. 2016b) over coral reefs, there have been almost no observational studies focusing on the potential enhancement of bottom drag by surface waves over shallow coral reefs (though see Hearn 1999). Failure to consider surface wave enhancement may result in overestimating hydrodynamic roughnesses and drag coefficients for coral reefs.
There are two basic models for enhancement of the drag by surface wave orbital velocities. One model assumes wave-induced stresses are confined to a thin wave boundary layer. In this case, large turbulent momentum fluxes in a very thin (order cm) wave boundary layer result in an “apparent” enhanced hydrodynamic roughness acting on the lower-frequency flow (e.g., Grant and Madsen 1986). This increased bottom drag is due to the enhanced communication of the no-slip condition at the bottom to the low-frequency flow by the turbulence in the thin wave boundary layer. Formally, these wave-current boundary layer models assume that the wave-boundary layer thickness is [Inline formula omitted: See PDF] (κ is von Kármán’s constant, [Inline formula omitted: See PDF] is the shear velocity, and ω is...