Wave Setup

EM 1110-2-1100 (Part II)

31 July 2003

break, and then reform on the reef flat. Irregular transformation models based on Equation II-4-13 give

reasonable results for reef applications (Young 1989), even though assumptions of gentle slopes are violated

at the reef face. Wave reflection from coral reefs has been shown to be surprisingly low (Young 1989; Hardy

and Young 1991). Although the dominant dissipation mechanism is depth-limited wave breaking, inclusion

of an additional wave dissipation term in Equation II-4-13 to represent bottom friction on rough coral

improves wave estimates. General guidance on reef bottom friction coefficients is not available, site-specific

field measurements are recommended to estimate bottom friction coefficients.

(5) Advanced modeling of surf zone waves. Numerical models based on the Boussinesq equations have

been extended to the surf zone by empirically implementing breaking. In time-domain Boussinesq models,

a surface roller (Schffer et al. 1993) or a variable eddy viscosity (Nwogu 1996; Kennedy et al. 2000) is used

to represent breaking induced mixing and energy dissipation. Incipient breaking for individual waves is

initiated based on velocity at the wave crest or slope of the water surface. These models accurately represent

the time-varying, nonlinear wave profile (including vertical and horizontal wave asymmetry) and depth-

averaged current. Boussinesq models also include the generation of low-frequency waves in the surf zone

(surf beat and shear waves) (e.g., Madsen, Sprengen, and Schffer 1997; Kirby and Chen 2002). Wave runup

on beaches and interaction with coastal structures are also included in some models. Although Boussinesq

models are computationally intensive, they are now being used for many engineering applications (e.g.,

Nwogu and Demirbilek 2002). The one-dimensional nonlinear shallow-water equations have also been used

to calculate time-domain irregular wave transformation in the surf zone (Kobayashi and Wurjanto 1992).

This approach has been successful in predicting the oscillatory and steady fluid motions in the surf and swash

zones (Raubenheimer et al. 1994). Reynolds Averaged Navier Stokes (e.g., Lin and Liu 1998) and Large

Eddy Simulation (Watanabe and Saeki 1999; Christensen and Deigaard 2001) models have been developed

to study the turbulent 3-D flow fields generated by breaking waves. These models can represent obliquely

descending eddies generated by breaking waves (Nadaoka, Hino, and Koyano 1989) which increase the

turbulent intensity, eddy viscosity, and near-bottom shear stress (Okayasu et al. 2002). Results from these

models may help explain the difference in sediment transport patterns under plunging and spilling breakers

(Wang, Smith, and Ebersole 2002). These detailed large-scale turbulence models are still research tools

requiring large computational resources for short simulations. However, results from the models are

providing insights to surf zone turbulent processes that are difficult to measure in the laboratory or field.

II-4-3. Wave Setup

a. Wave setup is the superelevation of mean water level caused by wave action (additional changes in

water level may include wind setup or tide, see Part II-5). Total water depth is a sum of still-water depth and

setup

d'h%η

(II-4-19)

where

h = still-water depth

& = mean water surface elevation about still-water level

b. Wave setup balances the gradient in the cross-shore directed radiation stress, i.e., the pressure

gradient of the mean sloping water surface balances the gradient of the incoming momentum. Derivation of

radiation stress is given in Part II-1.

II-4-12

Surf Zone Hydrodynamics