coefficient that was not the same as that proposed by Battjes (1975) , based 

 on momentum principles. An expression is also hypothesized for the eddy 

 viscosity that minimizes dissipation in wave re-forming areas (troughs) and 

 relates dissipation to a ratio between the "...real and possible maximum wave 

 heights at any location." The theory is found to simulate laboratory and field 

 wave height distributions over uniform, plane, and step-type beach profiles 

 as discussed in Chapter 4. The theory is extremely crude yet reflects the 

 current primitive state of understanding concerning energy dissipation in the 

 surf zone. 



More detailed measurements of the velocity distributions and spectral 

 characteristics are needed under laboratory and field conditions. Laboratory 

 contributions toward this end have recently been reported by Battjes and 

 Sakai (1980) and Stive (1980). The field effort of Thornton (1977, 1979), 

 Thornton and Schaeffer (1979), and Thornton, et al. (1976) to understand the 

 kinematics of breaking waves is a major step in this direction. Kinematic 

 energy spectra made from field velocity measurements in the surf zone re- 

 veal the highly nonlinear transfer processes resulting in energy transfer to 

 both higher and lower frequencies from the primary incident wave frequency. 

 Higher frequency harmonic peaks appear indicative of the peaked crests and 

 broad troughs of shoaling waves. The spectrum then tails off at a -3 slope 

 because breaking induces a saturation region where energy transfer is con- 

 strained. Finally, the highest frequency region of the spectrum decays at 

 a -5/3 slope as found in all isotropic turbulence. Better surf zone energy 

 dissipation models will result from this type of information and ultimately 

 lead to improved methods to estimate wave height distributions across all 

 types of beach profiles. Refined theoretical models of longshore current 

 profiles will be the end result. 



5. Nonuniform Longshore Current Profiles . 



The analytic theory of longshore currents described in this report is 

 for steady, uniform wave conditions on an infinite beach. As observed in the 

 field (see Ch. 2) variations in breaker height can readily occur along the 

 coast for various reasons (Table 1) but usually due to offshore bathymetry. 

 The alongshore gradient of breaker height produces additional stresses in the 

 y-direction momentum balance (eq. 42). As can be deduced from Figure 23, an 

 alongshore gradient of wave height establishes a gradient in wave setup to 

 produce a net hydrostatic force in the y-direction. In addition, the gradient 

 of radiation stress, dS /dy is no longer zero, but also plays a role in the 

 y-direction momentum balance. 



Using these two additional stress components, Komar (1975a, 1976) ex- 

 tended the original theory of Longuet-Higgins (1970) to include the along- 

 shore variation in wave height. Convective acceleration terms and variations 

 in surf zone width are neglected. Komar used the same weak current small- 

 angle bed shear stress and lateral turbulent mixing stress formulations as 

 Longuet-Higgins (1970) but included the normalized wave setup. A series of 

 examples of longshore current profiles for various wave setup gradients in 

 the alongshore direction is shown in Figure 32, where the data for the compu- 

 tation are also shown (after Komar, 1975a). A negative surface slope gradient 

 in the +y-direction contributes an additional driving force to create a 

 stronger current than when 8ri/9y = 0. For this example, a positive MWL slope 



112 



