Infragravity Waves on Nonplanar Beaches in the 

 Presence of Longshore Currents 



Analytical descriptions of edge wave dynamics have primarily been restricted 

 to two beach types, one with plane parallel contours (Eckart 1951, Ursell 1952) 

 and one with an exponential profile (Ball 1967). Solutions for beaches with 

 irregular bathymetry are typically found with numerical models (e.g., Howd, 

 Bowen, and Holman 1992; Falques and Iranzo 1992). Holman and Bowen 

 (1979) presented numerical solutions for complex beach profiles, showing that a 

 plane beach assumption could yield estimates of edge wavelength with ±100 

 percent error. They emphasized the importance of profile changes with varying 

 stages of the tide, and the subsequent effects on edge wave amplitudes and 

 modifications to the nodal structure. Kirby, Dalrymple, and Liu (1981) also used 

 a numerical solution to study the effects of nonplanar bathymetry on the cross- 

 shore structure of edge wave nodes and antinodes. They found that for a barred 

 topography, an edge wave elevation antinode would be attracted to the bar crest, 

 resulting in a cross-shore velocity node at the bar and providing a mechanism for 

 bar stabilization. 



Recently, Howd, Bowen, and Holman (1992) examined edge wave solutions 

 for the effects of mean alongshore currents, allowing for slow cross-shore 

 variations in the longshore current and in the depth (mild slope assumption). 

 They demonstrated that longshore currents can significantly modify edge wave 

 refraction in the nearshore waveguide, altering both the edge wave dispersion 

 relation and the cross-shore nodal structure. These waveguide modifications are 

 similar to those produced by sandbars (Kirby, Dalrymple, and Liu 1981). Edge 

 waves opposing the longshore current are refractively focussed to the bar 

 (Figure 9). However, edge waves traveling in the same direction as the 

 longshore current will diverge in the longshore current maximum, similar to their 

 divergence in a trough where the local celerity is a maximum. Thus, as seen in 

 Figure 9, a barred topography will symmetrically modify progressive edge waves 

 whereas the mean longshore current will have a different effect depending on the 

 direction of travel. 



Howd, Oltman-Shay, and Holman (1991) introduced a hypothesis on the role 

 edge waves in strong longshore currents would have on the formation and 

 migration of linear sandbars. They suggested the concept of an "effective beach 

 profile" associated with the modification of edge waves by the cross-shore 

 structure of the longshore current. This model was described in more detail by 

 Howd, Bowen, and Holman (1992). A summary of their work is included here to 

 illustrate the effect of longshore currents on edge wave solutions (see also 

 Oltman-Shay and Howd 1993). 



Howd, Bowen, and Holman (1992) numerically modeled the nearshore 

 waveguide using the invisid shallow- water equations of momentum and mass, 

 including alongshore currents with the total velocity vector 



1 8 Chapter 2 Infragravity Wave Dynamics 



