Surfrider Foundation: Mitigation Through Surf Enhancement

CHAPTER 3
Modeling Wave Transformation Over An Artificial Reef
(Page 1 of 7)

Introduction:
Now that a collaborative effort between Surfrider Foundation, Chevron, and the California Coastal Commission has been established to enhance the surf near El Segundo the task at hand is to create an artificial surfing reef that creates a "ridable" wave. Although there have been extensive studies on the effects of submerged breakwaters both on the transformation of wave energy and on shoreface response (Kobayashi and Wurjanto, 1989, Grilli, et al., 1994, Dalrymple and Martin, 1990, and Hsu, 1990) no such structure has been created specifically to enhance recreational surfing. In order to examine the important reef characteristics involved in creating a "surfable" wave at the El Segundo sight before the actual reef is constructed, I employed a computer model of wave refraction and diffraction to simulate waves breaking on a reef-enhanced shoreline. Using Kirby and Dalrymple's (1994) REF/DIF1 wave model, simulated waves were propagated cross-shore over bathymetries that included a reef design on a planar beach characteristic of the El Segundo area. By manipulating the reef shape and location and examining the wave response, the model predictions can be examined to identify important reef design characteristics.

Waves and Wave Modeling:
REF/DIF1 is representative of a new group of water wave models that have significantly improved accuracy in comparison to previous models. Until recently, only very approximate models existed which relied on ray tracing techniques and excluded diffraction. These models had difficulties modeling waves propagation over complex bathymetries. REF/DIF1 is a weakly non-linear combined refraction and diffraction model that models waves on a uniform grid, thus avoiding many of the shortcomings in ray tracing techniques (Kirby and Dalrymple, 1994). Some explanation of wave propagation and transformation as waves approach the shore will clarify the modeling procedure.
Most ocean waves are generated by winds offshore. The size of the waves is dependent on three factors: wind speed, the duration of the wind, and the fetch or distance over which the wind blows (Denny, 1988). As this wind-generated chaotic sea moves away from the source their character changes. The waves organize into swells and tend to propagate in groups and their shape becomes sinusoidal. Because of the relatively simple shape and behavior of these waves traveling in very deep water, they can be described by what is known as linear wave theory, a simple water wave description. Linear wave theory has a number of assumptions, the most important for the modeling application discussed here is that linear wave theory assumes that wave height is infinitesimal relative to water depth (Denny, 1988).
As waves approach the shoreline and shoal (interact with the ocean floor) they transform dramatically in several ways. Waves can be refracted, reflected, diffracted, and they can break. Diffraction occurs as waves pass a structure (i.e. island or a jetty) and energy is propagated around the structure causing the wave to "wrap" around the structure. This "wrap around" effect is responsible for many great surfing areas located near headlands where the waves "wrap around" the headland into the shadowed area and form clean, surfable waves [See Figure 3.1].

Picture of Rincon Point

Figure 3.1: A large swell "wrapping" into the shadow of Rincon Point in the Santa Barbara Channel, CA (Bascom, 1980).

A simple example of refraction occurs when obliquely approaching waves encounter a straight coast with parallel contours, the inshore part of each wave crest is slowed compared to the offshore part of the wave front as wave speed is roughly dependent on depth.

(where C is wave speed, g is the acceleration of gravity, and h is water depth)

The result is that the offshore part of the wave front swings forward relative to the slowing part and the wave crests tend to align with the coastal contours (Bascom, 1980) [See Figure 3.2]. On an irregular coast wave crests tend to converge at the headlands and concentrate wave energy.

Graph of Longshore current

Figure 3.2: Longshore current generated from oblique wave approach (Bascom, 1980).

Conversely, wave crests tend to diverge in bays and coves resulting in a reduction of wave energy [See Figure 3.3]. Refraction can be an important factor in creating "peaky" waves in the surfing in areas with broad flat sand bars. The sand bars acts as a submerged micro-headland that acts to focus wave energy at the reef site. The refractive response of the waves to the sandbar will focus wave energy creating a peak in the wave crest, this can result in a wave that is suitable for surfing.

$Graph of wave refraction$

Figure 3.3: Wave refraction causes a concentration of energy at headlands (A) and a distribution of wave energy in bays (B) (Bascom, 1980).

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