Center for Applied Coastal Research
University of Delaware
Newark, DE 19716
In the November, 1998 issue of National Geographic Magazine, there is an article by Joel Achenbach about on a surfing area off the north shore of Maui called Jaws. About twelve times a year, the wave conditions are just right for the occurrence of extremely large waves at Jaws. Surfers and wind surfers are shown on the Jaws Maui Web page, riding these monster waves.
As waves travel from the deep ocean to a shoreline, they undergo a number of transformations. The most significant is the effect of shallow water, which causes the waves to shoal, refract, and break. (An explanation of these terms is found by clicking here).
Bathymetric (depth) surveys undertaken by the National Geographic Society (NGS) show a large underwater ridge there that juts out from the shoreline towards the northwest as shown in Figure 1. Note south is up in all of our figures and the ridge trends from the shore (top of figure) to the northwest (bottom right). This figure shows the depth contours of the ocean bottom, measured in feet, out to the 100 ft contour. This figure is a representation of the NGS chart obtained by digitizing the bathymetry into a 32x32 matrix of data points (for numerical modelling purposes). Each grid point is 85.9 feet apart.
The waves were modelled by a computer program called REF/DIF 1, which is a combined refraction/diffraction model written by Kirby and Dalrymple (1983, 1996). This program predicts wave behavior over irregular bottom bathymetries.
The principal effect of the Jaws ridge is to cause the waves to refract. Refraction occurs because the part of a wave in shallow water (over the ridge) moves more slowly than waves in deeper water. So when the depth under a wave crest varies along the crest, the wave bends, so that the crest tends to become parallel to the depth contours. (Bascom, 1964)
The REF/DIF program takes the depth values along with the size of the reference grid, the size of each square, and other information and performs calculations to find the predicted water surface information. This program can also subdivide the grid to have a finer resolution. The 32 x 32 grid was subdivided to a 311 x 311 grid.
Figure 2 is a map of the water surface obtained from the REF/DIF model. You should view it as a aerial photograph of the site, except that the high parts of the waves are red and the low parts are blue to show the water surface elevation. The waves from from the bottom of the figure and propagate to the top left corner of the figure. The waves in the top left corner are very small due to the wave breaking that has occurred over the reef. The figure shows the waves bending around the underwater ridge. The darker red areas are where the wave crests are the largest. As the waves propagate further towards the island, the wave crests reach a maximum value and then start to break-- note that the color intensity decreases due to the wave breaking (towards the upper left in the figure. In this picture, the offshore wave is 10 ft high with a 15 sec. wave period. The grid points here are about 8.8 feet apart.
If you click on the picture above, a gif animation shows the waves actually propagating to the shore.
Figure 3 is a 3-dimensional view of figure 2. You can see where the wave heights are maximum--the red peaks.
Figure 4 shows the water surface for a 10 foot wave with a 5 second period. There is not much refraction by the underwater ridge for this wave with a shorter wave period and wave length. Only close to the shore does the wave start to bend a little and then break.
Figure 5 shows where a 10 foot wave of different periods would break according to the wave model. The longer the wave, the further from shore it should break. This is true in this picture except for the 20 second wave.
Figure 6 shows where different height waves all of period 15 sec would break. The taller the wave height, the further from shore it breaks.
The waves at Jaws actually peak near the 30 ft depth contour line near the middle of the ridge. On these graphs the 10 ft high and 15 sec wave peaks near this place.
Kirby, J. T., and R.A. Dalrymple, REF/DIF 1. Version 2.5. Research Report no. CACR-94-22, 1994.
Kirby, J.T. and R.A. Dalrymple, ``A Parabolic Equation for the Combined Refraction-Diffraction of Stokes Waves by Mildly Varying Topography,'' Journal of Fluid Mechanics , 136, 453-466, 1983.