Figure 1
Figure 1
Oblique interaction of two nearly solitary waves in shallow water. (Photograph courtesy of T. Toedtemeier.)
Figure 2
Periodic waves in shallow water. The original caption read: "As they near shallow water close to the coast of Panama, huge deep-sea waves, relics of a recent storm, are transformed into waves that have crests, but little or no troughs. A light breeze is blowing diagonally across the larger waves to produce a cross-chop. Three Army bombers, escorted by a training ship, are proceeding from Albrook Field, Canal Zone, to David, Panama." (Taken from National Geographic 63 (1933).)
Figure 3a
Figure 3b
Figure 3c
Mosaic of two overhead photographs, showing surface patterns of waves in shallow water. Each of these waves has a basic hexagonal template; one such hexagon is drawn in the middle figure. (Taken from Hammack, McCallister, Scheffner & Segur, J. Fluid Mechanics 285 (1995) 95-122.)
Figure 4
Aerial Photograph of waves off the southern coast of Long Island. The beack is between Lido Beach and Point Lookout, west of Jones Inlet. Beyond the surf zone, the wave patterns are two-dimensional, and approximately periodic. They have flat troughs, sharp crests, and approximately hexagonal shape. (Taken from Hammack, McCallister, Scheffner & Segur, J. Fluid Mechanics 285 (1995) 95-122.)
Figure 5
A picture of a storm caused by Hurricane Grace, the "Halloween Storm of 1991". This storm became famous as the storm in the book and movie "The Perfect Storm". Note the hexagonal shape and approximate periodicity of the wave pattern (Picture bravely taken by Carl Miller, from a small plane along the coast of the barrier islands in North Carolina during the storm).
Figure 6
This photo was taken February, 1993 on the south shore of Molokai in the Hawaiian Islands, just west of the town of Kaunkakai. Molokai has a 40 mile long reef located about 1 mile offshore, which runs almost the full length of the island. The inshore lagoon is almost constant depth at about 1 meter at high tide. The bottom is very uniform and mostly smooth with sand farther offshore and silt closer to shore. In the winter distant Pacific storms produce waves, which are almost normally incident on the reef where they break, driving the edge of the lagoon very uniformly. Near perfect KdV solitons separate from the initial disturbance caused by the breaking waves, and are observed to propagate shorewards almost from the reef edge. Note the very weak transverse modulation of the wave. (Photograph and caption courtesy of Robert I. Odom, Applied Physics Laboratory, University of Washinton)
Figure 7
Photo taken late February, 2003 at Maalea Bay on Maui in the Hawaiian Islands. Although Maui does not have the long south shore reef that Molokai does, Maalea Bay in central Maui has a very shallow bottom slope, which allows the incoming ocean swell waves to steepen without breaking into near perfect solitons. Because there is a slight slope to the bottom, higher order effects such as the formation of a trailing "shelf" and secondary wave peak are occasionally observed. (Photograph and caption courtesy of Robert I. Odom, Applied Physics Laboratory, University of Washinton)
Figure 8
A photo of a CERC harbor model with two incoming plane wave trains interacting with each other and the harbor walls. A region with hexagonal wave patterns is clearly visible (Source unknown)
What happens when hexagonal shallow-water waves hit a beach?