ABSTRACT
Shallow surface water žows refer to problems where the horizontal dimension of the dominant žow process far exceeds the water depth. When waves are the dominant žow process, such žows are o¢en referred to as shallow water waves and are characterized by wavelengths signiŸcantly larger than the mean water depth (see Figure 40.1a). Examples of shallow water waves include tsunamis, tidal and žood waves, where the wavelength is o¢en 100-1000 times larger than the water depth. For example, a typical length scale of a tsunami wave with a period of 20 min in an ocean with a depth of the order of 4 km is about 200 km. When turbulence is the dominant process of interest, such žows are o¢en called shallow turbulent žows and are characterized by vortical structures aligned with the gravitational axis and whose diameter is far greater than the water depth (see Figure 40.1b). For example, the horizontal scale of the eddies in the wake of Rattray Island in northeast Australia is of the order of 1000 m, while the water depth is of the order of 20 m (Wolanski et al. 1984). In addition, the horizontal scale of the eddies in the wake of islands in Rupert Bay in northern Canada ranges from 100 to 3000 m, while water depth ranges from 1 to 4 m (Ingram and Chu 1987). Moreover, the horizontal scale of the eddies in the mixing layer downstream of a junction of the Mekong river is of the order of a 1000 m, while the water depth ranges from 5 to 10 m (Jirka and Seol 2010).
