Transport and Mixing Processes in Lakes and Reservoirs - Hydro-Environmental Analysis: Freshwater Environments - page 350

FIGURE 13.1 Storm surge on Lake Superior. (Photo from Great Lakes Storms Photo Gallery, October 25-27,
2001, Lake Superior Storm Surge Photos.)

Crest Crest

Wavelength ( L )

Wave
height ( H )

Trough

FIGURE 13.2 Wave characteristics.

As fetch increases, the wavelength increases. Long wavelengths are only produced in the pres-
ence of a long fetch. In addition, with greater fetch, larger waves are produced that can, in turn,
increase shoreline erosion and sediment resuspension. The height of the highest wave is propor-
tional to the square root of the fetch (Wetzel 2001). For example, Wetzel (2001) showed that the
maximum wave height is about 1% of the square root of the fetch ( F , in kilometers):

H = 001 . F (13.1)

max

As an example, for Lake Superior the observed and estimated maximum wave height using this
relationship is about 6.9 m for a fetch of 482 km.
Fetch also impacts habitats. For example, Prince (2011) found signiicant relationships between
fetch and water depth and the occurrence of Eurasian milfoil. Fetch may also have other impacts.
In Lake Michigan, a longer fetch results in stronger lake-effect snow bands due to more warmth
and moisture being added to the air as it crosses the lake. Fetch length is commonly determined
using methods outlined in the U.S. Army Corps of Engineers (the Corps) shore protection manual
(USACE 1984). Rohweder et al. (2008) incorporated the Corps' methods (USACE 1984) along with
a wind wave model, into an ArcGIS platform for assessing the impacts of fetch on habitat rehabilita-
tion and enhancement projects.
The shortest wavelengths require only limited contact between wind and water. Waves with a wave-
length less than 2π cm (6.28 cm) are capillary waves. The more important gravity waves have wave-
lengths longer than 2π cm. The two types of gravity waves are short waves and long waves, distinguished
by the interaction with the lake bottom. The wavelength of short waves is much less than the water depth
(depth < L /2, where L is the wavelength; Figure 13.3a), thus they are not affected by shear at the water
bottom. The waves seen by eye on lake and reservoir surfaces are typically short waves. Long waves,
such as the lake seiche, do interact with and are inluenced by bottom friction (Figure 13.3b). The distinc-
tion between gravity waves is important because of the differences in the resulting mixing.