In this situation of a gravel shore, because most material remains at the updrift side of
the channel, little depth is lost (Fig. 6). However, after 2 years, the updrift side of the
channel has intruded about 37 percent of the way across the channel (Fig. 7), becoming a
hazard to navigation. The side of the channel grows approximately linearly, because little
material is deposited in the channel bottom through suspension. Therefore, the governing
equation is only weakly nonlinear, and the linearized (analytical) solution and numerical
solution produce almost the same results. Figure 8 shows that most of the material is
deposited into the channel, with little bypassing.
Fig. 6. Increase in elevation (decrease in depth) in channel on gravel shore: comparison of non-
linear model (numerical solution) and linearized model (analytical solution)
Fig. 7. Increase in intrusion distance (decrease in width) in channel on gravel shore: comparison
of non-linear model (numerical solution) and linearized model (analytical solution)
Kraus and Larson
11
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