. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 1 2 ALONGSHORE DISTANCE (x/a) Figure 12. Shoreline evolution of an initially triangular beach was made between the analytical solution and a numerical solution with the original sand transport equation (Equation 7). Figure 13 shows the result as a function of the height-to-width ratio and elapsed time. 43. It is quite clear that the analytical solution produces a higher rate of shoreline change by overestimating the longshore sand transport rate (since a > sin a). Thus,
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 1 2 ALONGSHORE DISTANCE (x/a) Figure 12. Shoreline evolution of an initially triangular beach was made between the analytical solution and a numerical solution with the original sand transport equation (Equation 7). Figure 13 shows the result as a function of the height-to-width ratio and elapsed time. 43. It is quite clear that the analytical solution produces a higher rate of shoreline change by overestimating the longshore sand transport rate (since a > sin a). Thus, if the analytical solution is used to estimate the time scale involved in beach nourishment problems, a higher rate of attenua- tion of the fill will always be obtained than is expected to actually occur. Trapezoidal-Shaped Beach 44. A trapezoidal beach form is described by the following initial conditions: y(x,0) = y-i - yi X + ylX2 " Xly2 (34) X xr 27. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Larson, Magnus; Hanson, Hans; Kraus, Nicholas C; U. S. Army Engineer Waterways Experiment Station; Coastal Engineering Research Center (U. S. ); United States. Army. Corps of Engineers. [Vicksburg, Miss. : U. S. Army Engineer Waterways Experiment Station ; Springfield, Va. : available from National Technical Information Service]
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