. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. Here y. and y~ denote shoreline positions corresponding to the longshore locations x and x„ . The solution is y(x,t) = 1 / y2 " yl . ylX2 - Xly2 2\ x2 - xL x + k2 Al X„ - X \ fx. - J erf I — - erf ' 2/et 2/et yo - y, 1\ let r(xrx)2/Aet_ -(x2-x)2/4, (35) for t > 0 and. 0 1 ALONGSHORE DISTANCE (x/a) Figure 13. Comparison between analytical solution with the linearized transport equation and numerical solution with the original transport equation for a triangular beach fil
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. Here y. and y~ denote shoreline positions corresponding to the longshore locations x and x„ . The solution is y(x,t) = 1 / y2 " yl . ylX2 - Xly2 2\ x2 - xL x + k2 Al X„ - X \ fx. - J erf I — - erf ' 2/et 2/et yo - y, 1\ let r(xrx)2/Aet_ -(x2-x)2/4, (35) for t > 0 and. 0 1 ALONGSHORE DISTANCE (x/a) Figure 13. Comparison between analytical solution with the linearized transport equation and numerical solution with the original transport equation for a triangular beach fill (for height-to-width ratios and ) The solution for the triangular beach form (Equation 33) can be obtained by superimposing two trapezoidal beach shapes which reduce to triangles. In the same way, in principle, the analytical solution for any arbitrary shoreline shape may be obtained by approximating the shoreline with a series of straight lines. Even though the sand transport at each boundary of the trapezoids in 28. 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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