. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 4 6 TIME (et/aa) Figure 8. Percentage of sand volume lost from a rectangular fill as a function of dimensionless time Sand has to be added to the corner of the fill at the following rate: 2y, Q = (27) The spread of the moving shoreline front (Equation 26) is illustrated in Figure 9. 37. It is advisable to use the analytical expressions describing shore- line evolution for a rectangular fill with great care, even for rough estima- tions, because the linearization procedure (Equation
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 4 6 TIME (et/aa) Figure 8. Percentage of sand volume lost from a rectangular fill as a function of dimensionless time Sand has to be added to the corner of the fill at the following rate: 2y, Q = (27) The spread of the moving shoreline front (Equation 26) is illustrated in Figure 9. 37. It is advisable to use the analytical expressions describing shore- line evolution for a rectangular fill with great care, even for rough estima- tions, because the linearization procedure (Equation 8) is based on small shoreline orientation angles, a condition which is violated on the sides of the rectangle. In fact, the linearized transport equation implies an infi- nitely large initial sand transport rate at the edges of the fill. However, the original transport equation (Equation 7) gives a zero transport rate at the corners; thus, a rectangular beach form is stable to parallel incident waves. In reality, sand transport occurs at the corners because of 22. 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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