. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 0 ALONGSHORE DISTANCE (x/W) Figure 33. Shoreline evolution between two groins initially filled with sand (L/W = , a = rad) o From Equation 71, the sand bypassed (discharge rate) at x = W can be obtained. The sand transport rate as a function of time can be written (if it is assumed that tan a « a ) o o Q( t) = 4Q a V (-l)n „ | .. o o Z^ (2n + l)n -e(2n+l)2ir2t/4W2 n=0 (73) for t > 0 and x = W . In Equation 73, the quantity 2Q a is the sand transport rat
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. 0 ALONGSHORE DISTANCE (x/W) Figure 33. Shoreline evolution between two groins initially filled with sand (L/W = , a = rad) o From Equation 71, the sand bypassed (discharge rate) at x = W can be obtained. The sand transport rate as a function of time can be written (if it is assumed that tan a « a ) o o Q( t) = 4Q a V (-l)n „ | .. o o Z^ (2n + l)n -e(2n+l)2ir2t/4W2 n=0 (73) for t > 0 and x = W . In Equation 73, the quantity 2Q a is the sand transport rate along a straight beach exposed to the incident breaking wave angle a . (This is the transport initially existing when the groin compartment is completely filled.) If Q in Equation 73 is normalized with this quantity, the bypassing sand discharge at the downdrift end groin is conveniently displayed in dimension- less form. Figure 34 shows such a curve. 54. 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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