. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. where 2 AA = change in cross-sectional beach area (m ) Ay = change in shoreline position (m) D = maximum depth for sand motion (depth of closure) (m) 6. The principle of mass conservation must apply to the system at all times. By considering a control volume of sand and formulating a mass balance during an infinitesimal interval of time, the following differential equation is obtained (see Figure 1): 9Q + ^ = 0 9x 3t (2) where Q = longshore sand transport rate (m /sec) 2 A = cross-
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. where 2 AA = change in cross-sectional beach area (m ) Ay = change in shoreline position (m) D = maximum depth for sand motion (depth of closure) (m) 6. The principle of mass conservation must apply to the system at all times. By considering a control volume of sand and formulating a mass balance during an infinitesimal interval of time, the following differential equation is obtained (see Figure 1): 9Q + ^ = 0 9x 3t (2) where Q = longshore sand transport rate (m /sec) 2 A = cross-sectional area of the beach (m ) x = space coordinate along the axis parallel to the trend of the shoreline (m) t = time (sec) Shoreline. Figure 1. Schematic illustration of a hypothetical equilibrium beach profile 7. Equation 2 states that the longshore variation in the sand transport rate is balanced by changes in the shoreline position. If, in addition to longshore transport, a line source or sink of sand at the shoreline is con- sidered, Equation 2 takes the following form:. 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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