. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. where p = density of water (kg/m ) 2 g = acceleration of gravity (m/sec ) H = significant breaking wave height (m) sb Cg, = wave group velocity at breaking point (m/sec) b K = nondimensional empirical constant 3 p = density of sand (kg/m ) X = porosity of sand. Figure 2. Definition sketch for geometric properties at a specific location as related to shoreline change 11. If Equation 5 is substituted into Equation 4, the sand transport rate can be written: Q = Q sin (2[% - ™ «• (If)]
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. where p = density of water (kg/m ) 2 g = acceleration of gravity (m/sec ) H = significant breaking wave height (m) sb Cg, = wave group velocity at breaking point (m/sec) b K = nondimensional empirical constant 3 p = density of sand (kg/m ) X = porosity of sand. Figure 2. Definition sketch for geometric properties at a specific location as related to shoreline change 11. If Equation 5 is substituted into Equation 4, the sand transport rate can be written: Q = Q sin (2[% - ™ «• (If)]} (7) 12. For beaches with mild slopes, it can safely be assumed that the breaking wave angle relative to the shoreline and the shoreline orientation are small. The consequences and validity of this assumption, which linearizes Equation 7, are discussed further in this report. Under the assumption of small angles, to first order in a Taylor series, 10. 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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