GenCade Sand Transport Rates

As stated on the Governing Equations page, the governing equation of GenCade is

${\frac {\delta y}{\delta t}}+{\frac {1}{(D_{B}+D_{C})}}\left({\frac {\delta Q}{\delta x}}-q\right)=0$

This equation is solved with the inputs of boundary conditions and values for Q, q, DB and DC given.

The sand transport rates, Q, is taken from the 'CERC' equation for calculating longshore sediment transport. As formulated in Komar (1969):

$Q=\left(H^{2}C_{g}\right)_{b}a_{1}\sin 2a_{b}$

where H is the wave height (meters), $C_{g}$ is the group wave celerity (meters/second), $a_{b}$ is the angle of the breaking waves to the shoreline, with the subscript b indicating the wave breaker position. Lastly, $a_{1}$ is a non-dimensional parameter:

$a_{1}={\frac {K_{1}}{16\left({\frac {\rho _{s}}{\rho -1}}\right)(1-p)1.416^{5/2}}}$

where K₁ is an empirical coefficient with a nominal value of 0.77, p_s and p are the density of sand and water, respectively, and p is the porosity of sand. In the GENESIS model (Hanson 1987) used an extended version of this relation (Kraus and Harikai 1983):

$Q=\left(H^{2}C_{g}\right)_{b}\left(a_{1}\sin 2a_{b}-a_{2}\cos a_{b}{\frac {\delta H_{b}}{\delta x}}\right)$

where $a_{2}$ is a non dimensional parameter given by:

$a_{2}={\frac {K_{2}}{8\left({\frac {\rho _{s}}{\rho -1}}\right)(1-p)\tan \beta 1.416^{5/2}}}$

where $\tan \beta$ is the average bottom slope from the shoreline to the "maximum depth of longshore transport" (See Empirical Parameters). The nominal value of Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_1} is 0.39 if waves are specified in terms of RMS wave heights (Komar 1976) and 0.77 when using significant wave heights. As a rule of thumb, based on modeling experience, Hanson and Kraus (1989) recommend Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 0.5K_1 < K_2 < 1.5K_1} .

In the calibration and verification process, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_1} and Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_2} values are determined by reproducing changes in shoreline position measured over a certain time interval. Adjusting the Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_1} coefficient will effect the entire modeling domain while $K_{2}$ will only affect the evolution in areas influenced by wave diffraction near structures. In the calibration process, it is recommended that the Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_1} value is adjusted first to get a reasonable agreement with respect to annual transport rates and overall shoreline evolution. Then, the Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_2} value may be altered to improve predicted shoreline response near structures.

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