Our innovation was to aggregate the longshore transport gradients contributions to the shoreline changes S(t) of the cross-shore equation. Using the assumption that an average shape of the beach on the long term exists, the model describes the fluctuations induced by the varying wave forcing. The curvature of an embayed beach is related to the refraction and diffraction of the waves as they propagate from deep water towards the breaking point. A stretch of beach is at equilibrium if the average wave direction is orthogonal to the beach. Any wave forcing which departs from that average direction will create a longshore sediment transport and since the beach orientation changes alongshore, it produces a transport gradient that results in a change of shoreline position. To account for this we based our model on the one-line approach
The model was calibrated and tested on the Narrabeen beach data (Turner et al., 2015) and also on the Nha Trang beach in Vietnam which is low energy embayed beach. This work was part of the COASTVAR project and is one the research topics of the CARE laboratory (International lab. Between Grenoble INP, IRD and HCMUT).
http://coastaldynamics2017.dk/onewebmedia/247_tran_yen.pdf
https://www.paralia.fr/jngcgc/15_34_tran.pdf
Yen Tran Hai & Eric Barthélemy