LONGMOR model; modelling of longshore transport and morphology

This model is an advanced Fortran-model which computes the longshore (see Plots below):

1) sand or gravel (shingle) transport,
   (three formulae are available: CERC, KAMPHUIS and VAN RIJN),

2) shoreline changes (including structures such as groynes).

Shoreline changes can be computed by considering the sand continuity equation for the littoral zone (surf zone) with an alongshore length of DX, a cross-shore length of DY  and a vertical layer thickness (h). The sand balance reads as (see upper plot):

h [d(Ys)/dT] + d(Qs)/dX - qs=0

with: ys=cross-shore position of shoreline, x=longshore coordinate, h=thickness of active littoral zone layer, Qs=longshore transport, qs=source, sink or cross-shore transport contribution.

This expression states that: a coastal section will erode if more sand is carried away than supplied; vice versa coastal accretion will occur if there is a net supply of sand.
The longshore sand or gravel transport depends on the angle of the wave direction at the breaker line and the shoreline angle.

The lower plot shows the computed shoreline position of shingle (size of 20 mm) between groynes after 60 days with offshore waves of 2 m coming from an angle of 30 degrees with the coast normal.