sediment motion will tend again towards equilibrium, with sediments
moving along the face of the breakwater and depositing at its lee side.
Waves approaching the shore can cause dominant movement of sedi-
ments cross-shore to shape the beach profile. The shape of the beach will
also be affected by the presence of coastal structures. An approximate cri-
terion for the direction of movement of sediments due to Dean (1973) is: if
H 0 /(wsT)1, sediment movement is onshore and if H 0 /(wsT)1, it is off-
shore. The method of Bailard (1982) is widely used to estimate the volume
of cross-shore sediment transport.
It is assumed that over a long period of time, the beach profile tends
to a state of equilibrium. The equilibrium profile proposed by Bruun and
Dean (Dean, 2002) is
dAx2/3 (15.6)in which dis the depth and xis the seaward distance, and A0.067ws0.44.
The limit of the profile is taken to extend closure depth d*1.57Hs12
(Birkemeier, 1985). Hs12is the significant wave height with the frequency
of occurrence of 12 hours per year.
Beach profile and closure depth are useful to compute sediment
volume in beach nourishment schemes. For further details about the shore
evolution and beach nourishment, reference is made to Pilarczyk and
Zeidler (1996), Kamphuis (2000), Dean (2002) and Reeve et al. (2004).
15.2.2 Coastal modelsMany coastal numerical models couple hydrodynamic equations with equa-
tions for transport of sediments, pollutants etc. The hydrodynamic equations
represent the presence of waves, currents and water levels. They also include
forces arising from sources such as Coriolis acceleration, wind stresses and
density effects. Some form of turbulence structure and empirical expression
for boundary friction are assumed. The three dimensional equations are
usually difficult to solve and hence are simplified into two dimensional ones.
Kamphuis (2000) discusses the suitability of these models such as 2 DH
(depth-integrated) and 2 DW (width-integrated) in predicting short term,
medium term and long term morphological changes based on time and
spatial scales. DELFT 3D of Delft Hydraulics Laboratory and MIKE 21 of
Danish Hydraulics Institute are commercial softwares that are popular in the
numerical study of the hydrodynamics, sediment transport, pollutant disper-
sion, morphological changes etc., over extensive coastal regions.
In the numerical models uncertainties remain with respect to bed
forms, bed shear and turbulent stresses, and the interaction between the flow
and the sediment motion is complicated. As coastal morphology depends on
sediment transport, many developed models are deficient in these areas.