ffl. Sediment Transport
129
where :
d
Y
V¢
H,j
t~
= depth below water level
= distance from the shoreline
= fall velocity of the sand related to Dso
= significant wave height in deep water during the storm
= wave length in deep water = 1.56 T 2
3
Coastal Morphology Models
3.1
One-Line and Two-Line Theory
3.1.1
Introduction
Based on longshore transport and coastline configuration, the theory of PelnardConsid6re (1956) gives the basic equations describing the morphological
processes of coastline evolution due to longshore sand transport. These equations
lead to the well-known diffusion equation. The fundamental equation may be
solved point by point (both in space and time) by means of numerical methods if
an accurate description of the wave climate and of its influence on the longshore
transport is known.
A computation program has to include two parts:
a. computation of the longshore transport along a straight coastline and of the
variations in this transport as a function of the coastline direction;
b. computation of the morphological evolution of the coastline by means of the
basic equations.
3.1.2
Basic Equations
For the one-line theory the coastal profile is schematized according to Fig. 28(a).
The equation of continuity is derived from Fig. 28(b). The x-axis is chosen along
the original coastline and the y-axis in a direction perpendicular to the original
coastline in offshore direction. When considering an infinitesimal element with
length dx, the equation of continuity yields:
~1
)
S l +
.dx .dt+ ph dx dt - $1 dt = 3y h dx dt
(69)