302
8 Transport in the Oceans and Coastal Zone
equations we obtain a sediment transport distribution ql(X) along a beach transect, which constitutes the longshore component of the sediment transport
vector as shown in Fig. 8.18. Figure 8.21 gives an example of the calculated
distribution of the longshore sediment transport across Lamberts Beach (east
coast of Australia) induced by wave approaching at an angle of 20° to the normal to the beach (Massel, B., 1998). Waves were induced by tropical cyclone
'Charlie' (27.02-1.03.1988) moving along the Australian coast southwards. Figure 8.21 corresponds to the situation when incident waves form an angle 20°
with direction normal to the Lamberts Beach. The maximum of the resulting
sediment transport rate is located very close to the breaking line and coincides
with the maximum of the longshore current velocity.
8.6.2 Sediment Budget and Depth Changes
For a given littoral cell, the total volume of sand added to the beach from
various sources can be balanced against the total losses. If the losses are greater
than the gains, then a net deficit takes place and the beach erodes. Similarly,
if the sand added to the beach exceeds the losses, the beach accretes. The lack
of either erosion or deposition indicates the state of equilibrium between the
sources and losses.
Beach erosion or deposition can generally be evaluated by comparing a series
of beach transects. Assuming that these transects are separated by i:1y, and
along the transects the points are separated by i:1x, the sediment budget can
be written as (Fig. 8.22):
(8.128)
in which q2 n ) and q~out) are the cross-shore transport rates, and q?n) and qIout)
are the longshore transport rates, entering and leaving the particular grid cell,
respectively; i:1h is the depth change due to both sediment transport components during time step i:1t.
It is assumed that water depth change in a given grid cell, due to erosion
or deposition, is distributed uniformly on the cell surface. If q~out) > q~in) and
q;out) > q?n) , then water depth in a given cell increases by i:1h. More general,
if the left-hand side of Eq. (8.128) is positive (negative), a given cell is eroded
(deposited) .
The relationship described by Eq.(8.128), can be rewritten more precisely as
follows:
oh
oqc
oql
-+-+-=0.
at ax oy
(8.129)
8 Transport in the Oceans and Coastal Zone
equations we obtain a sediment transport distribution ql(X) along a beach transect, which constitutes the longshore component of the sediment transport
vector as shown in Fig. 8.18. Figure 8.21 gives an example of the calculated
distribution of the longshore sediment transport across Lamberts Beach (east
coast of Australia) induced by wave approaching at an angle of 20° to the normal to the beach (Massel, B., 1998). Waves were induced by tropical cyclone
'Charlie' (27.02-1.03.1988) moving along the Australian coast southwards. Figure 8.21 corresponds to the situation when incident waves form an angle 20°
with direction normal to the Lamberts Beach. The maximum of the resulting
sediment transport rate is located very close to the breaking line and coincides
with the maximum of the longshore current velocity.
8.6.2 Sediment Budget and Depth Changes
For a given littoral cell, the total volume of sand added to the beach from
various sources can be balanced against the total losses. If the losses are greater
than the gains, then a net deficit takes place and the beach erodes. Similarly,
if the sand added to the beach exceeds the losses, the beach accretes. The lack
of either erosion or deposition indicates the state of equilibrium between the
sources and losses.
Beach erosion or deposition can generally be evaluated by comparing a series
of beach transects. Assuming that these transects are separated by i:1y, and
along the transects the points are separated by i:1x, the sediment budget can
be written as (Fig. 8.22):
(8.128)
in which q2 n ) and q~out) are the cross-shore transport rates, and q?n) and qIout)
are the longshore transport rates, entering and leaving the particular grid cell,
respectively; i:1h is the depth change due to both sediment transport components during time step i:1t.
It is assumed that water depth change in a given grid cell, due to erosion
or deposition, is distributed uniformly on the cell surface. If q~out) > q~in) and
q;out) > q?n) , then water depth in a given cell increases by i:1h. More general,
if the left-hand side of Eq. (8.128) is positive (negative), a given cell is eroded
(deposited) .
The relationship described by Eq.(8.128), can be rewritten more precisely as
follows:
oh
oqc
oql
-+-+-=0.
at ax oy
(8.129)