420
14 Tides and Waves on Vegetated Coasts
the concept of a bottom friction coefficient. However, at this stage, the bottom
friction will be omitted from consideration as the bottom friction coefficient for
mangrove forests is not known.
In the simplest representation, mangrove trunks and roots can be treated
as cylindrical elements located in the water (Fig. 14.2). In areas occupied
by Rhizophora species, the density of mangrove trunks and roots is greater in
the bottom layer than in the upper layer, where only the vertical trunks are
observed (Wolanski et aI, 1992). Wave induced forces on trunks and roots are
inertial and drag type forces, and for typical mangrove trunks and roots the
drag force dominates.
Because of the proximity of other trunks, some interactions between trunks
can be expected. To include these interactions in the resulting drag force, an
appropriate modification of the drag coefficient, Cd, depending on the density
of the mangrove trunks, has been proposed using the discrete vortex method
(Massel et at., 1998).
Wave motion within the mangrove forest is subjected to strong dissipation
due to the multiple interactions with mangrove trunks. Hence, the momentum equation for motion with dissipation can be written as follows (see Appendix C.3):
au 1
1
- = -\7 (p+pgz) - -F,
at p
p
(14.1)
in which u = (u, w) is the wave-induced velocity vector, p is the corresponding
dynamic pressure, and F is the force vector (per unit volume).
Let us now consider a unit control area of mangrove and assume that in this
area there are N u trunks piercing the sea surface (usually N u is of the order of
1-10 per m 2 ), each of mean diameter Du. In the bottom layer of thickness, hI,
(usually thickness hi is of the order of 0.3 m-1.0 m) mangroves are very dense
and smaller trunks and roots are randomly oriented. It is assumed that the
number of trunks, NI, each of mean diameter, DI, is of the order of 10-30 per
m 2 . The control area has to be selected sufficiently large to accommodate Nu
and Nl trunks, where Nu > 1 and Nl » 1. On the other hand, this area has to
be sufficiently small in order to neglect the variation of wave velocity within the
control area and to neglect the exact location of each trunk within the control
area. The spacing ~x = ~y = 1 m is probably a reasonable compromise for
the above requirements.
As the mangrove roots are randomly oriented against the water flow direction,
it is impossible to exactly reproduce the mangrove geometry. However, in order
to get some insight into the problem, we consider the simpler problem of a
mangrove forest where all trunks in the upper layer are vertical (see Fig. 14.2).
The inclination of mangrove roots and trunks in lower layer is parameterized
through the mean inclination angle, ii, measured with respect to the vertical
axis, z. Observations suggest that the angle ii is of the order of 30°.
14 Tides and Waves on Vegetated Coasts
the concept of a bottom friction coefficient. However, at this stage, the bottom
friction will be omitted from consideration as the bottom friction coefficient for
mangrove forests is not known.
In the simplest representation, mangrove trunks and roots can be treated
as cylindrical elements located in the water (Fig. 14.2). In areas occupied
by Rhizophora species, the density of mangrove trunks and roots is greater in
the bottom layer than in the upper layer, where only the vertical trunks are
observed (Wolanski et aI, 1992). Wave induced forces on trunks and roots are
inertial and drag type forces, and for typical mangrove trunks and roots the
drag force dominates.
Because of the proximity of other trunks, some interactions between trunks
can be expected. To include these interactions in the resulting drag force, an
appropriate modification of the drag coefficient, Cd, depending on the density
of the mangrove trunks, has been proposed using the discrete vortex method
(Massel et at., 1998).
Wave motion within the mangrove forest is subjected to strong dissipation
due to the multiple interactions with mangrove trunks. Hence, the momentum equation for motion with dissipation can be written as follows (see Appendix C.3):
au 1
1
- = -\7 (p+pgz) - -F,
at p
p
(14.1)
in which u = (u, w) is the wave-induced velocity vector, p is the corresponding
dynamic pressure, and F is the force vector (per unit volume).
Let us now consider a unit control area of mangrove and assume that in this
area there are N u trunks piercing the sea surface (usually N u is of the order of
1-10 per m 2 ), each of mean diameter Du. In the bottom layer of thickness, hI,
(usually thickness hi is of the order of 0.3 m-1.0 m) mangroves are very dense
and smaller trunks and roots are randomly oriented. It is assumed that the
number of trunks, NI, each of mean diameter, DI, is of the order of 10-30 per
m 2 . The control area has to be selected sufficiently large to accommodate Nu
and Nl trunks, where Nu > 1 and Nl » 1. On the other hand, this area has to
be sufficiently small in order to neglect the variation of wave velocity within the
control area and to neglect the exact location of each trunk within the control
area. The spacing ~x = ~y = 1 m is probably a reasonable compromise for
the above requirements.
As the mangrove roots are randomly oriented against the water flow direction,
it is impossible to exactly reproduce the mangrove geometry. However, in order
to get some insight into the problem, we consider the simpler problem of a
mangrove forest where all trunks in the upper layer are vertical (see Fig. 14.2).
The inclination of mangrove roots and trunks in lower layer is parameterized
through the mean inclination angle, ii, measured with respect to the vertical
axis, z. Observations suggest that the angle ii is of the order of 30°.