14.4 Waves at Coral Reefs
437
At the frontal reef slope, wave-induced velocity is higher than current velocity and velocity U max can be considered as maximum orbital velocity. In
Fig. 14.l1a, a variation of wave height and corresponding orbital velocity at
sea bottom, over the reef slope, is shown. When the wave height is known
(see previous section), wave-induced orbital velocity can be calculated from
Eq. (4.25) as:
gkH
1
umax(O) = 2;;- cosh kh
(14.22)
Using the values of stress, IJu , and water density, Pw, as 22 x 10 6 Pa and
1023 kg/m 3 , respectively, and substituting Eq. (14.22) into Eq. (14.21), the
minimal value of non-dimensional branch diameter, at each point of reef slope,
is obtained. As was shown in Fig. 14.l1a, the maximum value of D Il rv 0.025
corresponds to the highest flow velocity at the vicinity of reef edge, as expected. This figure illustrates the variations of the D Il values, necessary for
coral survival. The results are valid only for a given reef geometry and incident wave parameters. For example, during tropical cyclone wave heights and
wave-induced velocity can be higher and higher value of D Il is needed for coral
survival. Moreover, as the velocity u has been represented as bottom velocity,
an estimated value of D II is restricted to rather short coral branch, located
close to sea bottom.
From Eq. (14.16) it follows that bending moment induced by uniform flow
changes along coral branch, being zero at the free end of branch and reaching
its maximum of 1/2 Fd12. Therefore, to keep the stress IJ u constant along
coral branch, it is sufficient that dimension D of branch satisfies the following
condition:
(14.23)
or:
D = 8pw C d U2 (l - z).
7f'IJ u
(14.24)
The stress remains constant along coral branch when its dimension increases
in proportion to the distance from the free end. The greater is the velocity, u,
the faster branch must grow. Conversely, the stronger is branch material (the
larger value of IJu ), the slower branch growth can be.
In general, coral branches are not perfect circular cylinders and elliptical
cross-sections are very common. Using a similar reasoning, it can be found
that flow induced moment, M, and bending stress, IJb, are:
437
At the frontal reef slope, wave-induced velocity is higher than current velocity and velocity U max can be considered as maximum orbital velocity. In
Fig. 14.l1a, a variation of wave height and corresponding orbital velocity at
sea bottom, over the reef slope, is shown. When the wave height is known
(see previous section), wave-induced orbital velocity can be calculated from
Eq. (4.25) as:
gkH
1
umax(O) = 2;;- cosh kh
(14.22)
Using the values of stress, IJu , and water density, Pw, as 22 x 10 6 Pa and
1023 kg/m 3 , respectively, and substituting Eq. (14.22) into Eq. (14.21), the
minimal value of non-dimensional branch diameter, at each point of reef slope,
is obtained. As was shown in Fig. 14.l1a, the maximum value of D Il rv 0.025
corresponds to the highest flow velocity at the vicinity of reef edge, as expected. This figure illustrates the variations of the D Il values, necessary for
coral survival. The results are valid only for a given reef geometry and incident wave parameters. For example, during tropical cyclone wave heights and
wave-induced velocity can be higher and higher value of D Il is needed for coral
survival. Moreover, as the velocity u has been represented as bottom velocity,
an estimated value of D II is restricted to rather short coral branch, located
close to sea bottom.
From Eq. (14.16) it follows that bending moment induced by uniform flow
changes along coral branch, being zero at the free end of branch and reaching
its maximum of 1/2 Fd12. Therefore, to keep the stress IJ u constant along
coral branch, it is sufficient that dimension D of branch satisfies the following
condition:
(14.23)
or:
D = 8pw C d U2 (l - z).
7f'IJ u
(14.24)
The stress remains constant along coral branch when its dimension increases
in proportion to the distance from the free end. The greater is the velocity, u,
the faster branch must grow. Conversely, the stronger is branch material (the
larger value of IJu ), the slower branch growth can be.
In general, coral branches are not perfect circular cylinders and elliptical
cross-sections are very common. Using a similar reasoning, it can be found
that flow induced moment, M, and bending stress, IJb, are: