166
W.M. Hamner and J.L. Largier
A large transient aggregation, such as for Nassau grouper, will occupy an area
perhaps 30–50 m in radius, but when actually spawning will occupy a much smaller
volume of water (as little as 1–2 m across, see Chaps. 1 , 5 and Glossary have defi nitions of aggregation types). Some spawning aggregations are elongate, as adults
spawn along an escarpment (e.g. humphead wrasse – Cheilinus undulatus Colin
2010 , or various parrotfi sh (Scaridae) and surgeonfi sh (Acanthuridae), see Fig. 5.13,
Chap. 5 ). Given that aggregation spawning on any given day usually occurs for a
period of an hour or less, even if currents are relatively weak (<0.05 m/s), the gamete clouds may stretch over a distance of 100 m or more due to advection. In a sense,
successive spawnings from an aggregation which itself does not move signifi cantly
can be thought of as “puffs of smoke” produced in an area where the wind is blowing them away, to be replaced by the next puff. The result is either a single mass of
gametes or a succession of “puffs” in a “line” determined by the current speed and
direction combined with the timing of spawning. Typical concentrations are obtained
by dividing the number of propagules by the volume of the overall cloud, providing
information on egg density prior to the continual process of dispersion after
spawning.
It seems reasonable to assume that the spawning process creates a vertically
mixed cloud near the ocean surface due to the innate buoyancy of eggs and that the
subsequent cloud dispersion is largely due to horizontal mixing processes. Even if
spawned at some depth, the buoyancy of eggs would bring them close to the surface
prior to hatching (Chap. 5 ) and the same horizontal mixing processes would cause
the egg cloud to expand outward as it ascends. Away from the immediate effect of
small-scale shear and eddies due to the interaction of fl ow with the roughness of the
reef (which are minimized by spawning well above the bottom), Richardson ( 1926 ) ,
Okubo ( 1980 ) and many later studies (e.g. Stacey et al. 2000 in nearshore waters)
have shown that horizontal diffusivity scales with L
4/3 where L is the cloud size –
with values of K of order 0.01 m
2 /s for a cloud of order 30 m and K of order
0.001 m
2 /s for a cloud of order 5 m ( Fischer et al. 1979 ; L ~ 3 s where s is variance
of particle positions). The time scale for mixing can be scaled as t ~ a.L
2
/K where
a ~ 0.05. A 5 m diameter cloud would mix on a time scale of t ~ 1,250 s (21 min)
while a 30 m diameter cloud would mix on a time scale of t ~ 4,500 s (75 min).
The above Okubo-based estimates of cloud dispersion rates should be considered
a minimum, corresponding to dispersion in the absence of local fl ow-topography
interactions (see Sect. 6.4 ). There are few quantitative reports on the actual development of gamete clouds. Heyman et al. ( 2005 ) qualitatively report clouds of cubera
snapper eggs of 64 m
3 some 15 s after spawning (order 5 m horizontal scale) expanding
to 1,800 m
3 after 1 min (order 30 m horizontal scale), although there is some question
that this expansion rate is overstated (Patrick L. Colin personal communication
2010). This rate of mixing is much faster than expected from diffusive effects
alone (K ~ D L
2 /18. D t ~ 1 m
2
/s), which either requires that small-scale (1–10 m
scale) shear and eddies in the fl ow fi eld greatly dominate the background eddy diffusion effects (cf. Clarke et al. 2007 ) or suggest that the fi eld estimates are in error.
The rapid growth of the cloud observed by Heyman et al. ( 2005 ) (concentration
diluted 28-fold in less than a minute) underscores the importance of spawning
W.M. Hamner and J.L. Largier
A large transient aggregation, such as for Nassau grouper, will occupy an area
perhaps 30–50 m in radius, but when actually spawning will occupy a much smaller
volume of water (as little as 1–2 m across, see Chaps. 1 , 5 and Glossary have defi nitions of aggregation types). Some spawning aggregations are elongate, as adults
spawn along an escarpment (e.g. humphead wrasse – Cheilinus undulatus Colin
2010 , or various parrotfi sh (Scaridae) and surgeonfi sh (Acanthuridae), see Fig. 5.13,
Chap. 5 ). Given that aggregation spawning on any given day usually occurs for a
period of an hour or less, even if currents are relatively weak (<0.05 m/s), the gamete clouds may stretch over a distance of 100 m or more due to advection. In a sense,
successive spawnings from an aggregation which itself does not move signifi cantly
can be thought of as “puffs of smoke” produced in an area where the wind is blowing them away, to be replaced by the next puff. The result is either a single mass of
gametes or a succession of “puffs” in a “line” determined by the current speed and
direction combined with the timing of spawning. Typical concentrations are obtained
by dividing the number of propagules by the volume of the overall cloud, providing
information on egg density prior to the continual process of dispersion after
spawning.
It seems reasonable to assume that the spawning process creates a vertically
mixed cloud near the ocean surface due to the innate buoyancy of eggs and that the
subsequent cloud dispersion is largely due to horizontal mixing processes. Even if
spawned at some depth, the buoyancy of eggs would bring them close to the surface
prior to hatching (Chap. 5 ) and the same horizontal mixing processes would cause
the egg cloud to expand outward as it ascends. Away from the immediate effect of
small-scale shear and eddies due to the interaction of fl ow with the roughness of the
reef (which are minimized by spawning well above the bottom), Richardson ( 1926 ) ,
Okubo ( 1980 ) and many later studies (e.g. Stacey et al. 2000 in nearshore waters)
have shown that horizontal diffusivity scales with L
4/3 where L is the cloud size –
with values of K of order 0.01 m
2 /s for a cloud of order 30 m and K of order
0.001 m
2 /s for a cloud of order 5 m ( Fischer et al. 1979 ; L ~ 3 s where s is variance
of particle positions). The time scale for mixing can be scaled as t ~ a.L
2
/K where
a ~ 0.05. A 5 m diameter cloud would mix on a time scale of t ~ 1,250 s (21 min)
while a 30 m diameter cloud would mix on a time scale of t ~ 4,500 s (75 min).
The above Okubo-based estimates of cloud dispersion rates should be considered
a minimum, corresponding to dispersion in the absence of local fl ow-topography
interactions (see Sect. 6.4 ). There are few quantitative reports on the actual development of gamete clouds. Heyman et al. ( 2005 ) qualitatively report clouds of cubera
snapper eggs of 64 m
3 some 15 s after spawning (order 5 m horizontal scale) expanding
to 1,800 m
3 after 1 min (order 30 m horizontal scale), although there is some question
that this expansion rate is overstated (Patrick L. Colin personal communication
2010). This rate of mixing is much faster than expected from diffusive effects
alone (K ~ D L
2 /18. D t ~ 1 m
2
/s), which either requires that small-scale (1–10 m
scale) shear and eddies in the fl ow fi eld greatly dominate the background eddy diffusion effects (cf. Clarke et al. 2007 ) or suggest that the fi eld estimates are in error.
The rapid growth of the cloud observed by Heyman et al. ( 2005 ) (concentration
diluted 28-fold in less than a minute) underscores the importance of spawning