167
6 Oceanography of the Planktonic Stages of Aggregation Spawning Reef Fishes
at times and places where fl ow speeds are weak. The time it takes before gamete
contact rate declines enough to affect fertilization rate depends on the initial concentration and the strength of turbulence in the gamete cloud and the duration of egg
viability after release. However, initial concentrations may be extremely high so
that gamete contact rates are suffi cient even after dilutions of orders of magnitude –
as would happen in this case within the 8 min when the cloud was visually evident.
Intuitively there are major differences between the types of gamete clouds produced
by large transient aggregations and the larval dispersal of gametes released during
pair-spawning by smaller reef fi shes. But at present it is not possible to accurately
compare costs and benefi ts between these different modes of spawning.
Irrespective of the ambient fl ows at the time of spawning, the fi sh themselves
ensure small-scale turbulent mixing (Colin 1992 ; Heyman et al. 2005 ) through
vigorous swimming motions (e.g. Chap. 12 ), which have been observed in both
“burst” and “broad launch” modes (Chap. 7 ). This suggests that broad-launch
spawning may work to place gametes in mid-water shear layers (typical in a stratifi ed
water column). In such a shear layer, shear dispersion will rapidly bring about
contact between “particles” across this vertically confi ned horizontal layer, at the
same time as the shear spreads out the cloud horizontally (which may be useful for
broader fi nal dispersal outcomes).
6.2.3 Dispersion of Gamete Cloud
It is expected that eggs and yolk-sac larvae act as passive particles, normally slightly
buoyant but readily mixed downward from the surface under all but the calmest
conditions (e.g. Ellis et al. 1997 ; Hamner et al. 2007 ) . In water depths of 10 m or
less, one can expect neutrally buoyant particles to mix throughout the water column
within a few hours, from t ~ H
2 /K z where K z is vertical diffusivity (and assuming
K z ~ 0.01 m
2
/s from above, or from K z ~ k .u * .H/6 where k is von Karman constant
and u * is friction velocity ~0.01 m/s). For slightly buoyant particles, a quasi-steady
vertical distribution with concentration decreasing with depth (if spawned at or near
the surface) will be attained in a similar amount of time. We thus continue to assume
that cloud dispersion is dominated by 2-dimensional horizontal mixing.
Recent studies of water fl ow over and around coral reefs and associated modelling of fl ows promise credible computer simulations of dispersing larval clouds at
selected locations (for review see Monismith 2007 ) . However, the need to characterize
the dispersal of egg and larval clouds in general, and the overall lack of either
detailed observations or models of water fl ow at almost all locations, lead to the
emphasis here on relative scale estimates of this problem. Continuing to use scale expressions for diffusive mixing (as above), one can note that diffusivity K ~ D L
2 /18. D t
and thus the time for a cloud of size L 1 to mix out to L 2 can be estimated by
D t ~ 0.05(L 2
2 –L 1
2
)/K. Since K increases with the size of the cloud (see above) this
problem is best solved numerically. Nevertheless one can obtain an idea of the rate
of mixing by considering stages of mixing. A 30 m cloud (K ~ 0.01 m
2 /s) mixes to
6 Oceanography of the Planktonic Stages of Aggregation Spawning Reef Fishes
at times and places where fl ow speeds are weak. The time it takes before gamete
contact rate declines enough to affect fertilization rate depends on the initial concentration and the strength of turbulence in the gamete cloud and the duration of egg
viability after release. However, initial concentrations may be extremely high so
that gamete contact rates are suffi cient even after dilutions of orders of magnitude –
as would happen in this case within the 8 min when the cloud was visually evident.
Intuitively there are major differences between the types of gamete clouds produced
by large transient aggregations and the larval dispersal of gametes released during
pair-spawning by smaller reef fi shes. But at present it is not possible to accurately
compare costs and benefi ts between these different modes of spawning.
Irrespective of the ambient fl ows at the time of spawning, the fi sh themselves
ensure small-scale turbulent mixing (Colin 1992 ; Heyman et al. 2005 ) through
vigorous swimming motions (e.g. Chap. 12 ), which have been observed in both
“burst” and “broad launch” modes (Chap. 7 ). This suggests that broad-launch
spawning may work to place gametes in mid-water shear layers (typical in a stratifi ed
water column). In such a shear layer, shear dispersion will rapidly bring about
contact between “particles” across this vertically confi ned horizontal layer, at the
same time as the shear spreads out the cloud horizontally (which may be useful for
broader fi nal dispersal outcomes).
6.2.3 Dispersion of Gamete Cloud
It is expected that eggs and yolk-sac larvae act as passive particles, normally slightly
buoyant but readily mixed downward from the surface under all but the calmest
conditions (e.g. Ellis et al. 1997 ; Hamner et al. 2007 ) . In water depths of 10 m or
less, one can expect neutrally buoyant particles to mix throughout the water column
within a few hours, from t ~ H
2 /K z where K z is vertical diffusivity (and assuming
K z ~ 0.01 m
2
/s from above, or from K z ~ k .u * .H/6 where k is von Karman constant
and u * is friction velocity ~0.01 m/s). For slightly buoyant particles, a quasi-steady
vertical distribution with concentration decreasing with depth (if spawned at or near
the surface) will be attained in a similar amount of time. We thus continue to assume
that cloud dispersion is dominated by 2-dimensional horizontal mixing.
Recent studies of water fl ow over and around coral reefs and associated modelling of fl ows promise credible computer simulations of dispersing larval clouds at
selected locations (for review see Monismith 2007 ) . However, the need to characterize
the dispersal of egg and larval clouds in general, and the overall lack of either
detailed observations or models of water fl ow at almost all locations, lead to the
emphasis here on relative scale estimates of this problem. Continuing to use scale expressions for diffusive mixing (as above), one can note that diffusivity K ~ D L
2 /18. D t
and thus the time for a cloud of size L 1 to mix out to L 2 can be estimated by
D t ~ 0.05(L 2
2 –L 1
2
)/K. Since K increases with the size of the cloud (see above) this
problem is best solved numerically. Nevertheless one can obtain an idea of the rate
of mixing by considering stages of mixing. A 30 m cloud (K ~ 0.01 m
2 /s) mixes to