model of flow across the reef, shown in Figure 1, and
based on a traditional quadratic friction law using
a coefficient of friction on the fore reef of 0.1. This illustrates the importance of the spatial variability of roughness
in a reef system across its many zones.
Currents around reefs
Currents flow around reefs, as well as over, and through,
the actual structure of the reef. As they do so, they create
a series of coastal boundary layers near the reef and form
island wakes. The structure of these wakes is controlled
by the frictional Reynolds number (Hearn, 2008). The
high friction, and limited water depth, associated with
reefs lowers this Reynolds number and so causes island
wakes around these structures (Tomczak, 1988). There
are a series of studies of these wakes and the role of friction; for a good review see Wolanski (1994). Local artisan
fisheries use their knowledge of these wakes, and whirlpools, around reefs, and their variation with the state of
the moon, to navigate these waters and optimize catches
(Johannes, 1981).
Waves on reefs
Wave processes
The hydrodynamics of reef systems is closely connected
with the processes of wave propagation and breaking on
reefs. Waves are present on reef flats whenever there are
incoming waves on the fore reef, and in the presence of
breaking on the fore reef, the waves on the reef flat are just
below the height at which they would break (for example,
waves of height 0.8 m on a reef flat of depth 1 m). There
are very considerable areas of research devoted to wave
breaking and its dependence on the depth and shoaling
of the reef and to the effect of the strong wave-current
interaction on wave propagation, refraction and diffraction over reefs (“entry Wave refraction”). These processes
have many interesting, and distinct, forms on reefs due to
their unique structural and hydrodynamic properties.
Wave boundary layer
After breaking on the fore-reef, smaller waves ( just below
breaking height) continue to propagate over the reef flat
and these effectively increase friction on the reef flat. In
the solid reef model, this wave-current interaction occurs
through the “wave boundary layer.” The usual situation
of waves propagating in the ocean is that their associated
currents are not affected significantly by bottom friction.
The reason is that the bottom stress is oscillatory and
therefore has only the very limited time of half a waveperiod to propagate up through the water column. Consequently, until waves enter very shallow water they do not
feel significant influences of bottom friction; the vertical
current is zero at the bottom of the water column (it is this
constraint that changes the speed of propagation of waves
in shallow water and produces refraction).
The limited time for propagation of the bottom stress
into the water column restricts its influence to a bottom
layer (called the “wave boundary layer”). This layer is
very thin in most coastal situations and so it just has the
simple effect of increasing the coefficient of quadratic friction through the “wave-current” interaction. This situation
is changed on reefs because the greater friction produces
considerable turbulence from waves with much greater
penetration into the water column. Consequently, the
wave boundary layer on reefs can have a thickness comparable to the height of the water column and this effectively
increases the roughness of the reef. The usual quadratic
friction which we find in most coastal situations is
a consequence of the current being responsible for both
the generation of turbulence and bottom stress. Within
the wave boundary layer, that turbulence is created by
the waves. A consequence is that at low currents the bottom frictional stress on the reef can be linearly related to
the current. This affects some of the basic hydrodynamics
such at the relationship between incoming wave height
and current (Hearn, 2008). The current-wave interaction
always increases friction; it acts by preventing bottom
stress decreasing quadratically at low currents. Parts of
the wave boundary layer lie inside the troughs, or cavities,
of the roughness elements. These are regions with only
marginal penetration by the residual currents from the
main part of the water column, and so (depending on their
size) some of the cavities may be dominated by wave currents (Lowe et al., 2005a, b).
Wave breaking can produce currents in the order of
1 meter per sec on the reef flat although this is very dependent on the width of the reef flat and its friction. Currents
in narrow lagoons behind wave-forced reefs can also be
high and especially if there is a deeper trench, or “gully,”
running through the lagoon. Nearshore reefs parallel to
shore (“entry Fringing reef circulation”) have breaks in
the reef line for water to exit the lagoon (“entry Boat channel”), and during heavy-swell conditions, currents can
become extremely high and dangerous to swimmers and
novice boaters. Currents on reefs advect and disperse
suspended material, and particulate and our knowledge
of currents and circulation is vital to an understanding of
sediment dynamics and all mass transport (“entry sediment-dynamics”).
Tidal influences
Astronomical tides modulate all of the hydrodynamic processes in a reef system (“entry Tidal effects on coral
reefs”). Within the solid reef model, shallow reefs may
be completely dry at spring low tides so that the wave
set up is confined to the face of the fore reef. In a porous
reef model, water continues to have limited flow at these
low tides. The overall effect of astronomical tides is to create a net inflow, or outflow (considering all boundaries of
the reef system) that is controlled by the tidally varying
water level in the reef system. Without the tide, this net
flow will be essentially zero. These net tidal currents do
depend on the size of the reef system but for small systems
the net current is 90 degrees out of phase with the water
HYDRODYNAMICS OF CORAL REEF SYSTEMS
567
based on a traditional quadratic friction law using
a coefficient of friction on the fore reef of 0.1. This illustrates the importance of the spatial variability of roughness
in a reef system across its many zones.
Currents around reefs
Currents flow around reefs, as well as over, and through,
the actual structure of the reef. As they do so, they create
a series of coastal boundary layers near the reef and form
island wakes. The structure of these wakes is controlled
by the frictional Reynolds number (Hearn, 2008). The
high friction, and limited water depth, associated with
reefs lowers this Reynolds number and so causes island
wakes around these structures (Tomczak, 1988). There
are a series of studies of these wakes and the role of friction; for a good review see Wolanski (1994). Local artisan
fisheries use their knowledge of these wakes, and whirlpools, around reefs, and their variation with the state of
the moon, to navigate these waters and optimize catches
(Johannes, 1981).
Waves on reefs
Wave processes
The hydrodynamics of reef systems is closely connected
with the processes of wave propagation and breaking on
reefs. Waves are present on reef flats whenever there are
incoming waves on the fore reef, and in the presence of
breaking on the fore reef, the waves on the reef flat are just
below the height at which they would break (for example,
waves of height 0.8 m on a reef flat of depth 1 m). There
are very considerable areas of research devoted to wave
breaking and its dependence on the depth and shoaling
of the reef and to the effect of the strong wave-current
interaction on wave propagation, refraction and diffraction over reefs (“entry Wave refraction”). These processes
have many interesting, and distinct, forms on reefs due to
their unique structural and hydrodynamic properties.
Wave boundary layer
After breaking on the fore-reef, smaller waves ( just below
breaking height) continue to propagate over the reef flat
and these effectively increase friction on the reef flat. In
the solid reef model, this wave-current interaction occurs
through the “wave boundary layer.” The usual situation
of waves propagating in the ocean is that their associated
currents are not affected significantly by bottom friction.
The reason is that the bottom stress is oscillatory and
therefore has only the very limited time of half a waveperiod to propagate up through the water column. Consequently, until waves enter very shallow water they do not
feel significant influences of bottom friction; the vertical
current is zero at the bottom of the water column (it is this
constraint that changes the speed of propagation of waves
in shallow water and produces refraction).
The limited time for propagation of the bottom stress
into the water column restricts its influence to a bottom
layer (called the “wave boundary layer”). This layer is
very thin in most coastal situations and so it just has the
simple effect of increasing the coefficient of quadratic friction through the “wave-current” interaction. This situation
is changed on reefs because the greater friction produces
considerable turbulence from waves with much greater
penetration into the water column. Consequently, the
wave boundary layer on reefs can have a thickness comparable to the height of the water column and this effectively
increases the roughness of the reef. The usual quadratic
friction which we find in most coastal situations is
a consequence of the current being responsible for both
the generation of turbulence and bottom stress. Within
the wave boundary layer, that turbulence is created by
the waves. A consequence is that at low currents the bottom frictional stress on the reef can be linearly related to
the current. This affects some of the basic hydrodynamics
such at the relationship between incoming wave height
and current (Hearn, 2008). The current-wave interaction
always increases friction; it acts by preventing bottom
stress decreasing quadratically at low currents. Parts of
the wave boundary layer lie inside the troughs, or cavities,
of the roughness elements. These are regions with only
marginal penetration by the residual currents from the
main part of the water column, and so (depending on their
size) some of the cavities may be dominated by wave currents (Lowe et al., 2005a, b).
Wave breaking can produce currents in the order of
1 meter per sec on the reef flat although this is very dependent on the width of the reef flat and its friction. Currents
in narrow lagoons behind wave-forced reefs can also be
high and especially if there is a deeper trench, or “gully,”
running through the lagoon. Nearshore reefs parallel to
shore (“entry Fringing reef circulation”) have breaks in
the reef line for water to exit the lagoon (“entry Boat channel”), and during heavy-swell conditions, currents can
become extremely high and dangerous to swimmers and
novice boaters. Currents on reefs advect and disperse
suspended material, and particulate and our knowledge
of currents and circulation is vital to an understanding of
sediment dynamics and all mass transport (“entry sediment-dynamics”).
Tidal influences
Astronomical tides modulate all of the hydrodynamic processes in a reef system (“entry Tidal effects on coral
reefs”). Within the solid reef model, shallow reefs may
be completely dry at spring low tides so that the wave
set up is confined to the face of the fore reef. In a porous
reef model, water continues to have limited flow at these
low tides. The overall effect of astronomical tides is to create a net inflow, or outflow (considering all boundaries of
the reef system) that is controlled by the tidally varying
water level in the reef system. Without the tide, this net
flow will be essentially zero. These net tidal currents do
depend on the size of the reef system but for small systems
the net current is 90 degrees out of phase with the water
HYDRODYNAMICS OF CORAL REEF SYSTEMS
567