of these sub-systems are connected hydrodynamically by
processes on the reef and these processes are the focus of
the present article. Much of what happens on the reef, in
terms of hydrodynamics, is controlled by the topographic
complexity of the reef and is also affected by the surrounding environment of the reef system. Our attention is primarily directed towards shallow reefs and these may be
either sub-tidal, or inter-tidal. Reefs may have varying
types of benthos (coral, algae and sand) and are zonated
in a way that affects bottom friction and many other
aspects of their hydrodynamics. A recent survey of coral
reef hydrodynamics is given by Monismith (2007).
Coral reef hydrodynamics differs in many important
respects from the hydrodynamics of other coastal systems
and these differences will be discussed here. The science
of water flow over reefs is the cornerstone of much of our
understanding of the ecology and biogeochemical dynamics of reefs. Its effects are multifarious and occur at many
space and time scales. Coral reefs efficiently dissipate wave
energy and constitute some of the best submerged breakwaters in the natural world (von Arx, 1948). This creates lowenergy lagoons, which are fed with water from the reef
(Hench et al., 2008) and also have their own patterns of
water circulation (“entry lagoons”; “entry lagoon circulation”). Reef hydrodynamics can be greatly affected by conditions in the lagoons, and the outside ocean, and there are
processes of continual recirculation of water that are augmented by astronomical tides.
Coral reefs have high biological productivity that is the
marine equivalent of tropical rain forests (Hatcher, 1998).
There are many similarities between the two systems: the
structural complexity of reefs seems to have an important
analog in tropical rain forests with the same degree of ecological complexity and biodiversity (Brown et al., 2002).
At the heart of the processes which control such productivity are the dynamics, transport and recycling of nutrients and their dependence on the hydrodynamic
processes at a variety of space and time scales (Hatcher,
1997). This includes all of the complex small scale vortices, and wave motions found on reefs, which are part of
the turbulence field. Unlike most coasts systems, the spectrum of significant topographic complexity in reefs
appears almost continuous from scales of hundreds of
meters down to millimeters. There is a possible distinct
change in the nature of this complexity at the scale of individual coral colonies and this is a physical scale that can be
utilized in conceptual (and numerical) models of reef
hydrodynamics.
Reef currents are produced by many types of environmental forcing of which the most important are breaking
surface waves (“entry Waves and wave driven currents”),
astronomical tides, and wind stress (Munk and Sargent,
1954; Kench, 1998). Other influences may also be present
on some reefs such as the thermohaline processes
(Monismith et al., 2006) and long period ocean oscillations; for the Great Barrier Reef see the excellent volume
by Hopley et al. (2007). Of all these forcing processes,
the most important is wave breaking and the
quintessential, and fundamental, problem of water flow
in coral reefs involves waves breaking on a well-defined
fore-reef (“entry Fore reef/reef front”) and flowing across
the adjoining reef flat into a lagoon. The waves are usually
ocean swell but can be wind waves (Kraines et al., 1998).
This topography fits many reef systems and has been studied through conceptual and numerical models by Tait
(1972); Symonds et al. (1995); and Hearn (1999) and
recently reviewed by Monismith (2007). This “classical
reef flow” problem is illustrated in Figure 1 and we shall
discuss this prototype of all reef models in some detail.
There are two basic conceptual models of the physical
structure of a coral reef. The first is the “solid reef model,”
in which the reef is represented as a solid body (without
reentrant surfaces in the vertical plane) to which are added
“roughness elements.” This can alternatively be described
as a “bathymetry model” since it can be totally described
by a conventional bathymetry dataset with depth as
a function of horizontal position. It is discussed in the following sections. The other type of model is the “porous
reef model” mentioned later in this article. These conceptual models, which are used for analytical and numerical
simulations, have been accompanied by so-called “physical models” built in many laboratories and also, at larger
scale, as the coral reef mesocosm at the Biosphere 2 facility in Arizona (Atkinson et al., 2001). Such physical
models provide much important hydrodynamic, chemical
and biological data although there is limited guidance as to
the correct physical, and ecological scaling parameters to
be used in this model building.
In the solid reef model, the reef can, in principle, be
treated by conventional coastal models (Peterson et al.,
2006; Hearn, 2008). However, there are many aspects of
flow over a reef that make it distinct from conventional
coastal flow and these will be explored in this article.
Friction on reefs
Part of the hydrodynamic uniqueness of coral reefs is that
they are submerged natural structures that have the same
efficacy as do solid barriers in dissipating ocean waves
and creating calm lagoons. Their dissipation of waves is
due to a resistance to water flow that can be treated as friction although it cannot be purely “skin friction” as in most
coastal models. Instead, the friction comes primarily from
“form drag” created by the irregularity and complexity of
the structure. In solid reef models, the friction offered by
reefs is created by the “roughness elements.” The simplest
representation of such friction is a frictional drag coefficient. Approximate coefficients for bottom friction on reef
flats were originally derived from field data relating
incoming wave height and reef current (Hearn, 2008).
A coefficient of friction for coral can also be obtained by
measuring the current produced by a known head of water
in a flume filled with living coral cut from a reef (Atkinson
and Bilger, 1992). It is also possible to estimate friction
coefficients from acoustic measurements of current either
using profiles of current against height or by determining
564
HYDRODYNAMICS OF CORAL REEF SYSTEMS
processes on the reef and these processes are the focus of
the present article. Much of what happens on the reef, in
terms of hydrodynamics, is controlled by the topographic
complexity of the reef and is also affected by the surrounding environment of the reef system. Our attention is primarily directed towards shallow reefs and these may be
either sub-tidal, or inter-tidal. Reefs may have varying
types of benthos (coral, algae and sand) and are zonated
in a way that affects bottom friction and many other
aspects of their hydrodynamics. A recent survey of coral
reef hydrodynamics is given by Monismith (2007).
Coral reef hydrodynamics differs in many important
respects from the hydrodynamics of other coastal systems
and these differences will be discussed here. The science
of water flow over reefs is the cornerstone of much of our
understanding of the ecology and biogeochemical dynamics of reefs. Its effects are multifarious and occur at many
space and time scales. Coral reefs efficiently dissipate wave
energy and constitute some of the best submerged breakwaters in the natural world (von Arx, 1948). This creates lowenergy lagoons, which are fed with water from the reef
(Hench et al., 2008) and also have their own patterns of
water circulation (“entry lagoons”; “entry lagoon circulation”). Reef hydrodynamics can be greatly affected by conditions in the lagoons, and the outside ocean, and there are
processes of continual recirculation of water that are augmented by astronomical tides.
Coral reefs have high biological productivity that is the
marine equivalent of tropical rain forests (Hatcher, 1998).
There are many similarities between the two systems: the
structural complexity of reefs seems to have an important
analog in tropical rain forests with the same degree of ecological complexity and biodiversity (Brown et al., 2002).
At the heart of the processes which control such productivity are the dynamics, transport and recycling of nutrients and their dependence on the hydrodynamic
processes at a variety of space and time scales (Hatcher,
1997). This includes all of the complex small scale vortices, and wave motions found on reefs, which are part of
the turbulence field. Unlike most coasts systems, the spectrum of significant topographic complexity in reefs
appears almost continuous from scales of hundreds of
meters down to millimeters. There is a possible distinct
change in the nature of this complexity at the scale of individual coral colonies and this is a physical scale that can be
utilized in conceptual (and numerical) models of reef
hydrodynamics.
Reef currents are produced by many types of environmental forcing of which the most important are breaking
surface waves (“entry Waves and wave driven currents”),
astronomical tides, and wind stress (Munk and Sargent,
1954; Kench, 1998). Other influences may also be present
on some reefs such as the thermohaline processes
(Monismith et al., 2006) and long period ocean oscillations; for the Great Barrier Reef see the excellent volume
by Hopley et al. (2007). Of all these forcing processes,
the most important is wave breaking and the
quintessential, and fundamental, problem of water flow
in coral reefs involves waves breaking on a well-defined
fore-reef (“entry Fore reef/reef front”) and flowing across
the adjoining reef flat into a lagoon. The waves are usually
ocean swell but can be wind waves (Kraines et al., 1998).
This topography fits many reef systems and has been studied through conceptual and numerical models by Tait
(1972); Symonds et al. (1995); and Hearn (1999) and
recently reviewed by Monismith (2007). This “classical
reef flow” problem is illustrated in Figure 1 and we shall
discuss this prototype of all reef models in some detail.
There are two basic conceptual models of the physical
structure of a coral reef. The first is the “solid reef model,”
in which the reef is represented as a solid body (without
reentrant surfaces in the vertical plane) to which are added
“roughness elements.” This can alternatively be described
as a “bathymetry model” since it can be totally described
by a conventional bathymetry dataset with depth as
a function of horizontal position. It is discussed in the following sections. The other type of model is the “porous
reef model” mentioned later in this article. These conceptual models, which are used for analytical and numerical
simulations, have been accompanied by so-called “physical models” built in many laboratories and also, at larger
scale, as the coral reef mesocosm at the Biosphere 2 facility in Arizona (Atkinson et al., 2001). Such physical
models provide much important hydrodynamic, chemical
and biological data although there is limited guidance as to
the correct physical, and ecological scaling parameters to
be used in this model building.
In the solid reef model, the reef can, in principle, be
treated by conventional coastal models (Peterson et al.,
2006; Hearn, 2008). However, there are many aspects of
flow over a reef that make it distinct from conventional
coastal flow and these will be explored in this article.
Friction on reefs
Part of the hydrodynamic uniqueness of coral reefs is that
they are submerged natural structures that have the same
efficacy as do solid barriers in dissipating ocean waves
and creating calm lagoons. Their dissipation of waves is
due to a resistance to water flow that can be treated as friction although it cannot be purely “skin friction” as in most
coastal models. Instead, the friction comes primarily from
“form drag” created by the irregularity and complexity of
the structure. In solid reef models, the friction offered by
reefs is created by the “roughness elements.” The simplest
representation of such friction is a frictional drag coefficient. Approximate coefficients for bottom friction on reef
flats were originally derived from field data relating
incoming wave height and reef current (Hearn, 2008).
A coefficient of friction for coral can also be obtained by
measuring the current produced by a known head of water
in a flume filled with living coral cut from a reef (Atkinson
and Bilger, 1992). It is also possible to estimate friction
coefficients from acoustic measurements of current either
using profiles of current against height or by determining
564
HYDRODYNAMICS OF CORAL REEF SYSTEMS