Chapter 8 Fluid Dynamics in Seagrass Ecology
197
within seagrass canopies (e.g. Fonseca and Fisher,
1986; Gambi et al., 1990; Ackerman and Okubo,
1993). It is important to note that other engineering
models have been applied to rough canopies such as
corals and seagrasses with the direct measurement
of canopy friction and the use of the Stanton number, St (uptake rate by the surface/advection over
the surface), to determine the efficiency of canopy
uptake (e.g. Thomas et al., 2000; Thomas and Cornelisen, 2003). Reconfiguration of seagrass canopies
under higher flow conditions (e.g. Fonseca et al.,
1982; Ackerman, 1986), and/or unsteadiness due to
monamis (waving of the canopy; see Section V.C)
caused by an instability of the mean velocity profile
(Ackerman and Okubo, 1993; Ghisalberti and Nepf,
2002) and waves (Koch, 1996; Koch and Gust, 1999)
represents a challenge to researchers. Even so, τ is
the preferred form (over u) of expressing hydrodynamic conditions near boundaries (leaves, flowers,
sediment etc; see Nowell and Jumars, 1984).
Hydrodynamic conditions in the environment are
rarely stationary, especially in wave-dominated seagrass habitats where a more appropriate characterization of the fluid environment is that it varies in a
periodic fashion with each passing wave. Waves represent the movement of energy through a fluid and
exhibit a periodic motion, especially when viewed
at an interface (e.g. the water surface). In this case,
the passing wave (crest followed by trough) causes
a submersed object on the surface to move in a circular or orbital fashion, the diameter of which is
equal to the wave height (H ). The orbital motions
also extend downward through the fluid in a series
of orbitals that diminish in diameter with depth until
a depth (z) of 1/2λ (where λ is the wavelength) is
reached.
The classification of waves can be based on the
disturbing force that creates them, the restoring force
that destroys them, and their wavelength (Garrison,
2000). The disturbing force is the source of energy
that causes the wave, which can be (i) wind stress
acting on water surface causing capillary and gravity waves, (ii) the arrival of surge or sea wave causing swell, (iii) wind setup in an embayment creating seiches, (iv) a change in atmospheric pressure causing short-lived storm surge, and (v) large
disturbances (landslides, volcanic eruptions, earthquake) that cause seismic waves (or tsunami; the
so-called tidal waves that are actually due to gravitational inertial forces). The restoring forces that
reduce the disturbance to the water surface include
(a) surface tension due to the molecular cohesion of
water molecules, which works for small waves (i.e.
λ <1.73 cm; capillary waves) and, (b) gravity that
operates on larger waves (i.e. λ 1.73 cm). Whereas
the wavelength can be used to distinguish differences
among the smallest of waves, it really provides a
measure of wave size and relationship to energy; the
smaller the wavelength, the higher the energy. Some
typical relationships include (1) wind waves (λ <60–
150 m), (2) seiches (λ is large and a function of the
basin size), (3) seismic waves (λ <200 km), and (4)
tides (λ = 1/2 circumference of earth; note that tides
are caused by gravity and inertia).
Seagrasses experience each of these types of
waves, but the most common are wind waves, swell,
and tides (tides can be viewed as long waves). Wind
waves develop from capillary waves to gravity waves
as a function of the wind strength and direction and
the fetch (length of the unrestricted zone over which
the wind stress operates). Wind waves are affected by
local wind conditions, and are generally of a short
period, T (T is time it takes for a wave to pass a
fixed point). Wave action has a direct impact on the
ecosystem, with obvious effects on sediment transport, boundary layer processes and physical stresses
(Denny, 1988; Koch and Gust, 1999). There has also
been some suggestions that fetch (relative wave exposure index) is an important factor affecting seagrass on a landscape level (e.g. Fonseca and Bell,
1998; Hovel et al., 2002; Krause-Jensen et al., 2003).
Just as the size of the wave is determined by the
wavelength, the shape of the orbit is determined by
the water depth. In deep water (i.e. z > 1/2λ) the
orbits are circular, whereas in shallow water (i.e. z
<1/20λ) the orbits become elliptical or flatter due to
the influence of the bottom. Intermediate waves (i.e.
1/20λ < z < 1/2λ) are more complicated as they
combine characteristics of deep and shallow water
waves. Deep water waves travel at a celerity or phase
velocity C =
√
gλ/2π or λ/T (∼1.56 T ), but shallow water waves are slower due to the influence of the
bottom and travel at C =
√ gz (or 3.1
√
z), which is
why waves build up in shallow areas (Denny, 1988).
Waves travel in a wave train, which is a progression
of groups of waves of similar λ from the same origin.
Energy is lost by the leading wave, which eventually
dissipates, but a new trailing edge wave is created
from this energy. In deep water, the waves progress
with C ∝ λ but the wave train has a group velocity of
C ∝ 1/2λ, whereas in shallow water the celerity of
the individual waves slow until the wave and group
197
within seagrass canopies (e.g. Fonseca and Fisher,
1986; Gambi et al., 1990; Ackerman and Okubo,
1993). It is important to note that other engineering
models have been applied to rough canopies such as
corals and seagrasses with the direct measurement
of canopy friction and the use of the Stanton number, St (uptake rate by the surface/advection over
the surface), to determine the efficiency of canopy
uptake (e.g. Thomas et al., 2000; Thomas and Cornelisen, 2003). Reconfiguration of seagrass canopies
under higher flow conditions (e.g. Fonseca et al.,
1982; Ackerman, 1986), and/or unsteadiness due to
monamis (waving of the canopy; see Section V.C)
caused by an instability of the mean velocity profile
(Ackerman and Okubo, 1993; Ghisalberti and Nepf,
2002) and waves (Koch, 1996; Koch and Gust, 1999)
represents a challenge to researchers. Even so, τ is
the preferred form (over u) of expressing hydrodynamic conditions near boundaries (leaves, flowers,
sediment etc; see Nowell and Jumars, 1984).
Hydrodynamic conditions in the environment are
rarely stationary, especially in wave-dominated seagrass habitats where a more appropriate characterization of the fluid environment is that it varies in a
periodic fashion with each passing wave. Waves represent the movement of energy through a fluid and
exhibit a periodic motion, especially when viewed
at an interface (e.g. the water surface). In this case,
the passing wave (crest followed by trough) causes
a submersed object on the surface to move in a circular or orbital fashion, the diameter of which is
equal to the wave height (H ). The orbital motions
also extend downward through the fluid in a series
of orbitals that diminish in diameter with depth until
a depth (z) of 1/2λ (where λ is the wavelength) is
reached.
The classification of waves can be based on the
disturbing force that creates them, the restoring force
that destroys them, and their wavelength (Garrison,
2000). The disturbing force is the source of energy
that causes the wave, which can be (i) wind stress
acting on water surface causing capillary and gravity waves, (ii) the arrival of surge or sea wave causing swell, (iii) wind setup in an embayment creating seiches, (iv) a change in atmospheric pressure causing short-lived storm surge, and (v) large
disturbances (landslides, volcanic eruptions, earthquake) that cause seismic waves (or tsunami; the
so-called tidal waves that are actually due to gravitational inertial forces). The restoring forces that
reduce the disturbance to the water surface include
(a) surface tension due to the molecular cohesion of
water molecules, which works for small waves (i.e.
λ <1.73 cm; capillary waves) and, (b) gravity that
operates on larger waves (i.e. λ 1.73 cm). Whereas
the wavelength can be used to distinguish differences
among the smallest of waves, it really provides a
measure of wave size and relationship to energy; the
smaller the wavelength, the higher the energy. Some
typical relationships include (1) wind waves (λ <60–
150 m), (2) seiches (λ is large and a function of the
basin size), (3) seismic waves (λ <200 km), and (4)
tides (λ = 1/2 circumference of earth; note that tides
are caused by gravity and inertia).
Seagrasses experience each of these types of
waves, but the most common are wind waves, swell,
and tides (tides can be viewed as long waves). Wind
waves develop from capillary waves to gravity waves
as a function of the wind strength and direction and
the fetch (length of the unrestricted zone over which
the wind stress operates). Wind waves are affected by
local wind conditions, and are generally of a short
period, T (T is time it takes for a wave to pass a
fixed point). Wave action has a direct impact on the
ecosystem, with obvious effects on sediment transport, boundary layer processes and physical stresses
(Denny, 1988; Koch and Gust, 1999). There has also
been some suggestions that fetch (relative wave exposure index) is an important factor affecting seagrass on a landscape level (e.g. Fonseca and Bell,
1998; Hovel et al., 2002; Krause-Jensen et al., 2003).
Just as the size of the wave is determined by the
wavelength, the shape of the orbit is determined by
the water depth. In deep water (i.e. z > 1/2λ) the
orbits are circular, whereas in shallow water (i.e. z
<1/20λ) the orbits become elliptical or flatter due to
the influence of the bottom. Intermediate waves (i.e.
1/20λ < z < 1/2λ) are more complicated as they
combine characteristics of deep and shallow water
waves. Deep water waves travel at a celerity or phase
velocity C =
√
gλ/2π or λ/T (∼1.56 T ), but shallow water waves are slower due to the influence of the
bottom and travel at C =
√ gz (or 3.1
√
z), which is
why waves build up in shallow areas (Denny, 1988).
Waves travel in a wave train, which is a progression
of groups of waves of similar λ from the same origin.
Energy is lost by the leading wave, which eventually
dissipates, but a new trailing edge wave is created
from this energy. In deep water, the waves progress
with C ∝ λ but the wave train has a group velocity of
C ∝ 1/2λ, whereas in shallow water the celerity of
the individual waves slow until the wave and group