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THE EFFECT OF KELP IN WAVE DAMPING
MARTIN MORK
SARSIA
MORK, MARTIN 1996 02 27.The effect of kelp in wave damping. – Sarsia 80:323-327. Bergen ISSN
0036-4827.
It is generally acknowledged that bottom vegetation enhances the damping of surface waves in shallow
waters. Thus the harvesting of kelp forests by trawling and associated change of conditions have given
rise to conflicts. In order to secure a scientifically good basis for management of the marine resources
and the environment, the role of the kelp forest as habitat for fish and marine animals and the wave
damping effect need to be investigated and quantified.
The hydrodynamical conditions in a kelp forest have been investigated with aid of ultrasonic current
meters (UCMs) attached to bottom mounted rigs. Data sampling at a rate of 2 Hz of the three velocity
components and pressure ensured adequate frequency resolution of the energy containing surface
waves of 5-15 sec. periods. Analysis of frequency spectra of wave energy suggested a new main mechanism of wave damping giving a model which has been formulated mathematically and compared with
observations.
Wave attenuation by kelp forests in shallow waters has been substantiated by measurements at
Hustadvika at a site which is strongly exposed to waves from the open ocean. The reduction of wave
energy from the outer to inner part of kelp belt over a distance of 258 m was 70-85 % with highest
value at low tide. Velocity measurements at two levels, above and below canopy, reveal almost identical results. This remarkable documentation contradicts earlier assumptions and findings concerning
sheltering effect of kelp, i.e. ECKMAN & al. (1989). The working hypothesis of the present analysis is
that the viscous drag of the kelp fronds is the dominating factor. The results from the corresponding
mathematical model are in good agreement with observations.
The wave conditions in a kelp forest have been measured and modelled. The results of the experiment provide a good basis for evaluation of wave damping effects and may be compared with laboratory experiments and field investigations after harvesting.
Martin Mork, Geophysical Institute, University of Bergen, Allégaten 70, N-5007 Bergen, Norway.
INTRODUCTION
It is generally acknowledged that bottom vegetation has
a wave damping effect in shallow waters. Yet the nature
of the frictional processes is not fully known and quantification of the forces involved are lacking. Research on
the topic is however in progress. Some pioneering works
are due to PRICE et al. (1968), KOBAYASHI et al. (1993) and
ASANO et al. (1992). In their studies the bottom vegetation has been considered as a layer with great resistance
due to viscous stresses and/or drag forces. DALRYMPLE et
al. (1984) have investigated the wave diffraction caused
by energy dissipation in zones with bottom vegetation.
WANG & TØRUM (1994) have dealt with the mutual interaction of waves and kelp plants and consequences for
transport of bottom sediments.
The bottom vegetation of greatest interest in our waters is the kelp called Laminaria hyperborea (Gunnerus)
Foslie. It consists of hapter (holdfast), stipe and frond
and grows on rock or stones. The stipe may in some
regions gain a height of more than 3 m and the frond may
attain an area of 2 m2. The kelp forests, which are found
along the coast of Norway, cover a total area which is
comparable to all farmed land in Norway. The ecology of
the kelp forest has been reviewed by FOSSÅ & SJØTUN
(1993). The kelp is considered to be of great importance
in many respects, economically in relation to kelp harvesting, for fish recruitment, as habitat for crabs and
lobsters and protection against beach erosion. Due to
conflicting interests there is demand for investigations of
the physical-biological interaction and consequences of
large scale harvesting (WOLL 1993).
THE FIELD EXPERIMENT
In order to resolve many of the questions related to the
wave damping effect of kelp a field experiment was carried
out at Hustadvika in August 1993. The chosen site, Fig. 1,
near Kvitholmen is within a region which is strongly exposed
to waves from the open ocean. The kelp forest was fairly
homogeneous due to harvesting four years ago. The average
stipe length was 1.6 m and frond areas 0.8 m2.
At one of the instrumented sites the average concentration
was 25 large kelp plants per square meter. Thus the wetted area
of fronds became about 40 m2 per square meter. It is therefore
argued that viscous drag must be taken into account as well as
form drag. Wave conditions were recorded by ultra sound cur-
Fig. 1. The map shows the site of the field experiments and location of the instrumented rigs.
rent meters and pressure gauges. Two types of experiments
were carried out. One experiment was to evaluate the reduction
of wave energy from the outer part to the inner part of a kelp
belt. For this purpose the current meter rigs were placed at
depths of 5-6 m some 258 m apart. The second experiment
was designed to resolve the vertical variation of wave induced
currents. Accordingly one current meter was placed with sensor
40 cm above bottom, while the other current meter was
recording above canopy 150 cm higher up.
RESULTS
The frequency spectra, Fig. 2, at both high and low tide
show the presence of swell of 12 sec. period and wind
sea with 7 sec. peak period. Spectra from both stations
are displayed. As expected the wave damping from the
outermost station to the inner side of the kelp belt was
great. The reduction of total wave energy was 70-85 %
over a distance of 258 m, where the highest reduction
occurred on low tide. The tidal range was 1.4 m. It is hard
to tell how much of the wave damping is caused by the
kelp forest or is due to refraction. The bottom was quite
irregular with depths in the range 5-15 m. If we only
consider the pronounced swell from the North the swell
energy is reduced by 60-75 % over the same distance and
the highest reduction occurred at low tide.
The dense kelp forest was cleared only at a small site
where instruments were positioned. It will be assumed
that the measurements are representative for the mean
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conditions in a broader region. The results from the experiment with instruments at two levels (40 cm and 190
cm above bottom), are shown in Fig. 3. The results represented as frequency spectra of the horizontal velocities, show almost identical energy distributions at the
two levels. That is a remarkable result. Since the water
depth is only about 5 m the wave energy is carried by
shallow water waves. The velocity profile may give a
clue to the development of a realistic model. Obviously
the kelp forest cannot be treated like a porous bottom
layer in this case.
THE MODEL
A simple linear model is proposed, Fig. 4, and is based on
the assumption that rotational and dissipative effects are
only important in vicinity of canopy level. Well above
and below canopy the velocity is derived from a potential. Thus for shallow water waves the horizontal velocity will be the same both above and below the canopy,
away from the stress layer. In underwater video recordings we have seen that the kelp is swaying with almost
the same harmonic mode as the current oscillations. A
small phase shift may be detected and the amplitude
may be somewhat reduced. In the model it is assumed
that the kelp is moving back and forth in an oscillatory
harmonic motion and that the viscous stress on top of canopy
to first order also varies harmonically and is proportional to
Fig. 2. Frequency spectra of the kinetic energy density at inner (dotted lines) and outer (continuos
lines) station. Due to the relative insignificance the square of vertical velocity has been neglected. A)
29 Aug. 93, 22.00 hrs, high tide. B) 30 Aug. 93, 04.00 hrs, low tide.
Fig. 3. Frequency spectra of the kinetic energy density at two levels at the inner site. The fully drawn
curves represent observations above canopy, (190cm above bottom). The dotted curves represent observations well beneath canopy, (40cm above bottom). A) 30 Aug. 93, 22.00 hrs, high tide. B) 31
Aug. 93, 05.00 hrs, low tide.
the horizontal velocity with a possible small phase shift.
The velocity vector and pressure is required to vary continuously across canopy level.
The linearized equations are
(3)
V = ∇φ + V*
and that V* may be derived from
(4)
V*t = υV*zz
it follows that
(1)
Vt = - ∇(p/ρ + gz) + υ Vzz ,
(5)
φt + p/ρ + gz = const. and furthermore
(2)
∇ · V = 0,
(6)
∇2φ = 0 and ∇.V* = 0
where V is the velocity vector, p is the pressure, the
density is ρ = constant and υ is the kinematic viscosity
coefficient. The differentiation is indicated by subletters.
Assuming that the velocity vector can be expressed as
The leading assumption is that viscous and rotational
effects are only significant in vicinity of the canopy layer.
Thus the boundary condition at the surface, p = 0 and at
the bottom, w = 0 can be expressed with aid of the veloc-
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Kinematic condition at bottom, (z = 0), stating that
vertical velocity is zero becomes
(9)
φz = 0
which determines the form of the velocity potential in
lower layer
(10) φ2 = A2 cosh(kz)exp(i(kx - σt))
Conditions of continuity and viscous drag at canopy
level, (z = h), are
Fig. 4. Sketch of the model and amplitude of the horizontal
velocity for shallow water waves for a special choice of parameters. The ultrasonic current meter (UCM) is mounted on a
vertical rod in the center of a rig with three legs.
(11) p1 = p2 , U1 = U2 , W1 = W2 , and υUz = Rφx
.
For 2-dimensional motion V* may be derived from a
streamfunction ψ where
(12) ψt = υψzz , giving
ity potential only. The general solution for the velocity
potential is
φ = (C exp(kz) + D exp(-kz)) exp (i(kx - σt)).
Application of boundary conditions determines the
coefficients.
Pressure condition at surface , (z = H), becomes from (5)
(7)
φt + gφz = 0.
t
Accordingly the velocity potential in upper layer becomes
(8)
φ1 = A1(cosh(k(z - H)) + (σ /(gk)) sinh(k(z - H)))
exp(i(kx - σt)).
2
(13) ψj = Bj exp(-(1-i)rj |z - h|) exp(i(kx - σt)) , where
(14) rj2 = σ/ (2υj) , j = 1 , 2 .
Application of boundary conditions give a (σ,k)-relationship
(15) σ2 - gkβ = - igk2R*Q/σ where
(16) R* = R(1 + r2/r1) and Q = (1 - αβ + (β-α)σ2/gk)/(1
- α2) where
(17) α = tanh(kh) and β = tanh(kH).
Here we have a complex wavenumber which is split in
a real and imaginary part
(18) k= k* + i K
List of symbols
V
velocity vector (m/s)
V* rotational part of velocity vector (m/s)
g
gravity (m/s2)
z
vertical coordinate (m)
x
horizontal coordinate (m)
ρ
density (kg/m3)
ν
kinematic viscosity coefficient (m2/s)
φ
velocity potential (m 2/s)
ψ
stream function (m2/s)
k
complex wave number (m-1)
k*
real part of wave number (m-1)
K
imaginary part of wavenumber or damping factor
(m -1)
Khw damping factor at high water
Klw damping factor at low water
σ
angular frequency (rad/s)
f
frequency (Hz)
U
horizontal velocity (m/s)
W
vertical velocity (m/s)
h
height from bottom to canopy (m)
H
water depth (m)
a
wave amplitude at surface (m)
R
drag coefficient (m/s)
E(f) frequency spectrum of kinetic energy density (m2/s)
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The solution in accordance with model assumptions
may be written
(19) η = a exp(-Kx)cos(k*x-σt)
for the surface elevation where a is the wave amplitude at
position x= 0. Correspondingly the velocity potensial at
the surface is
(20) φ1(z=H) = (ag/σ) exp(-Kx)sin(k*x- σt)
The frequency-wavenumber relationship is approximately
(21) σ2 = gk* tanh(k*H)
as in the non-viscous case, where H is water depth and g
is gravity.
The damping assumes the form of exponential decay
with e-folding length
(22) K-1 = Hσ(1 + sinh(2k*H)/(2k*H))/(k*R)
where R is the drag coefficient which has to be determined empirically. The drag coefficient is a function of
kelp concentration and morphology. It is interesting to
note that different model approaches lead to similar
expressions for the attenuation. However the velocity
distribution vertically may be quite different depending
on the assumptions of stress distribution. For shallow
water waves the relations become
(23) σ = k*(gH)1/2
and K–1 = 2H(gH)1/2/R.
Thus it is seen that damping is enhanced in shallow
waters and especially at low tide. The model results agree
with the observations at high water if we choose Khw =
0.0018 m-1. With assumed average depth at high water
equal to 8 m we obtain a ‘viscous drag coefficient’; R =
0.26 m/s.
As a check of the model we can evaluate a new K for
low water, when H = 6.6 m, and we obtain Klw = 0.0024
m-1. This result fits with the observed enhanced damping
at low water, but the energy reduction becomes a little
bit lower, 71 % compared to 75 % as observed. The
modulus of the horizontal velocity profile will be as shown
in Fig. 4.
DISCUSSION
Results from the field experiment must be applied with
caution. Inhomogeneties of bottom topography and kelp
distribution inhibit a clear separation of effects of refraction and reflection of wave energy and damping due to
kelp stands. Waves have different directions of propagation and that must also be taken into account when wave
paths through the kelp forest are estimated. The lucky
part of the experiment was the presence of a pronounced
swell from the North. The swell may be considered as a
plane sine wave travelling in direction from outer to inner
station. The observed damping is an integrated effect of
varying depths and kelp distributions between stations
and do not correspond directly to the simple model
concept. Still the model may give a clue to a better
understanding of the processes involved. It is a surprising
result that horizontal velocities of long waves were not
reduced below the canopy. This observation supports
the model concept with the kelp fronds as the most
effective wave damping factor. This is in contradiction
with earlier findings as reported by ECKMAN et al.
(1989).However the bottom vegetation was different in
their case. Conditions may be different with other types
of kelp than Laminaria hyperborea and with older plants.
But in our case it was found that there was no sheltering
below canopy except possibly at narrow spots close to
stipes etc.
ACKNOWLEDGEMENTS
The field experiment was supported by the Direktoratet
for Naturforvaltning. Thanks are due to Jan E. Stiansen for
work done in the field and with the analysis and to Siri
Ødegaard for diving support and biological advise. Logistic
support, knowhow and local knowledge obtained from Inge
Sandvik and Jan T. Slatlem are gratefully acknowledged.
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