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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 324 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- 325 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) 326 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. REFERENCES Asano,T., H. Deguchi & N. Kobayashi 1992. Interaction between water waves and vegetation. – Proceedings 23rd ICCE Conference ASCE, Venice, pp 2710-2723. Dalrymple, R.A., J.T. Kirby & P.A.Hwang 1984. Wave refraction due to areas of energy dissipation. – Journal of Waterways, Port, Coastal and Ocean Engineering. 110, No. 1:67-79. Eckman, J.E., D. Duggins & A. Sewell 1989. Ecology of understory kelp environments. I. Effects of kelp on flow and particle transport near the bottom. – Journal of Experimental Marine Biology and Ecology 129:173-187. Fosså, J.H. & K. Sjøtun 1993. Tareskogsøkologi - fisk og taretråling. – Fiskets Gang 2:15-26. Kobayashi, N., A.W. Raichle & T. Asano (1993). Wave attenuation by vegetation. – Journal of Waterways, Port, Coastal and Ocean Engineering, ASCE 199(1). Pp. 30-48 Price, W.A., K.W. Tomlinson and J.N. Hunt 1968. The effect of artificial sea weed in promoting the build up of beaches. – Proceedings 11th International Conference on Coastal Engineering, London, 570-578. Wang, H. & A. Tørum 1994. A numerical model on beach response behind coastal kelp fields. Report SINTEF, NHL, Trondheim. 42 pp. Woll, A. 1993. Konsekvenser av taretråling i Møre og Romsdal. Møreforsking rapport. 71 pp. Accepted 10 December 1995. 327 328