251
IMPACT OF SURFACE WAVES ON THE COASTAL ECOSYSTEMS
S.R. MASSEL1, E.N. PELINOVSKY2
1 Institute of Oceanology of the Polish Academy of Sciences
Powstańców Warszawy 55, 81-712 Sopot, Poland
2 Institute of Applied Physics of the Russian Academy of Sciences
Ulyanov 46, 603600 Nizhniy Novgorod, Russia
Abstract
Wave motion in vegetated coastal zones is relatively poorly understood when comparing
with non-vegetated coasts. This is mainly due to lack of good quality data as well as to lack
of the theoretical (or numerical) solutions. In this paper an attempt to model the wave
propagation in two vegetated coastal environments is demonstrated. The attenuation of
short surface waves as well as tsunami waves in the mangrove forest is determined by
treating the mangrove forest as a random media with certain characteristics depending on
the geometry of mangrove trunks and their locations. In the second example, the
transformation of surface waves on sandy beaches, their breaking, set-up and run-up are
determined and resulting fluctuations of the water table and groundwater flow are
discussed.
1. Introduction
We are living in the age of "environmental awareness", with increasing demands on
minimizing negative impacts of human activity on the environment. The environmental
factor becomes move and move important in traditional coastal management and
engineering. The necessity of inclusion of the environmental requirements is very clearly
seen at the vegetated coasts, especially in the tropical climate. In contrast to the nonvegetated coasts, the understanding of the physical processes at vegetated coasts is very
poor and it is not adequate to develop effective management plans or engineering designs
which are today subjected to very stringent requirements to minimize their impact on the
environment.
The role of waves in the coastal marine environment can not be overestimated. Waves
approaching the shoreline break and dissipate their energy in the very shallow water.
Tsunami, cyclone or storm waves impose large forces on natural coastal and man made
structures. Knowledge of wave motion and the sediment budget provides the key to the
proper selection of protecting structures and methods of coastal management [1]. However,
hydrodynamics of the vegetated coastal zones, especially the wave motion, are still very
poorly understood. Various types of ecological models are used to simulate the impact of
the specific project on the vegetated environment to provide the physical and biological
A. C. Yalçıner, E. Pelinovsky, E. Okal, C. E. Synolakis (eds.)
Submarine Landslides and Tsunamis 251-258.
@2003 Kluwer Academic Publishers. Printed in Netherlands
252
consequences of the alternative solution for the coastal regions [2] [3]. Most of the existing
ecological models are concentrated on the flow pattern and transport and dispersion of the
pollutants.
For the purpose of this paper, two examples of the surface wave impact on the ecology
of the coastal system are given. The first example deals with the surface waves attenuation
in the mangrove forest. Using the linearised governing equations, the rate of wave energy
attenuation is obtained in the closed form for a given geometry of mangrove trees and
roots. In the second example the main factors contributing to fluctuations in the water table
and groundwater flow induced by surface waves in the sandy beach are discussed.
2. Wave Propagation in Mangrove Forests
Mangroves are densely vegetated mudflats that exist at the boundary of marine and
terrestrial environments. Inherent in this habitat is their ability to survive in a highly saline
environment [4]. In recent years it has been realized that mangroves may have a special
role in supporting fisheries, stabilizing the coastal zone and protecting the lives and
properties of the people living near the sea and offshore islands [5][6][7]. For example,
after the 1998' tsunami in Papua New Guinea, the International Tsunami Survey Team
recommended to plant the Casuarina mangrove species in front of coastal communities.
They argued that the local Casuarina species withstood the wave attack significantly better
than coconut trees [8].
Hydrodynamic factors play a major role in the structure and function of mangrove
ecosystems. Biogeochemical and trophodynamic processes, and forest structure and growth
are intimately linked to water movement. However, studies of physical processes in tropical
mangrove swamps and mangrove-fringed estuaries are few, and far behind compared to
those of temperate estuaries.
During tsunami and tropical cyclones, however, energy of waves substantially exceeds
tidal energy. Due to the complexity of mangrove systems, the transmission of waves
through mangrove areas is still poorly understood and number of papers dedicated to the
mangrove hydrodynamics is very limited [9][10][11][12][13][14].
In the paper [15], the theoretical prediction model for attenuation of random surface
waves propagated through mangrove forests was developed. A full boundary value problem
was solved and attenuation of wave spectrum was predicted. Assuming that the diameter of
particular mangrove trunks is very small in comparison with wavelength, wave energy is
dissipated mostly due to drag forces induced on trunks by waves. Therefore within the
mangrove forest (Region II - see Fig. 1), the momentum equation for motion with
dissipation can be written as follows:

u 1
1 
  p  gz   F
t

 ,



(1)
in which u  u, w is a wave-induced velocity vector, p is a corresponding dynamic

 
pressure and F  0.5 Cd Du u is the drag force vector per unit volume [15].
253
Figure 1. Reference scheme
We assume that in a unit control area of mangrove there are Nu trunks piercing the sea

surface (usually Nu is of order of 1-10 per m2), each of the mean diameter Du . In the
bottom layer of thickness hl (usually thickness hl is of order 0.3 m - 1.0 m) mangroves are
very dense and smaller trunks and roots are randomly oriented. It is assumed that the

number of trunks, Nl, each of the mean diameter D l , is of the order of 10-30 per m2
(Fig. 1). The control area has to be selected sufficiently large to accommodate Nu and Nl
trunks, where Nu > 1 and Nl » 1. On the other hand, this area has to be sufficiently small in
order to neglect the variation of wave velocity within the control area and to neglect the
exact location of each trunk within the control area.
Equation (1) is the nonlinear equation due to a quadratic drag term involving absolute
value of local random orbital velocity. This equation cannot be solved exactly for a
mangrove forest of arbitrary density and for arbitrary forcing by a random wave field. To
get a practical solution, the linearization procedure, widely used in ocean engineering for
determination of the forces on offshore structures, was applied [16]. The nonlinear term
was replaced by the linear one under the condition that the mean error of this substitution
becomes minimal. In physical terms, it means that instead of the mangrove forest with a
complicated spatial net of trunks and roots, we are dealing with a medium for which the

energy dissipation is characterised by term f e p u x, z  , where fe is the linearization
coefficient and p is the peak frequency. Hence we have:

u 1

  p  gz   f e p u
t 
(2)
The details of solution of the boundary value problem and linearization procedure are
given by in [15].
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Figure 2. Wave spectrum at three cross-sections (x = 0, 25, 50 m) in densely populated forest
To illustrate developed model let us assume the following parameters of the mangrove
forest: forest width l = 50 m, water depth h = 1 m, number of trunks in upper layer
N = 16/m2, number of trunks in lower layer Nl = 49/m2, mean diameter of upper layer


trunks Du  0.08 m m and mean diameter of lower layer trunks Dl  0.02 m . The
mangrove forest is subjected to surface waves characterized by a typical spectrum for
shallow water [2]. In the calculation, the significant wave height Hs = 0.6 m and the peak
period is Tp = 5 s. In Fig. 2, the frequency spectra at three cross-sections (x = 0, 25, 50 m)
from the mangrove front are shown. Numerical calculations indicate that for a given
incident wave spectrum and given mangrove density 99% of energy is dissipated within
mangrove forest [17][15].
3. Groundwater Circulation due to Wave Set-up and Run-up
Transformation of waves on the sandy beach, their breaking, set-up and run-up are the main
factors contributing to fluctuations in the water table and groundwater flow. Sandy beaches
are highly exploited but very dynamic and fragile environments. The beach system is
driven by the physical energy induced by waves and tides. The water flow through the
beach body is of great importance in introducing water, organic materials and oxygen to the
ground environment. Moreover, it controls the vertical and horizontal, chemical and
biological gradients, and nutrient exchange in the beach [18]. Also water filtration through
a sandy beach is considered to be significant for water improvement as the beach retains
and processes organic matter and pollutants. Some pollutants, like hydrocarbons and heavy
metals are sorbed on the surface of microbes and diatoms the more numerous and diverse
the organisms, the more effective the area of sorption [19].
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Figure 3. Relationships between wave run-up, infiltration and coastal watertable
Wave motion on the beach is very complex and the groundwater flow is different in
different beach regions. In Region 3, between points D and E (see Fig. 3), the wave run-up
infiltration contributes mainly to the raising of the coastal water table. The hypothetical
distribution of the infiltration velocity Uf induced by the run-up is shown in the same
figure, and the vertical axis ni N-1 denotes the ratio of the events when the beach surface is
covered by water to the total number of events.
The beach groundwater flow in the set-up region, between points Bb and D (see Fig. 3),
induces groundwater circulation which contributes to the submarine groundwater discharge
[20][21]. Little is known about the groundwater flow in this region. One of the models of
the groundwater flow is the Longuet-Higgins analytical solution for the circulation induced
by wave set-up in a semi-infinite domain [22].
In the run-up region, between points D and E, wave uprushes on the beach and the
water level reaches the height Rmax, defined as the maximum vertical height above still
water level. The run-up height is always greater than the wave set-up. The wave run-up
limit and induced water infiltration into beach body is a response to the instantaneous flow
of the surface water. Massel and Pelinovsky [23] developed the analytical model for the
run-up of dispersive breaking and non-breaking waves. Waves approaching the shallow
water area were modelled by the mild-slope equation [2] [3]. The wave run-up during
256
Figure 4. Streamlines contours (in cm2/s) in a porous bed induced by wave set-up
tsunami waves attack is particularly high. At very small water depths, the non-linear and
linear equations for shallow water waves were considered and the dissipation due to wave
breaking was included, providing a more realistic estimation of run-up characteristics [24].
The experimental data on the wave run-up are numerous. However, they are mostly
related to the long or solitary waves propagating on steep slopes, especially on marine
revetments (see for example [25]). On the other hand, the data on run-up of short waves on
the gentle slopes of the natural beaches are rather rare. In paper [23], the predicted wave
run-up heights have been compared with data reported in [26] [27] [28] showing a good
agreement.
However, the beaches consisting sand or unconsolidated sediment are porous and any
changes of pressure associated with the wave set-up produce flow of sea water within the
beach itself (see Fig. 3). Moreover, the wave motion percolated in a permeable bottom
influences the wave forces on the hydraulic structures founded on or extended into the
bottom. Using set-up and run-up values, calculated in [23], the streamlines of flow in a
porous medium beneath the sea bottom in Region 3 were calculated by the approximate
method suggested by Longuet-Higgins [22]. Example of streamlines distribution for the
incident deepwater wave height H0 = 1.95 m and period T = 6 s propagating on beach with
the slope 0.1 is shown in Fig. 4.
The pattern of streamlines indicates that the induced circulation begins with infiltration
close to profile D and ends with exfiltration at the lower part, close profile C, as was shown
schematically in Fig. 3. Move detail description of the water infiltration due to wave set-up,
based on the conformal mapping approach will be published in a separate paper.
257
4. Conclusions
The following major conclusions can be drown from this short paper:
1. Tsunami waves or tropical cyclone induced waves are extraordinary events and their
energy substantially exceeds the usual energy level at a given location. These waves are the
dominant cause of water movement, sedimentation and coast erosion.
2. Wave motion in vegetated coasts subjected to the tsunami waves or tropical
cyclones is relatively poor understood, when comparying with non-vegetated coasts. This
paper presents some results on the mangrove forest which is a good example of the
vegetated coast. The energy dissipation is determined by treating the mangrove forest as a
random media with certain characteristics determined using the geometry of mangrove
trunks and their locations. Example given in this paper as well as in other papers by one of
the authors, showed that mangrove species withstood the wave attach significantly better
than for example coconut trees.
3. The wave run-up on a beach face is one of the basic factors that determines beach
stability and sediment transport, induces beach groundwater flow and raises the
groundwater table. Driven by waves, the water flow through the beach body is able to
transport oxygen, and hence helps to maintain biological activity in the porous media. In
particular, the pressure changes associated with the wave set-up, through small, produces
effects that, because they are cumulative in time, may be more far-reaching. Two systems
of circulations have been discovered, related to different gradients of the set-up height. The
pattern of groundwater flow is of vital importance to the status of the organisms inhabiting
the beach sand.
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