(1)
V.K. Tsoukala, Ε.Ι. Daniil and C.I. Moutzouris
Laboratory of Harbour Works, Faculty of Civil
Engineering,
National Technical University of Athens, Athens,
Greece
5 Iroon Polytechniou, 15773 Zografou, Greece
Tel: –30-1-7722367, Fax: 30-1-7722368, E-mail:
V.Tsoukala@hydro.ntua.gr
Abstract: Oxygenation experiments under breaking waves in the coastal zone
in small and large-scale experimental facilities are presented. Small-scale
experiments were performed at the wave flume of the Laboratory of Harbour Works,
NTUA with a uniformly sloping beach and a
rubble mound breakwater. Large-scale Experiments were performed with a sloping
beach at the wind wave flume of Delft Hydraulics and a three-layer rubble mound
breakwater at the Schneideberg wave flume of Franzius Institut in Universitat
Hannover. Although the apparent transfer coefficients for the large scale
experiments were lower than those determined from small scale experiments, the
actual oxygen transfer coefficients, as computed using a discretized form of the
transport equation and accounting for dispersion, are in the same order of
magnitude for small and large scale experiments. A modified vorticity based
renewal model incorporating the breaking wave Reynolds number is proposed, that
describes both small and large scale experimental data well. Additionally, field
measurements of dissolved oxygen concentrations around a harbour area near
Athens indicating the positive effect of the rubble mound breakwater on the
water quality of the area are presented. Measured concentrations on the seaward
side of the breakwater are significantly
higher compared to those measured in the harbour basin and along the
neighbouring beaches.
Keywords: coastal structures, water quality, breaking waves, oxygenation
Water quality in the vicinity of coastal structures and beaches is of particular interest in nearshore areas used as summer resorts, for swimming and recreation, as well as those used for effluent disposal. The Ministry of the Environment and Public Works of Greece has already established a sampling program to evaluate the suitability of greek beaches for swimming. Dissolved Oxygen (D.O.) is a major water quality parameter, one of its main sources being oxygenation, i.e. oxygen transfer through the air-water interface. The role of coastal structures in seawater oxygenation has become an issue of interest in the last decade. Wave-breaking in the vicinity of breakwater structures and beaches results in high oxygenation rates and improvement of water quality in the surrounding area. Experimental results obtained in the Laboratory of Harbour Works (LHW), NTUA show that significant harbour basin oxygenation can be the result of horizontal oxygen flux through the body of the structure, originating from oxygenation in the wave influenced area. Theoretical analysis has shown that the oxygenation induced by breaking waves is segmented into increase of D.O. concentration in the seaward side of the breakwater and oxygenation of the harbour basin [Daniil et al, 1998]. For the investigation of scale effects large-scale experiments were conducted in Delft Hydraulics, The Netherlands and at Franzius Institut, Germany, financed by European Union Programmes. The research has been further expanded to include a field measurement program in a harbour area in East Attica near Athens. An overview of the research conducted so far is presented in this paper.
For the laboratory experiments the test method is based upon removal of dissolved oxygen (D.O.), by chemical deoxygenation or the nitrogen stripping method, from the water volume followed by reoxygenation to near saturation level under the influence of the imposed waves. Water temperature and pressure were recorded for the determination of the saturation concentration. D.O.–time histories were obtained for all experiments and sampling locations. The measurements of D.O. concentration commenced immediately upon wave generation and continued until the D.O. value reached ~80% of the estimated saturation level. Details on the experimental procedure and facilities have already been presented [Tsoukala et al, 2001; Tsoukala, 2000; Daniil et al, 1998].
Small-scale experimental measurements were performed in the
wave flume (27x0.60x1.53m) of LHW with waves breaking on a smooth sloping beach
with uniform slope of 1:2.3 and 1:5 and on a rubble mound breakwater with a
1:1.5 sloping front. Wave heights used ranged from 5.6 – 28.0cm and wave periods from 0.75
– 1.75 sec. The water depth ranged from 0.56 – 0.83m.
Large-scale oxygenation experiments under breaking waves were performed at the Wind Wave Flume of Delft Hydraulics (DH) in The Netherlands and at the Schneideberg Wave Flume at Franzius Institut (FI) at the University of Hannover in Germany.
The wave flume of Delft Hydraulics is “T” shaped with a total length of 100m and 8m width. The flume is equipped with a hydraulic dual piston wave maker for the generation of mechanical waves. Waves are generated by a computer controlled wave board with adjustable rotation and translation. Waves with heights 7.5–28.3cm and wave periods 1.07 – 1.90sec were produced. Two series of experiments were conducted. In the first series (DH-A) waves were produced without a coastal structure in the flume. In the second series (DH-B) a concrete structure with a uniform slope of 1:2.3 was placed at the one end of the flume in order to model a sloping beach and initiate wave breaking. The structure was watertight allowing no water exchange between the two sides. The water depth was 0.72 m for all experiments.
In the Schneideberg wave flume (100x2x2m) of FI
a three-layer breakwater model with 1:1.5 slope was constructed. The armor layer
consisted of stones of mean diameter 3.5cm and mean weight W=100gr. For the
underlayer and the core, stones of W/15¸20 and W/2000 were used. Two series of
experiments were conducted. For the first series the breakwater structure was
impermeable. A wooden barrier was placed in the middle of breakwater body
prohibiting any transport through the structure. In the second series of experiments
the barrier was removed but the breakwater remained almost impermeable due to
the layering of the structure. Wave height used in the experiments ranged from
9.2 to 16.5cm, wave periods from 1.11 to 1.43sec and the water depth was 0.72 m
with the exception of one experiment with 0.80 m depth.
The transfer
coefficient is determined indirectly through the mass transport equation, when
the rest of the terms are known. For laboratory flumes the 1-D transport
equation is usually used:
(1)
where C is the
concentration of dissolved oxygen, U is the mean stream velocity in the
x-direction (U=0 for the wave flume), Dx is the longitudinal
dispersion coefficient in the x-direction, S is source (S>0) or sink (S<0)
term per unit volume. The oxygen transfer through the
air water interface can be expressed as a source term as:
(2)
where
KL is the oxygen transfer coefficient, t is time, AS is
the average air-water surface area on the horizontal plane and V is the aerated
water volume. If the only source term is the air-water gas transfer, and
horizontal transport and dispersion terms can be neglected, the transport
equation is reduced to a first order differential equation. For initial
condition C=C0 at t=0, and constant saturation concentration the
solution is:
(3)
The transfer coefficient can be determined from Eq. (3) using linear regression and the measured DO concentrations. The transfer coefficients computed from Eq. (3) for the large-scale experiments reported were lower than those from the small-scale experiments [Tsoukala and Moutzouris, 1997].
For the performed
experiments the effect of increased longitudinal dispersion due to wave breaking
on the structures, and sometimes by the wave maker, has been considered. Eq. (1)
was discretized using a control volume approach [Patankar, 1980]. Integrating
over a control volume of length Li, volume Vi, cross
sectional area equal to W (width of the channel) times d (the water depth),
assuming that ¶C/¶t and S can
be represented by their values at point i and a linear profile between grid
points for ¶C/¶x, Equation
(1) can be written:
(4)
where Li,i+1, Li-1,i is the distance and Di,i+1, Di-1,i the horizontal diffusion coefficient between grid points i, i+1 and i-1, i respectively.
As no longitudinal variation in D.O. concentration was observed for the DH-A experiments, Eq. (3) was used for the determination of the oxygen transfer coefficient. In DH-B, where the waves were breaking and longitudinal variation was observed the oxygen transfer coefficients were determined based on the numerical scheme described by Eq. (4). Five control volumes were used, each control volume containing at least a sampling point. The system of equations described by Eq. (4) was solved numerically using a TDMA algorithm. The initial concentrations measured at each sampling point were used as inputs. The gas transfer and diffusion coefficients were adjusted till a best fit with observed D.O. values was obtained. The actual oxygen transfer coefficients are in the same order of magnitude for small and large-scale experiments [Tsoukala, 2000]. For the FI experiments similar analysis is presently underway and the actual oxygen transfer coefficient are anticipated to be on the order of 25-50% higher than those determined from Eq. (3).
According to the first surface renewal model [Dankwerts, 1951] the gas transfer coefficient can be expressed as a function of the rate of surface renewal:
or
(5)
where KL is the gas transfer coefficient, Dm (m2/s)
is the molecular diffusivity of the gas in the water, ν (m2/s)
is the kinematic viscosity of the water, and r (sec-1) is the average
surface renewal rate and Sc the Schmidt number.
From an
engineering point of view, the primary research goal should be the prediction of
the surface renewal rate based on the wave characteristics. Daniil and
Moutzouris [1995] presented a vorticity–based renewal model, for gas transfer
under breaking waves, expressing the surface renewal rate as:
(6)
where ar is a constant of proportionality,
is the wave vorticity at the water surface (sec-1),
f (sec-1) is the wave frequency, H(m) is the wave height, L(m) is
the wave length. The factor Gr
was expressed as Gr =(L/d)2 in order to incorporate the influence
of relative depth, where d(m) is the water depth. The following expression was
fitted to data from experiments with a sloping beach and a rubble mound breakwater
performed at LHW [Daniil et al., 1998].
(7)
The actual
transfer coefficients both for the sloping beach and the breakwater [Daniil et al., 1998; 2000] give the same correlation with the wave characteristics (α=3.03 and β=0.00236 m/s).
Analysis of large-scale experiments indicated it was essential to incorporate in the Gr factor an expression describing the type of wave breaking. Dimensionless parameters reported in the literature for indexing of wave breaking [Zhang and Sunamura, 1990] were used in the Gr term. The best correalation was obtained by using a breaking wave Reynolds number [Tsoukal et al, 2001].
(8)
where
Hb, Lb is the wave height and wave length in the wave
breaking zone, T is the wave period. For the conducted experiments the wave
heights in the breaking zone were calculated from the equation of Le Mehaute
and Koh [1967],
, where γο=L/d is the wave steepness, tanα is the slope of the beach or the coastal structure, and the wavelengths,
from the relation suggested from the US Army Corps of Engineers [1990],
, where db is the water depth in the wave breaking zone.
In Figure 1 oxygen
transfer coefficients are plotted against the parameter
. The actual transfer coefficients correlate quite well with this parameter.
The vorticity model is thus modified to:
(9)
The constant a=0.102 was determined by best fitting the experimental results of LHW and DH-B with a very good correlation coefficient (r=0.80). It also describes data from literature fairly well. Data from DH-A are also shown in Fig. 1 substituting the deepwater wave characteristics H and L in place of the breaking wave characteristics Hb and Lb. They also plot quite close to Eq. (9) [Tsoukala, 2000]. Apparent transfer coefficients from FI experiments plot below the proposed equation, but the corresponding actual transfer coefficients are expected to follow the equation closely as well. The proposed equation improves the equation of Daniil and Moutzouris [1995] and can be used with rather good precision in the case of non-breaking waves, if the breaking wave characteristics Hb and Lb are substituted with the corresponding deepwater characteristics [Tsoukala, 2000].
In Figure 2 the variation of D.O. oxygen concentration measurements on the seaward side of the breakwater, in the harbour basin and in the neighbouring beaches, taken in a small harbour near Athens during the spring and summer period of 2000 are presented. It is observed that concentrations on the seaward side of the breakwater are quite high with a slight decreasing trend with increasing temperature. Concentrations measured along the neighbouring beaches are significantly lower and in some cases even lower than those measured in the harbour basin.
Experimental results and field measurements show that coastal structures have a positive effect on water quality of the surrounding area. Wave breaking is an important factor resulting in increased seawater oxygenation. Actual oxygen transfer coefficients, as computed from a discritized form of the transport equation and accounting for longitudinal dispersion, are found to have the same relation with wave characteristics both for small and large scale experimental data. The inclusion of the wave Reynolds number in the expression of the surface renewal rate along with the vorticity parameter was shown to improve the gas transfer coefficient prediction model. The proposed modified vorticity model describes gas transfer well both for breaking and non breaking waves.
Acknowledgements
This work was partly supported by the European Programme Human Capital Mobility -Access to Large Installation Facilities (1994) and Training and Mobility of Researchers -Access to Large Scale Facilities Programme (1999).
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Fig.1 Correlations
of the oxygen transfer coefficients with the parameter
Fig.2
D.O. Concentration variation around a harbour area for spring and summer 2000.