NDIAN/CEAN334
2.7 Wave Propagation and Dissipation
1997 1998 1999 2000 2001 2002 2003 2004 2005
Wave height (m)
12 10 8 6 4 2 0
1997 1998 1999 2000 2001 2002 2003 2004 2005
Wave direction
360 300 240 180 120 60 0
J F M A M J J A S O
2003
Wave period (s)
25 20 15 10 5 0
data model
Figure 2.32: Wave characteristics near the Geographe Bay as predicted by WAVEWATCH III model.
114.6 114.8 115.0 115.2 115.4 115.6 115.8 114.6 114.8 115.0 115.2 115.4 115.6 115.8
a) b)
-32.2 -32.4 -32.6 -32.8 -33.0 -33.2 -33.4 -33.6 -33.8
-32.2 -32.4 -32.6 -32.8 -33.0 -33.2 -33.4 -33.6 -33.8 200 180 160 140 120 100 80 60 40 20 0
3.0 2.5 2.0 1.5 1.0 0.5 0.0
m m
Figure 2.33: Geographe Bay (a) bathymetry and (b) simulated significant wave height for south-westerly waves (SWAN model). The square dot in (a) indicates location of the measurement site.
a)
J J A S O
2003
Wave height (m)
9 8 7 6 5 4 3 2 1 0
b)
J J A S O
2003
Wave height (m)
9 8 7 6 5 4 3 2 1 0
DataWW3
DataWW3 calibrated
Figure 2.34: Significant wave height predicted by WAVEWATCH III model vs measurements at Cape Naturaliste Station (a) original model output (b) the model output scaled by factor 9/11.
a)
J J A S O
2003
J J A S O
2003
Wave height (m)
9 87 6 54 32 1 0
b)
Wave height (m)
98 76 5 43 21 0
Data WW3
Data
WW3 calibrated
Figure 2.35: Significant wave height predicted by WAVEWATCH III model vs measurements at Rottnest Island Station (a) original model output (b) the model output scaled by factor 9/12.
Wave measurement over Marmion reef
As a first step towards quantifying wave dissipation due to bottom friction over reefs, direct measurements of wave attenuation were made. Four, 3D acoustic doppler velocimeters, were deployed across a section of the reefs off Marmion, south of the Hillary’s boat harbour, as shown in Figure 2.36. The bathymetry shown in figure 2.36 was derived from soundings provided by the W.A. Department of Planning and Infrastructure and gridded to 30m horizontal resolution.
The velocimeters were set to record at 2Hz for two hours every four hours and were deployed for the period December 2-19, 2005. The current meters were bottom mounted on rigid frames and measured the three components of velocity at a height of 0.6m above the bottom.
Corresponding pressure measurements were made 0.1m above bottom. The measurement site was chosen because very high resolution (sub-metre horizontal) bathymetry was available from a multi-beam survey undertaken by Fugro Pty Ltd allowing the opportunity to quantify bottom roughness. The bathymetry measured by Fugro (decimated to 2.5m horizontal resolution) is shown in Figure 2.37 which also shows the measurement locations and the depth profile along the instrument transect. The instruments had to be separated far enough that we might hope to see measurable attenuation in wave height, yet not so far apart that other effects such as refraction might dominate changes in wave height. The reef crests in this region are also deep enough to avoid any dissipation due to depth-induced wave breaking, which to a first approximation is where the wave height is 0.8 times the water depth. In the absence of any previous measurements, the maximum distance between velocimeters was determined by the size of the Fugro survey region. Instruments ADV1, ADV3 and ADV4 were located on and near the base of reefs in depths of 10.4m, 10.5m and 9m, respectively. ADV2 was located near the top of a reef in a depth of 7.8m.
3.5 3.6 3.7 3.8
Easting (m)
Northing (m)
6.51
6.5
6.49
6.48
6.47
6.46
x 105 x 106
Figure 2.36: Map showing the location of the ADV deployments in the blue box labelled measurement site.
See figure 2.37 for detail.
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Northing (m)
-6 -7 -8 -9 -10 -11 -12 -13 -14 -15
x 106
-4 -6 -8 -10 -12 -14 -16 -18 -20
x 105 Easting (m)
Depth (m)Depth (m)
Distance (m)
0 -10 -20 -306.4745
6.474 6.4735
6.473 6.4725
6.472 3.77 3.775 3.78 3.785 3.79
Figure 2.37: Locations of the four Nortek Vector Velocimeters plotted on the multibeam bathymetry, decimated to 2.5m horizontal resolution. (bathymetry courtesy of Fugro Pty Ltd).
The significant wave height (Hs) is calculated from the zeroth moment of the sea surface elevation spectrum calculated from the measurements according to
2
1
4 ( )
f s
f
H = ∫ E f df
h(3)
Where Eη(f) is the spectrum of sea-surface elevation, f1 and f2 were set at .05 and 0.15 Hz, respectively, and a trapezoidal method used to integrate the spectrum. Time-series of the significant wave height for each two-hour measurement period, calculated from the observed pressure at each of the ADVs, are shown in Figure 2.38. Also shown in Figure 2.38 is the time-series of significant wave height from the Rottnest Island wave buoy located in 80m water depth about 30km south west of the Marmion reefs.
(RMSM
$ECEMBER
!$6
!$6
!$6
!$6 2OTTNEST
Figure 2.38: Time series of significant wave height (Hs) derived from adv measurements and Rottnest wave buoy.
The velocity measurements are not reported here because the velocity range was set too low to accommodate the larger than expected wave heights. Velocities that exceed the set range are wrapped back into the range and can in principle be unwrapped. However, this has not been attempted.
Moving inshore from the outermost location, the wave height increases at the reef top (ADV2) as the waves shoal over the shallow reef. The wave height then decreases to ADV3 where the wave height is similar to the offshore site (ADV1). Between ADV3 and ADV4 there is a significant reduction in wave height. Though not shown, power spectra showed little evidence of any frequency dependence in dissipation.
Modelling waves over the Marmion reef
To assess the relative importance of dissipation through bottom friction the wave model SWAN was used to simulate wave propagation across the instrument array. Two cases were considered, distinguished by the size of the model domain and the forcing along the offshore boundary.
Case 1.
In this case the model domain stretched from Rottnest Island in the south to Two Rocks, about 40km north of Hillary’s boat harbour with bathymetry specified on a 300m grid. The model was forced along the offshore boundary with the observed wave heights and directions from the Rottnest wave buoy. Nested within the 300m grid, and centred over the instrument array, was a smaller 30m grid, where the forcing at the three open boundaries was provided from the larger scale model.
4 3.5 3 2.5 2 1.5 1 0.5 0 6.51
6.5 6.49 6.48 6.47 6.46
Significant wave height x 106
3.4 3.6 3.8 5
Figure 2.39: Model predicted significant wave height (
H
s= H
rms2
) on the 300m grid. The location of the ADV’s is indicated by the small blue squares.An example of the model predicted significant wave height is shown in Figure 2.39 for the offshore forcing conditions: Hs=3.7m, T=15s and dir=71°. Wave heights at the measurement site are seen to be reduced in part by refraction and the presence of Rottnest Island. A series of model runs was done, each run being forced by the Rottnest wave height, period and direction corresponding to each two-hour measurement period at the Marmion site. The model was run with the Madsen et al. (1988) formulation of bottom friction using the default bottom roughness length-scale kn= 0.05, which is consistent with relatively smooth sandy bottoms. Over rough reefs, it was expected that a significant increase in the roughness length would be needed to match model and observations. However, a comparison of the predicted and observed wave heights in Figure 2.40 clearly shows the model underestimates the wave heights, suggesting that friction in the model might be too high, or that some other aspect of the model is causing an anomalous decrease in wave height.
Hs Large grid MAD = .05
SWAN
3.0
2.5
2
1.5
1
0.5
00 0.5 1 1.5 2 2.5 3
Observed
Figure 2.40: Observed Hs versus model forced by Rottnest wave buoy observations. Colour code same as legend in figure 2.38.
Case 2.
In this case a smaller model domain was centred on the instrument array with bathymetry specified on a 30m grid everywhere. The offshore boundary was located close to the position of the offshore ADV. A series of model runs was done, each run being forced by the measured wave height, period and direction at the offshore ADV.
Hs (GEN3)
SWAN
3.0
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3
Observed
Significant height
SWAN
3.0
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3
Observed
Figure 2.41: Observed Hs versus model with offshore boundary at the location of ADV1. left panel, Madsen friction coefficient 0.05, right panel, Madsen friction coefficient 0.16. Colour code same as legend in figure 2.38.
A comparison of predicted and observed wave heights using kn=0.05 is shown in Figure 2.41. Clearly the agreement between model and data is much better since the forcing is given by the offshore ADV. With the instruments relatively close together, a surface gravity wave will take approximately 3 minutes to propagate from the offshore to the inshore ADV.
However the observations from the inner ADV are consistently above the line, suggesting bottom friction may be too low. Results for a model run with kn=0.16 are also shown in Figure 2.41. While the reduction in wave height is relatively small it has been achieved with a significant increase in bottom roughness length scale, three times higher than accepted values for sandy bottoms.
This required increase in friction is consistent with recent observations of frictional
dissipation of waves propagating over coral reefs reported by Lowe et al. (2005). This in turn implies a more turbulent bottom boundary layer which will affect the turbulent transfer of water and particles between the water column and the underlying canopy. Enhanced bottom stress in the presence of waves can increase the rate of nutrient uptake (Falter et al. 2004).
Hearn et al. (2001) suggest that uptake rates are a function of the rate at which wave energy is dissipated by bottom friction.