Spectral distribution of wave energy dissipation by salt marsh vegetation
Introduction
Wave propagation through vegetation is an important physical process along many coastal regions of the world, and along the shores of large inland lakes. Waves approaching vegetated shores lose energy due to obstructing vegetation. This reduces shore erosion and is of engineering significance for shoreline protection. The role and importance of coastal wetlands as a natural defense system against storm waves is generally acknowledged (e.g., Costanza et al., 2008, Dixon et al., 1998, Gedan et al., 2011, Lopez, 2009). Utilization of coastal wetlands to augment structural measures for mitigation of coastal flooding due to storm surge and waves is promoted in several regions of the world (e.g., Borsje et al., 2011, CPRA, 2012).
A body of literature exists quantifying reduction rates of integral wave heights due to vegetation (for summary, see Anderson et al., 2011, Jadhav and Chen, in review). Theoretical models based on energy conservation, have been proposed for application to both monochromatic waves (Dalrymple et al., 1984), and for narrow-banded random waves (Mendez and Losada, 2004). Kobayashi et al. (1993) presented an approach based on continuity and momentum equations, which assumed an exponential decay of integral wave height. Chen and Zhao (2012) proposed a vegetation-induced dissipation model based on the formulation of Hasselmann and Collins (1968) for energy dissipation of random waves by bottom friction. All these models assume rigid vegetation. A number of recent studies have underscored the importance of accounting for the stem and blade motion of flexible vegetation, and have proposed models that account for it (Bradley and Houser, 2009, Mullarney and Henderson, 2010, Riffe et al., 2011). Wave attenuation has been studied in a controlled laboratory environment (Augustin et al., 2009, Dubi and Tørum, 1996, Løvås and Tørum, 2001, Stratigaki et al., 2011), in field conditions involving salt marshes (Bradley and Houser, 2009, Cooper, 2005, Jadhav and Chen, in review, Möller, 2006, Möller and Spencer, 2002, Möller et al., 1999, Riffe et al., 2011), coastal mangrove forests (Mazda et al., 2006, Quartel et al., 2007), and vegetated lakeshores (Lövstedt and Larson, 2010). Most of these studies primarily focused on the attenuation of integral wave heights or wave energy, and estimation of integral bulk vegetation drag coefficients. As a step beyond integral dissipation characteristics, Lowe et al. (2005) developed an analytical model to predict the magnitude of the in-canopy velocity of waves propagating over a model canopy made up of rigid cylinders. Lowe et al. (2007) extended this model to random waves and predicted that high frequency components of wave energy would dissipate more efficiently inside the canopy. The model was verified with measurements taken from an artificial rigid cylinder canopy submerged on a barrier reef (random wave conditions) for 2 h and assuming a constant drag coefficient.
In the case of natural vegetation under random waves generated by a tropical cyclone, there are no published studies that examine in detail the frequency-based characteristics of wave energy dissipation and drag coefficient, though some studies have illustrated such characteristics with an example (Bradley and Houser, 2009, Paul and Amos, 2011). The present study investigates the spectral characteristics of wave energy dissipation due to natural vegetation, and the relationship between dissipation and the incident wave energy spectrum, using comprehensive field data. The study also identifies spectral variation of the vegetation drag coefficient. We hypothesize that the frequency-varying spectral drag coefficient will predict spectral distribution of energy dissipation more accurately than an integral drag coefficient. To test the hypothesis, a new method is developed to parameterize the spectral drag coefficient over the entire range of measured wave spectra. The spectral and integral drag coefficients are then both used to estimate energy dissipation losses, and these estimates are compared to the observed dissipation to assess the validity of the hypothesis.
The following section describes the spectral energy dissipation model proposed by Chen and Zhao (2012) which is used to estimate drag coefficients and introduces the velocity attenuation factor. 3 Study area and field program, 4 Overview of wave conditions describe the field program and the wave conditions. Section 5 contains data analysis, where spectral characteristics of the observed energy dissipation are examined. In Section 6, spectral variation of estimated drag coefficient is demonstrated, and the spectral behavior of the mean velocity attenuation parameter is quantified. The mean velocity attenuation parameter and average drag coefficients are then applied to predict energy dissipation and compared with the existing prediction methods in Section 7. Finally the results are discussed, followed by a summary and conclusions.
Section snippets
Spectral energy dissipation model
Assuming the linear wave theory holds, the evolution of normally-incident random waves propagating through vegetation can be expressed with the following wave energy balance equation,where subscript j represents the jth frequency component of a wave spectrum, E is the spectral wave energy density, Cg = nc is the group velocity, is the phase speed, k is the wave number, h is the still water depth, g is the acceleration due to gravity and coefficient n is given by n = (1 /
Study area and field program
The study site was a salt marsh wetland in Terrebonne Bay on the Louisiana coast of the Gulf of Mexico (Fig. 1) west of the Mississippi River bird-foot delta. The shallow (depth, 1–3 m), micro-tidal (diurnal tidal range < 0.5 m) bay is bordered by salt marsh to the north, and a series of narrow, low-lying barrier islands to the south. The waves in the bay consist of frequent low-energy offshore swell and locally generated seas which intensify during the passages of annual winter cold fronts and
Overview of wave conditions
A total of 177 wave records (59 records at each of the 3 gages) were analyzed in this study. Table 1 lists summary statistics of water depth, zero-moment wave height, mean period and some derived parameters characterizing the wave conditions. The statistics in Table 1 describe only the analyzed data, not the entire measured dataset. As stated in the previous section, the wave records that violated assumptions of Eq. (1) were removed from analysis. With the diurnal tide augmented by the storm
Observed spectral wave energy dissipation characteristics
Measured spectra showed significant wave energy reduction over vegetation, as evidenced by the reduction in wave heights (Table 1). Energy reduction with respect to frequency was calculated between pairs of wave gages (W1–W2 and W2–W3) based on the measured wave energy density spectra, using Eq. (1). Ensemble averages of all analyzed energy density spectra, along with the ensemble average of the energy dissipation are shown in Fig. 3 for reaches W1–W2 (between gages W1 and W2) and W2–W3
Estimates of integral and frequency-dependent bulk drag coefficients
The integral energy dissipation formulations (e.g., Mendez and Losada, 2004) assume the drag coefficient is independent of frequency and determine its single value, , for the entire spectrum, which is assumed to be narrow-banded. The variation of drag coefficient with the hydrodynamics has been typically related to the Reynolds (Re) and Keulegan–Carpenter (KC) numbers using empirical relationships. Several studies have developed empirical formulations for integral estimates of (Bradley
Prediction of energy dissipation using estimated drag coefficients
To estimate energy dissipation due to vegetation in practical applications, selection of the appropriate drag coefficient is necessary. This section compares two approaches for selecting drag coefficients to determine which approach results in the better prediction of wave spectra in the presence of rigid-type vegetation. In the first, simple approach (existing standard practice), an integral drag coefficient, (such as would be calculated using Eq. (13)) is specified and then spectral
Discussion
The Chen and Zhao (2012) formulation for energy dissipation through rigid vegetation has been reorganized by introducing the velocity attenuation parameter, α. In this study, α is defined as the ratio of vegetation-attenuated orbital velocity inside the canopy at a given elevation, to the orbital velocity in the absence of vegetation at the same elevation. This is similar to the velocity attenuation parameter of Lowe et al. (2005), which was defined as the ratio of the velocity inside canopy to
Summary and conclusions
Random wave spectra were measured over salt marsh vegetation to study vegetation induced energy dissipation along a marsh transect with two reaches. The waves in the leading reach of the transect were more energetic, highly nonlinear, occurred in shallower water, and exhibited greater energy dissipation compared to the subsequent reach, where waves were less energetic, significantly less nonlinear, and exhibited less energy dissipation. Waves propagating over salt marsh vegetation dissipate
Acknowledgments
The study was supported by the US Department of Homeland Security (DHS) through the Southeast Region Research Initiative (SERRI) and by the US National Science Foundation (NSF) (Grant Nos. CBET-0652859 and DMS-1115527). We thank T. Baker Smith, LLC for the logistical support and topographic surveying, and the Louisiana Universities Marine Consortium (LUMCON) for providing meteorological data. Graduate students Kyle Parker, James Chatagnier and James Bouanchaud assisted in the field study. We
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