# A Field Study of How Wind Waves and Currents May Contribute to the Deterioration of Saltmarsh Fringe

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## Abstract

Deltaic landscapes, such as the Mississippi River Delta, are sites of extensive conversion of wetlands to open water, where increased fetch may contribute to erosion of marsh edges, increasing wetland loss. A field experiment conducted during a storm passage tested this process through the observations of wave orbital and current velocities in the fringe zone of a deteriorating saltmarsh in Terrebonne Bay, Louisiana. Incident waves seaward of the marsh edge and wave orbital and current velocities immediate landward of the marsh edge were measured. Through a dimensional analysis, it shows that the current and orbital velocities in the marsh fringe were controlled by the incident waves, inundation depth, submergence ratio, and vegetation density. Similarly, it is shown that the longshore currents in the inundated saltmarsh fringe depended on the local wave-induced momentum flux, vegetation submergence, and vegetation density in the fringe zone. The cross-shore current showed the presence of a return flow in the lower region of the velocity profile. A high correlation between the current direction and the local flow-wave energy ratio as well as the vegetation submergence and density is found, indicating the important role of surface waves in the fringe flow landward of an inundated wetland under storm conditions. The field observations shed light on the potential ecological consequences of increased wave activities in coastal saltmarsh wetlands owing to subsidence, sea level rise, limited sediment supply, increases in wind fetch, and storm intensity.

## Keywords

Saltmarsh wetland Wave-induced current Wave orbital velocity Vegetated flow Wetland erosion## Introduction

Coastal wetlands provide important benefits known as ecosystem services such as improving water quality, trapping sediments, reducing shoreline erosion rates, providing habitat for estuarine species, and contributing to the local economy through fishing and tourism industries (e.g., Gulf Restoration Network 2004; Barrett-O’Leary 2011; Louisiana Coastal Protection and Restoration Authority (CPRA) 2012). Another important ecosystem service is protecting coastal areas from storm impacts, as suggested by an estimate that wetlands provide US$23.2 billion per year in storm protection services in the USA (Costanza et al. 2008). Storm surge attenuation by wetlands depends on the extent of wetland area surrounding a coastal landscape, storm strength (e.g., Wamsley et al. 2010; Hu et al. 2015), and biomechanical properties of wetland vegetation (e.g., Zhao and Chen 2014; Lapetina and Sheng 2014).

All of these benefits are at risk due to the substantial degradation of wetlands along coastal landscapes. The northern Gulf of Mexico, which is among the largest coastal wetland areas in the conterminous USA (Stedman and Dahl 2008), lost about half of its wetlands from 1780 to 1980 (Dahl 1990). Louisiana alone accounts for 80–90 % of the coastal wetland losses in the USA (Tibbetts 2006; Couvillion et al. 2011). The average land loss in Louisiana during 1985 to 2010 was about 42.9 km^{2}/year (Couvillion et al. 2011). A total of 4869 km^{2} of wetlands have been converted to open water since 1930 in Louisiana, which is projected to lose another 4532 km^{2} by 2060 under current conditions (Louisiana Coastal Protection and Restoration Authority (CPRA) 2012). Much of this coastal wetland loss is attributed to submergence, given that reduced sediment supply limits the increase in marsh elevation relative to increase in water levels due to sea level rise and subsidence, causing the marsh surface to drown (Boesch et al. 1994; and others).

An increased fetch as a result of wetlands converting to open water over the last century has produced higher wind waves breaking on the marsh edge (e.g., Tonelli et al. 2010; Prahalad et al. 2014) causing considerable erosion of wetlands (Mariotti and Fagherazzi 2010; Mariotti et al. 2010; Marani et al. 2011; Fagherazzi et al. 2013; McLoughlin et al. 2014). This process of wetland loss has been less well documented in deltaic landscapes where large extensive wetland landscapes have been slowly replaced by shallow bays and estuaries. A majority of the studies on wetland edge erosion focused on the direct impact of waves on the marsh perimeter, and less research has been undertaken on the hydrodynamics of wave-induced flows on the surface of coastal wetlands. The wave power when water levels exceed the marsh platform was considered non-destructive to the marsh edge (e.g. McLoughlin et al. 2014). Although flows through vegetation have been studied extensively both in open channels and adjacent wetlands (e.g., Folkard 2011; Montakhab et al. 2012; Nepf 2012a, b), a majority of studies were focused on unidirectional flows through freshwater vegetation. Even though, recently, more attention has been paid to oscillatory flows in coastal vegetated areas, where both waves and currents coexist (e.g., Luhar et al. 2010; Callaghan et al. 2010; Manca et al. 2012), most of the existing studies focused on wave energy dissipation caused by vegetation (e.g., Paul and Amos 2011; Chen and Zhao 2012; Jadhav et al. 2013; Jadhav and Chen 2013; Ozeren et al. 2013; Anderson and Smith 2014; Blackmar et al. 2014; Möller et al. 2014). By contrast, there are few studies on the wave-induced currents on the surface of coastal wetlands, especially under storm and field conditions (e.g., Lacy and Hoover 2011; Truong et al. 2014). We propose that understanding the hydrodynamics of waves and currents within saltmarsh vegetation is necessary to identify how these flows may contribute to wetland loss.

Flow hydrodynamics in the fringe zone of a saltmarsh, also referred to as high marsh zone, were investigated using field experiments conducted in Terrebonne Bay, Louisiana, during the passage of a cold front, a frequent weather system on the northern Gulf of Mexico between late fall and early spring. The main research goal was to investigate currents and waves in the fringe zone of a saltmarsh as a function of the waves, inundation depth, and vegetation properties. The remainder of this paper is organized as follows. The study area and experimental methods are described first, followed by the data analysis method. Next, the correlations of the velocities in the saltmarsh fringe with incident and local waves, submergence ratio, and vegetation properties are presented, followed by discussion on the current direction in the saltmarsh fringe. Then, the ecological implications of waves and currents in the marsh fringe are discussed. The closing section provides a summary and conclusions of the study.

## Study Area and Methods

### Study Area

_{i}: for incident waves at 47 m seaward of the marsh edge; cross section 1 or CS

_{1}: at the shoreline; cross sections 2 (CS

_{2}), 3 (CS

_{3}), and 4 (CS

_{4}): 1, 2, and 3 m inland from the shoreline, respectively.

*Spartina alterniflora*during the experiments. The saltmarsh surface had a positive slope of 0.046 from the marsh edge landward. Properties of vegetation were sampled in three randomly selected quadrats of 0.5 m × 0.5 m, located around the deployment site. Live stems within each quadrat were counted, then cut at the soil surface level and brought back to the laboratory for further evaluation (Table 1 and Fig. 4).

Average properties of the vegetation at the study site

Physical property | Unit | Mean | Standard deviation |
---|---|---|---|

Stem population density, | Number of Stems/m | 454 | 189 |

Stem diameter, | mm | 5.0 | 1.6 |

Stem height up to bottom of first leaf | cm | 5.9 | 2.4 |

Stem height, | cm | 8.4 | 4.0 |

Total height, | cm | 38.3 | 10.3 |

Leaves height | cm | 34.0 | 9.8 |

Number of leaves | – | 5.0 | 1.6 |

Considering the spacing between plants as Δ*x* and Δ*y* in the *x* and *y* direction, respectively, the stem density which refers to the total number of plants per unit area is defined as \( {N}_v=\frac{\left(\mathrm{Unit}\ \mathrm{Area}\right)/\left(\Delta x\Delta y\right)}{\left(\mathrm{Unit}\ \mathrm{Area}\right)} \) or *N* _{ v } = 1/(Δ*x*Δ*y*). If the plants are homogeneously distributed, then *N* _{ v } = 1/Δ*s* ^{2}, where Δ*s* = Δ*x* = Δ*y*. The dimensionless vegetation density, which is proportional to the vegetated portion of the unit area, is defined by \( {N}_v\times {d}_v^2 \), where *d* _{ v } is the vegetation stem diameter. At the study site the mean value of \( {N}_v\times {d}_v^2 \) was equal to 0.0114.

To define how dense the vegetation was at the study site, the dimensionless relative density of the vegetation is calculated (Belcher et al. 2003). The relative density is defined by *a* _{ v } *h* _{ v }, where *a* _{ v } is the vegetation frontal area per canopy volume and *h* _{ v } is the vegetation height. The frontal area of the vegetation for the unit area of the bed is *N* _{ v } × *h* _{ v } × *d* _{ v } and the canopy volume is 1 × 1 × *h* _{ v }, which is equal to the volume of the cuboid with the base of unit area and height of *h* _{ v }. Then, the frontal area of vegetation per canopy volume, i.e., *a* _{ v } is equal to *a* _{ v } = (*N* _{ v } × *h* _{ v } × *d* _{ v })/(1 × 1 × *h* _{ v }) = *N* _{ v } *d* _{ v }, which has the unit of one over length (see Nepf 2012a). The dimensionless population density,\( {N}_v\times {d}_v^2 \), also can be written in terms of *a* _{ v } as *a* _{ v } *d* _{ v }. At the study site, on average, *a* _{ v } = 2.28 1/*m* and *a* _{ v } *h* _{ v } = 0.87, which is considered as a dense canopy (Belcher et al. 2003).

### Data Analysis Method

*H*

_{ m0}, at the offshore pressure sensor were calculated from the water surface elevation power spectral density,

*S*

_{ ηη }, as:

*ρ*is the water density,

*g*is the gravitational acceleration,

*f*is the frequency,

*S*

_{ pp }is the wave dynamic pressure spectrum,

*k*is the wave number,

*h*

_{ i }is the mean water depth in the bay at cross section

*i*,

*d*

_{ p }is the distance of the pressure sampling point from the bed, and

*K*

_{ p }is the pressure response factor, or the pressure to surface elevation conversion factor.

*E*

_{ w }, were calculated from the surface elevation power spectrum, using the wave orbital velocities as:

*x*and

*y*directions collected by an ADV, respectively, the

*S*

_{ ηη }in Eq. (4), was calculated from the orbital velocities following the steps described by Wiberg and Sherwood (2008):

*x*and

*y*directions, respectively. \( {S}_{\tilde{u}\tilde{v}}={S}_{\tilde{u}\tilde{u}}+{S}_{\tilde{v}\tilde{v}} \) is the power spectrum for the combined horizontal orbital velocities,

*h*is the mean water depth on the marsh, \( {d}_{\tilde{u}\tilde{v}} \) is the distance of the velocity sampling point from the bed, and \( {K}_{\tilde{u}\tilde{v}} \) is the surface elevation to the horizontal orbital velocity conversion factor.

Typically, the frequency range for applying the conversion factors, i.e., *K* _{ p } and \( {K}_{\tilde{u}\tilde{v}} \), would be around 0.02 ≤ f ≤ 0.2 Hz for the water depth of tens of meters, but this range should be extended to higher frequencies for the shallower water (Wiberg and Sherwood 2008). For the latter case, the higher frequency range for applying *K* _{ p } and \( {K}_{\tilde{u}\tilde{v}} \) should be chosen cautiously. In fact, the inflation of the high frequency noise by *K* _{ p } and \( {K}_{\tilde{u}\tilde{v}} \) can result in an overestimation of the wave energy and wave height. To prevent the high frequency energy from inflation, the conversion factors applied up to *f* ≤ 1 Hz in this study. Depending on the condition, it might be necessary to keep the conversion factor constant after a certain frequency limit in order to preserve the realistic spectral tail shape.

*θ*

_{1}is the mean wave direction for each frequency, \( {S}_{\eta \tilde{u}} \) and \( {S}_{\eta \tilde{v}} \) are the water level and orbital velocity cross spectrum in

*x*and

*y*directions, respectively, and

*a*

_{1}and

*b*

_{1}are the normalized Fourier coefficients. Note that, except for Fig. 6, the direction in all figures and equations is presented with respect to the shoreline, as illustrated in Figs. 1 and 3. However, the direction in Fig. 6 follows the meteorological convention, measuring from the true north, increasing clockwise, i.e., 0° from north, 90° from east, 180° from south, and 270° from west.

As mentioned earlier, sampling points for both ADVs were located 0.14 m above the marsh platform. Therefore, only the data associated with the mean water depth at ADVs’ locations larger than *h* ≥ 0.19 m were considered to allow at least a minimum of 5 cm of water on the top of the ADVs’ sampling point. This margin was selected to ensure the submergence of the ADVs’ sampling point during the passage of the wave trough. It is worth mentioning that under the storm conditions, the staff wave gauges may over-record the wave height, particularly when waves break at the marsh edge. This over-estimation mainly occurred in the reading of the wave crest as a result of the wave run-up and water spray on the staff. Wave breaking close to the staff can intensify this effect. Because of that and for the quality assurance, no wave data from the staff wave gauges were used in this paper. A lesson learned is that staff wave gages should be deployed away from the marsh edge to avoid the impact of wave breaking.

## Results

### Time Series of Water Level, Waves, and Currents

Measurements of the water depths, wave properties, and current velocities on the marsh and in the bay were conducted from April 12 to 20, 2012. During this period, the marsh was inundated from April 13 to 17, 2012, except for a short period of time on April 14, 2012. To guarantee the submergence of the ADVs’ sampling points, only the data from April 14 to 16, 2012 are analyzed and presented. Note that all the time in this paper is presented in Coordinated Universal Time, UTC.

*H*

_{ m0}, of 0.35 m and peak wave period,

*T*

_{ p }, of 2.9 s. On average, the zero-moment wave heights decreased by 28 % at cross section 2 and 52 % at cross section 3, compared to the incident waves.

### Dependence of Current and Orbital Velocities in Saltmarsh Fringe on Incident Waves

*H*

_{ m0i }; mean wave period,

*T*

_{ i }; and wavelength,

*L*

_{ i }; water depth inside the bay,

*h*

_{ i }; and water depth on the marsh,

*h*; as well as the vegetation properties, i.e., the stem density,

*N*

_{ v }; stem height,

*h*

_{ S }; and stem diameter,

*d*

_{ v }. The wavelength of the incident waves has the characteristics of both water depth in the bay and the incident wave period, which was almost constant throughout the measurement. Therefore, the current velocity averaged over each sampling burst, \( \overline{u} \), may be expressed as a function of

*H*

_{ m0i },

*L*

_{ i },

*h*,

*N*

_{ v },

*h*

_{ s },

*d*

_{ v }, and

*ν*:

*π*theorem for dimensional analysis,

*f*

_{1}can be written in terms of the dimensionless groups as \( {f}_1\left(\frac{\overset{-}{u}h}{\nu },\frac{H_{m0i}}{h},\frac{h}{L_i},\frac{h}{h_s},\frac{h}{d_v},\frac{1}{h^2{N}_v}\right)=0 \). These dimensionless groups are re-arranged and combined to represent the effect of a depth-limited wave breaking on the marsh edge by using a ratio similar to the breaker index,

*H*

_{ m0i }/

*h*, the effect of the incident waves by using the incident wave steepness, i.e.,

*H*

_{ m0i }/

*L*

_{ i }, the effect of inundation depth and stem height by using the vegetation submergence ratio, i.e.,

*h*/

*h*

_{ s }, the effect of stem diameter by using

*h*/

*d*

_{ v }, and the effect of stem density by using \( 1/{N}_v{d}_v^2 \). Then, Eq. (18) can be written as:

The term on the left-hand side of Eq. (19), i.e., \( \overset{-}{u}h/\nu \), represents the Reynolds-type number calculated from the time-averaged current velocity in the marsh fringe, \( \overline{u} \); the mean water depth on the marsh, *h*; and the kinematic viscosity of the water, *ν*. The first term on the right-hand side of Eq. (19), *H* _{ m0i }/*h*, represents the depth-limited wave breaking, as we hypothesized wave breaking was the major driving force for the measured current in the marsh fringe. Note that although *H* _{ m0i }/*h* is similar to the wave breaker index, unlike the breaker index that is the ratio of the local wave height to the local water depth, the *H* _{ m0i }/*h* is the ratio of incident wave height over local water depth. The wave steepness, *H* _{ m0i }/*L* _{ i }, represents the incident wave steepness. The submergence ratio, *h*/*h* _{ s }, has a direct impact on the current velocity in the marsh fringe, as its value plays an important role in the depth-limited wave breaking and the velocity profile of the landward and undertow flows on the marsh. The ratio of *h*/*d* _{ v } has a similar but less important role as the submergence ratio, since its effect can be represented by *h*/*h* _{ s } and \( 1/\left({N}_v\times {d}_v^2\right) \). The dimensionless stem density of vegetation, \( {N}_v\times {d}_v^2 \), has an inverse relationship with the flow in the marsh fringe. The larger value of \( {N}_v\times {d}_v^2 \) represents the denser vegetation coverage, which results in a higher resistance to the flow and thus weaker velocity. Resistant role of the vegetation has been investigated in the literature through solving the Navier-Stokes equations with vegetation (e.g., Marsooli and Wu 2014). The Navier-Stokes momentum equation governing the flow over vegetation can be written as \( \frac{\partial u}{\partial t}+\left(\nabla .u\right)u=-\frac{1}{\rho }{F}_b-\frac{1}{\rho}\nabla p+\nabla .\left(\nu \nabla u\right) \), where *u* is the velocity vector, *t* is the time, *p* is the pressure, *ν* is the molecular and turbulent kinematic viscosity of water, *F* _{ b } = ρg + *F* _{ v } is the external body force, and *F* _{ v } is the vegetation force. The *F* _{ v } represents the flow-induced drag force, i.e., 0.5*ρC* _{ D } *N* _{ v } *d* _{ v } *u*|*u*|, plus the inertia force, i.e., \( 0.5\rho {C}_M{N}_v{d}_v^2\frac{\partial u}{\partial t} \), where *C* _{ D } is drag coefficient and *C* _{ M } is inertia coefficient (Marsooli and Wu 2014). The external body force term in the Navier-Stokes equation for vegetated flows, i.e., *F* _{ b }, is a function of the vegetation population density and stem height, indicating the role of vegetation in the momentum balance of the flow through wetland vegetation.

As this study was carried out for a single type of vegetation, all the vegetation properties, i.e., the *h* _{ s }, *d* _{ v }, and *N* _{ v }, remained constant during the study. Therefore, the values of *A* _{ I } and *B* _{ I1} to *B* _{ I5} are specific for this type of vegetation, and likely to be different at a different site with different vegetation properties. Additionally, due to the fact that the last term on the right-hand side of Eq. (20), i.e., \( 1/{N}_v{d}_v^2 \), is constant in this study, the value of B_{I5} is assumed to be 1. This assumption remains to be evaluated for different types of vegetation in future studies. To define universal values for the coefficients in Eq. (20), additional studies with different types of vegetation are required. Using the best-fitted line to the data, for specific vegetation at this study site, coefficients *A* _{ I } and *B* _{ I } were obtained as *A* _{ I } = 2.081 × 10^{5}, *B* _{ I1} = - 1, *B* _{ I2} = 2, *B* _{ I3} = 0.0333, *B* _{ I4} = 0.0333, *B* _{ I5} = 1, with the coefficient of determination, *R* ^{2} = 0.61, for cross section 2. This confirms that waves were the dominant driver of the measured currents in the marsh fringe, especially near the marsh edge (Fig. 9). It can be expected that as incident waves propagate landward and wave energy is dissipated by vegetation, the correlation between the current and offshore waves became weaker because wave effects decreased in comparison with other forcing agents.

*H*

_{ m0i },

*L*

_{ i },

*h*,

*N*

_{ v },

*h*

_{ s },

*d*

_{ v }, and

*g*, or \( {f}_2\left({\tilde{u}}_{m-RMS},{H}_{m0i},{L}_i,h,{N}_v,{h}_s,{d}_v,g\right)=0 \). Using the Buckingham

*π*theorem,

*f*

_{2}can be written in terms of the dimensionless groups as \( {f}_2\left(\frac{{\overset{\sim }{u}}_{m-RMS}}{\sqrt{gh}},\frac{H_{m0i}}{h},\frac{h}{L_i},\frac{h}{h_s},\frac{h}{d_v},\frac{1}{h^2{N}_v}\right)=0 \). By re-arranging and combining the dimensionless groups to incorporate the effects of the depth-limited wave breaking,

*H*

_{ m0i }/

*h*; incident waves,

*H*

_{ m0i }/

*L*

_{ i }; water depth on the marsh,

*h*/

*h*

_{ s }; vegetation diameter,

*h*/

*d*

_{ v }; and the vegetation density, \( 1/{N}_v{d}_v^2 \), the relationship can be obtained as:

*h*. The RMS value of the maximum orbital velocity in the marsh fringe, \( {\tilde{u}}_{m-RMS} \), is calculated using Eqs. (16) and (17). As shown in Fig. 10, the RMS value of the maximum orbital velocity in the marsh fringe has a close relationship with the incident waves in the bay, submergence ratio and vegetation density as:

Following the same argument for Eq. (20), the values of *A* _{ II } and *B* _{ II1} to *B* _{ II5} are specific for this type of vegetation with the assumption of *B* _{ II5} = 1, and they are likely to be different at a different site with different vegetation properties. To define universal values for the coefficients in Eq. (22), additional studies with different types of vegetation are required. Applying the best-fitted line to the data, coefficients *A* _{ II } and *B* _{ II } in Eq. (22) for the specific vegetation at this study site were determined as *A* _{ II } = 3.137 × 10^{-4}, *B* _{ II1} = 1, *B* _{ II2} = - 2/3, *B* _{ II3} = 0.0333, *B* _{ II4} = 0.0333, *B* _{ II5} = 1, with *R* ^{2} = 0.75 for cross section 2.

Note that Eqs. (20) and (22) are introduced to characterize the physics of wave-generated currents in the marsh fringe zone, and to test the hypothesis that incident waves and wave breaking are the major driving force for the measured current in the marsh fringe. Although the general forms of Eqs. (20) and (22) may remain unchanged for other sites with different vegetation properties, the coefficients *A* _{ I }, *B* _{ I }, *A* _{ II }, and *B* _{ II } need to be re-calibrated. The values of coefficients *A* _{ I }, *B* _{ I }, *A* _{ II }, and *B* _{ II } presented here are only valid for *d* _{ v } = 0.005 m, *h* _{ s } = 0.084 m, *N* _{ v } = 454 stems/m^{2}, *a* _{ v } = 2.28 1/m, and \( {N}_v\times {d}_v^2=0.0114 \). The universal values of the coefficients could be defined by repeating this study for different vegetation. Ultimately, the single-point time-averaged velocity in this study could be replaced by a depth-averaged velocity if the velocity profile is known.

### Dependence of Current Velocity in Saltmarsh Fringe on Local Wave Energy

*H*

_{ b }, and breaking wave angle,

*α*

_{ b }, as follows:

*gH*

_{ b })

^{0.5}with (8

*gE*

_{ w }/

*ρ*)

^{0.25}and

*α*

_{ b }with \( {\overline{\theta}}_w \), similar relationships can be developed for the current velocities in the saltmarsh fringe. Incorporating the effect of the submergence ratio of the vegetation in the fringe zone,

*h*/

*h*

_{ s }, and the vegetation population density, \( 1/\left({N}_v{d}_v^2\right) \), the relationships as depicted in Figs. 11 and 12, can be obtained for the longshore component, \( {\overline{u}}_{LS} \), and the cross-shore component, \( {\overline{u}}_{CS} \), of the current velocity respectively as:

*n*is referring to the cross section

*n*with

*n*equal to 2 and 3. Subscript

*n*indicates that for the submergence ratio, the local values at each location, i.e., cross sections 2 and 3, were used in the equations. Unlike the submergence ratio, for the wave energy, only the values close to the edge, i.e., cross section 2, where most of the waves broke, were used in the equations. Following the same argument for Eq. (20), it is assumed that \( 1/{N}_v{d}_v^2 \) has a power of one, i.e., \( {\left(1/{N}_v{d}_v^2\right)}^1 \), in Eqs. (24) and (25). This assumption is yet to be tested with different types of vegetation in future studies. Applying the best-fitted line to the longshore data yields the coefficient

*A*

_{ III }= 0.0029 with

*R*

^{2}= 0.64 for cross section 2. Following the same argument for Eqs. (20) and (22), the value of

*A*

_{ III }is specific for this type of vegetation, and likely to be different at a different site with different vegetation properties. The correlation of the longshore current velocity and local waves in the marsh fringe is similar to the correlation of the current velocity in the marsh fringe and offshore waves, which provides strong evidence in support of our hypotheses that the observed currents in the marsh fringe were wave driven.

### Dependence of Current Direction in Saltmarsh Fringe on Local Wave Energy

*E*

_{ w2}; current energy at the marsh edge; vegetation submergence ratio; and vegetation density. The local wave energy in the marsh fringe that contributed to the longshore and cross-shore currents are \( {E}_{w2}. \sin \left|{\overline{\theta}}_{w2}\right|. \cos \left|{\overline{\theta}}_{w2}\right| \) and \( {E}_{w2}. \cos \left|{\overline{\theta}}_{w2}\right| \), respectively. The longshore and cross-shore components of the current energy in the fringe zone are \( 0.5\rho {h}_2{\left|{\overline{u}}_{LS}\right|}^2 \) and \( 0.5\rho {h}_2{\overline{u}}_{CS}^2 \), respectively. Then, the dimensionless energy in the marsh fringe can be written for the longshore direction as:

*h*

_{2}/

*h*

_{ s }, and the vegetation population density in the marsh fringe, \( {N}_v{d}_v^2 \), the current direction at the fixed elevation in the fringe zone can be expressed as:

*π*) converts the radian to degrees and (0.5

*h*

_{2}) × (

*ρg*/

*E*

_{ w2})

^{0.5}≈ 2(

*h*

_{2}/

*H*

_{ m0 - 2}), and

*H*

_{ m0 - 2}is a zero-moment wave height at cross section 2. Applying the best-fitted line to the longshore data yields the coefficients

*A*

_{ IV }= 1 and

*B*

_{ IV }= 0.035 with

*R*

^{2}= 0.86 and

*A*

_{ V }= 1.18 and

*B*

_{ V }= 2.38 × 10

^{-7}with

*R*

^{2}= 0.73, for cross section 2, indicating a very strong correlation between the current direction, local wave energy, submergence ratio, and vegetation density which supports our hypothesis of wave dominance in the marsh fringe flow. Following the same argument for Eqs. (20), the values of

*A*

_{ IV },

*B*

_{ IV },

*A*

_{ V }, and

*B*

_{ V }are specific for this type of vegetation, and likely to be different at a different site with different vegetation properties. Figure 15 and Eq. (27) show that, for a small value of \( {\widehat{E}}_{LS}\times \left(h/{h}_s\right)\times {\left({N}_v{d}_v^2\right)}^{-1} \), the current at the sampling elevation flowed toward the marsh, perpendicular to the shoreline. As the value of \( {\widehat{E}}_{LS}\times \left(h/{h}_s\right)\times {\left({N}_v{d}_v^2\right)}^{-1} \) became larger, the current in the fringe zone became more parallel to the shoreline. Similar trend is shown in Fig. 16 as the current direction is presented as a function of the waves, inundation depth, submergence ratio, and vegetation density in the fringe zone. The variability of the current direction at a fixed elevation above the marsh fringe indicates a complex three-dimensional (3D) structure of the wave-driven currents in the margin of flooded saltmarshes. Complex 3D flow patterns of wave-induced currents on an idealized wetland were observed in recent numerical simulations (Ma et al. 2013).

## Discussion

The physics that generate currents within fringe zone of inundated saltmarsh can be explained using similar wave-driven processes on a coral reef. The near-edge wave-induced currents over the reef are generated mainly by the wave breaking on the reef offshore face and the reef top (e.g., Monismith 2007). Using this concept, wave radiation stress gradients can be connected with the forces acting on the current to calculate the wave-driven current over the reef (e.g., Symonds et al. 1995; Gourlay 1996; Hearn 1999; Tartinville and Rancher 2000; Symonds and Black 2001; Gourlay and Colleter 2005; Monismith 2007). Similar to coral reefs, typical coastal wetlands have steep scarps of various heights, and wave breaking and current generation inland of a marsh edge have been reported in the literature (e.g., Tonelli et al. 2010; Truong et al. 2014). Considering the geometric and physical similarities, the same concept can be applied to the margin of inundated saltmarshes where wave radiation stress gradients drive the current in the marsh fringe under storm conditions. However, the effects of vegetation make the currents in saltmarsh fringes weaker and more complex.

Although wave breaking is the main driver of the current in a flooded saltmarsh fringe, it is not the only contributor. Astronomical tides and wind can also induce currents in tidal wetlands. The tidal range along the northern Gulf Coast is small and the wetlands are characterized as micro-tidal marshes (Stumpf and Haines 1998; Friedrichs and Perry 2001). Louisiana coast has tidal ranges varying from 0.1 to 0.2 m during neap tides to 0.3 to 0.6 m during spring tides (Leonard and Luther 1995). The tidal currents in micro-tidal wetlands are much smaller than the measured current velocity in this study. The tidal current velocity in the streamside of a marshland in Louisiana was less than 0.05 m/s, dropped to less than 0.03 m/s for the interior marsh (Leonard and Luther 1995). In another study in Chesapeake Bay with a larger tidal range, flow velocity measured was 0.02 ∼ 0.06 m/s adjacent to the canopy and 0.01 ∼ 0.04 m/s within the canopy (Leonard and Reed 2002). The much higher current velocity recorded in the marsh fringe in the present study suggests that wind waves rather than tides were the dominant driver of the current in the saltmarsh fringe under storm conditions.

Sea level rise, land subsidence, limited sediment supplies, wind wave impacts on the marsh boundaries and human activities are the main contributors to coastal wetland erosion (e.g., Ganju et al. 2013; Leonardi and Fagherazzi 2014). The northern Gulf Coast is subject to frequent, strong wind events due to cold front passages and tropical cyclones (e.g., Zhao and Chen 2008; Chen et al. 2008). As wind fetch increases due to the conversion of wetlands to open water, wave power impacting the perimeter of saltmarshes increases. Accelerated sea level rise along with land subsidence and reduced sediment supply that limits accretion, have increased wetland inundation frequency, and the inundation depth as elevations of the marsh surface decrease. Our field observations of waves and currents in a deteriorating saltmarsh fringe in Louisiana suggest that wind waves in marsh fringe zone can play a significant mechanism in the long-term stability and erosion of coastal wetlands under the conditions of accelerated sea level rise, subsidence, and reduction in sediment supplies. The field data also reveal the significance of vegetation submergence ratio. Although not investigated in this study, it can be deduced that taller and denser vegetation results in weaker currents and smaller wave orbital velocities in the wetland for a given inundation depth and offshore wave energy, because the vegetation drag is proportional to the stem height and vegetation density (e.g., Chen and Zhao 2012). However, vegetation density of saltmarshes depends on hydroperiod and flooding frequency, as lower elevations increase inundation depth. For instance, as inundation depth increases, stronger waves occur that generate undertows, or seaward currents on the surface of saltmarsh, which would promote the ebb flow of detritus on the marsh surface. This reduces the contribution of this organic matter to wetland accretion. Therefore, the conversion of coastal wetlands to open water in bays of deltaic environment may enhance the fetch that drives higher wave energy and increases the frequency of the undertow that erodes the surface of coastal wetlands. A restoration strategy that reduces wave energy with appropriately engineered systems and nourish the marshes with sediments simultaneously may be significant designs to allow saltmarshes to adapt to rising sea levels and subsidence.

## Conclusions

A field experiment was carried out to study wind waves and flows in an inundated saltmarsh fringe zone during a storm passage in Terrebonne Bay, Louisiana. A bottom-mount pressure transducer was deployed 47 m seaward of the marsh edge and two acoustic Doppler velocimeters (ADVs) were deployed 1 and 2 m landward of the shore edge in the marsh fringe. A new deployment technique was developed to install and secure the ADVs during the storm on the weak soil of coastal wetlands, with minimal damage to the adjacent vegetation. This new technique allows for rapid installation of velocity sensors prior to a storm, which is useful for hurricane-related field studies.

It was hypothesized that wave-driven currents dominate the flow in saltmarsh fringes under storm conditions. Based on the field data, relationships between the current velocity, current direction, and wave orbital velocity in the marsh fringe with the incident waves in the bay, local waves, inundation depth, vegetation submergence ratio, and vegetation density in the marsh fringe have been identified and quantified. Results show that the current velocity and wave orbital velocity in the marsh fringe were controlled by the incident waves, inundation depth, submergence ratio, and vegetation density (Figs. 9 and 10), which supports our hypothesis. The longshore and cross-shore currents in the marsh fringe correlated with the local wave energy, submergence ratio, and vegetation density inside the fringe zone. By introducing a dimensionless ratio of the current energy to the wave energy in the marsh fringe, it is shown that the current direction in the marsh fringe can be estimated by the wave energy, the submergence ratio and vegetation density in the saltmarsh fringe (Figs. 16). Further analyses of the velocity measurements have revealed the three-dimensional signature of the flow in the inundated saltmarsh fringe and the presence of an undertow in the velocity profile in the water column, which can negatively impact the health of coastal wetlands. It is worth noting that while these results show the dependency of the current in the marsh fringe on the incident and local waves, as well as on the inundation depth, submergence ratio, and vegetation density inside the fringe zone, it might not be the case for the internal marsh because the wave forcing is dissipated considerably by the vegetation as the distance from the marsh edge increases.

Although wind waves were a major driver of the currents in the saltmarsh fringe under storm conditions, tides and wind might also contribute to the observed flow. Our short-term deployment during the passage of a cold front system does not permit the separation of breaking-generated currents from tide-induced currents, but previous field studies showed much weaker currents in a micro-tidal wetland without waves than the measured current velocity in the present study. Obviously, more studies in other saltmarshes with higher platforms and different vegetation stem height or different population density as well as longer measurement duration are desirable to overcome the limitations of this field dataset. Although the single-point measurement of velocity by an ADV does not provide sufficient information about the vertical profile of the velocity in the marsh fringe, it provides the evidence for the presence of complex flow patterns. Future studies to resolve the vertical variation of currents in saltmarsh fringes are needed. Nevertheless, our field data show that the current and wave orbital velocities in the marsh fringe are the function of the inundation depth, submergence ratio, and vegetation density in the fringe zone and incident waves in the bay. Such a dataset will benefit the study of coastal wetland dynamics as well as the development and validation of three-dimensional models for waves and currents in saltmarsh wetlands in Louisiana and beyond.

## Notation

*a* _{ v } Vegetation frontal area per canopy volume

*a* _{1}, *b* _{1} Normalized Fourier coefficients

*C* _{ D } Drag coefficient

*C* _{ M } Inertia coefficient

*d* _{ p } Distance between the pressure sampling point and the bed

\( {d}_{\overset{\sim }{u}\overset{\sim }{v}} \) Distance between the velocity sampling point and the bed

*d* _{ v } Vegetation stem diameter

*E* _{ w } Local wave energy on the marsh

*f* Frequency

*F* _{ b } External body force

*F* _{ v } Vegetation force

*g* Gravitational acceleration

*h* Mean water depths on the marsh

*h* _{ i } Mean water depth in the bay

*h* _{1}–*h* _{4} Mean water depths on the marsh at cross sections 1 to 4

*H* _{ b } Breaking wave height

*H* _{ m0} Zero-moment wave height

*h* _{ s } Stem height

*h* _{ v } Vegetation height

*k* Wave number

*K* _{ p } Dynamic pressure to the surface elevation conversion factor

\( {K}_{\overset{\sim }{u}\overset{\sim }{v}} \) Surface elevation to the horizontal orbital velocity conversion factor

*L* _{ i } Wavelength in the bay

*N* _{ v } Vegetation population density

*p* Pressure

*R* ^{2} Coefficient of determination

*S* _{ pp } Wave dynamic pressure spectrum

\( {S}_{\overset{\sim }{u}\overset{\sim }{u}} \) Power spectrum for wave orbital velocity in the *x* direction

\( {S}_{\overset{\sim }{v}\overset{\sim }{v}} \) Power spectrum for wave orbital velocity in the *y* direction

\( {S}_{\overset{\sim }{u}\overset{\sim }{v}} \) Power spectrum for combined horizontal wave orbital velocity

*S* _{ ηη } Water surface elevation power spectral density

\( {S}_{\eta \overset{\sim }{u}} \) Water level and *x* direction orbital velocity cross spectrum

\( {S}_{\eta \overset{\sim }{v}} \) Water level and *y* direction orbital velocity cross spectrum

*t* Time

*T* _{ i } Mean wave period in the bay

*T* _{ p } Peak wave period

*u* Velocity vector

\( \overset{-}{u} \) Time-averaged horizontal current velocity

\( {\overset{-}{u}}_{CS} \) Time-averaged cross-shore current velocity

\( {\overset{-}{u}}_E \) Time-averaged current velocity in the east direction

\( {\overset{-}{u}}_{LS} \) Time-averaged longshore current velocity

\( {\overset{-}{u}}_N \) Time-averaged current velocity in North direction

\( \overset{\sim }{u} \) Horizontal component of the wave orbital velocity in the *x* direction

\( {\overset{\sim }{u}}_{m-RMS} \) Root mean square (RMS) of the maximum wave orbital velocity

*u* _{10} Offshore wind velocity

\( \overset{\sim }{v} \) Horizontal component of the wave orbital velocity in the *y* direction

\( {\overset{-}{V}}_l \) Longshore current velocity at the mid-surf zone

*α* _{ b } Breaking wave angle

Δ*s* Spacing between homogeneously distributed plants

Δ*x* Spacing between plants in the *x* direction

Δ*y* Spacing between plants in the *y* direction

\( {\overset{-}{\theta}}_c \) Mean current direction

\( {\overset{-}{\theta}}_w \) Mean wave direction of an entire spectrum

*θ* _{1} Mean wave direction for each frequency

*ν* Kinematic viscosity of water

*ρ* Water density

## Notes

### Acknowledgments

The study was supported in part by the National Science Foundation (NSF Grant Nos. DMS-1115527 and SEES-1427389) and the Louisiana Board of Regents. Ranjit Jadhav, Kyle Parker, Ling Zhu, and Qi Fan assisted in the field study. Any opinions, findings, conclusions and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.

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