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What is the primary focus of the approaches discussed in the document?
What is the primary focus of the approaches discussed in the document?
Which tool is mentioned as being used for the implementation of the new formulation?
Which tool is mentioned as being used for the implementation of the new formulation?
What species were included in the analysis for the linear relationship?
What species were included in the analysis for the linear relationship?
In the validation of the tool mentioned, which estuary was used?
In the validation of the tool mentioned, which estuary was used?
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What aspect of biomass is provided in the formulation discussed?
What aspect of biomass is provided in the formulation discussed?
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What is the range of the Reynolds number ($R_e$) according to the data provided?
What is the range of the Reynolds number ($R_e$) according to the data provided?
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Which drag coefficient ($C_D$) accounts for vegetation movement when calculating drag force?
Which drag coefficient ($C_D$) accounts for vegetation movement when calculating drag force?
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According to the data, what factor is included in the calculation of the drag force for vegetation motion?
According to the data, what factor is included in the calculation of the drag force for vegetation motion?
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What is the difference in drag coefficients identified in the data for the two situations described?
What is the difference in drag coefficients identified in the data for the two situations described?
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What type of waves were considered in the study by Mendez et Lab?
What type of waves were considered in the study by Mendez et Lab?
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What does the formula for flow energy attenuation involve when describing the relationship between wave height and wave period?
What does the formula for flow energy attenuation involve when describing the relationship between wave height and wave period?
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What is the significance of the variable β in the given formula?
What is the significance of the variable β in the given formula?
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In the context of the content provided, what does the term 'biomasa' refer to?
In the context of the content provided, what does the term 'biomasa' refer to?
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What kind of solutions does the concept of 'Nature-based Solutions' refer to?
What kind of solutions does the concept of 'Nature-based Solutions' refer to?
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Which aspect of coastal management is emphasized by the integration of drag formulas from literature?
Which aspect of coastal management is emphasized by the integration of drag formulas from literature?
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What is the purpose of wave damping as shown in the formula $H_{d} = H_{i} (1 + \beta X)$?
What is the purpose of wave damping as shown in the formula $H_{d} = H_{i} (1 + \beta X)$?
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In the context of the COCOTSU flume, what does the term 'solid lines' represent?
In the context of the COCOTSU flume, what does the term 'solid lines' represent?
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What is indicated by the 'dashed lines' in the wave damping representation?
What is indicated by the 'dashed lines' in the wave damping representation?
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Which species is referenced as a mature tree in the context of coastal management?
Which species is referenced as a mature tree in the context of coastal management?
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What is a primary function of capacity gauges in coastal management?
What is a primary function of capacity gauges in coastal management?
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Why is the definition of a control volume important in coastal management?
Why is the definition of a control volume important in coastal management?
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What scale is used for the IH Cantabria flume in the research?
What scale is used for the IH Cantabria flume in the research?
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What environmental factor does the wave-current-tsunami flume model best address?
What environmental factor does the wave-current-tsunami flume model best address?
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What does the wave attenuation coefficient ($eta$) indicate in the context of wave energy dissipation?
What does the wave attenuation coefficient ($eta$) indicate in the context of wave energy dissipation?
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Which approach was first introduced by Dalrymple et al. (1984) related to wave energy dissipation?
Which approach was first introduced by Dalrymple et al. (1984) related to wave energy dissipation?
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What does the equation $H_1 = H_0(1 + eta x)$ represent in wave energy attenuation?
What does the equation $H_1 = H_0(1 + eta x)$ represent in wave energy attenuation?
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In the analytical formulations, which aspect is assumed to be constant while calculating the drag force on the ecosystem?
In the analytical formulations, which aspect is assumed to be constant while calculating the drag force on the ecosystem?
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What is the main function of the drag force that is calculated in the context of waves interacting with coastal ecosystems?
What is the main function of the drag force that is calculated in the context of waves interacting with coastal ecosystems?
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Which method was used to extend wave energy dissipation analysis to irregular waves by Méndez and Losada in 2004?
Which method was used to extend wave energy dissipation analysis to irregular waves by Méndez and Losada in 2004?
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The steady flow condition is assumed in which aspect of wave energy dissipation analysis?
The steady flow condition is assumed in which aspect of wave energy dissipation analysis?
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What is the role of experimental data in the study of wave energy attenuation coefficients?
What is the role of experimental data in the study of wave energy attenuation coefficients?
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What is the significance of the two different drag coefficients mentioned for Zostera noltii in relation to vegetation movement?
What is the significance of the two different drag coefficients mentioned for Zostera noltii in relation to vegetation movement?
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How does the range of Reynolds numbers ($R_e$) affect the calculations for drag coefficients provided?
How does the range of Reynolds numbers ($R_e$) affect the calculations for drag coefficients provided?
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In the context of the study, what role does the introduced relative velocity between plants and fluid play?
In the context of the study, what role does the introduced relative velocity between plants and fluid play?
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What does the formula $C_D = 0.40 + \frac{1}{R_e}$ represent with respect to vegetation motion?
What does the formula $C_D = 0.40 + \frac{1}{R_e}$ represent with respect to vegetation motion?
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Which characteristic is true for the drag coefficient of $C_D = 0.08 + \frac{1}{R_e}$ in the absence of movement?
Which characteristic is true for the drag coefficient of $C_D = 0.08 + \frac{1}{R_e}$ in the absence of movement?
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What range of Reynolds numbers (Re) is considered for vegetation diameter in the study?
What range of Reynolds numbers (Re) is considered for vegetation diameter in the study?
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What fitted parameter value is associated with β1 in the drag coefficient formulation?
What fitted parameter value is associated with β1 in the drag coefficient formulation?
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Which ecological types were evaluated by Pinsky et al. in their review?
Which ecological types were evaluated by Pinsky et al. in their review?
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What is the important drag coefficient formula introduced by Ozeren et al. concerning vegetation?
What is the important drag coefficient formula introduced by Ozeren et al. concerning vegetation?
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What statistical approach is referenced in the drag coefficient formula derived from Pinsky et al.?
What statistical approach is referenced in the drag coefficient formula derived from Pinsky et al.?
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What is the primary variable affecting the drag coefficient in vegetation as discussed in the provided content?
What is the primary variable affecting the drag coefficient in vegetation as discussed in the provided content?
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Which formulation considers the motion of vegetation when calculating the drag coefficient?
Which formulation considers the motion of vegetation when calculating the drag coefficient?
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What does the parameter $α$ represent in relation to vegetation and water flow?
What does the parameter $α$ represent in relation to vegetation and water flow?
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In the context of the content provided, which drag coefficient is associated with no movement of vegetation?
In the context of the content provided, which drag coefficient is associated with no movement of vegetation?
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What significant factor differentiates the two drag coefficients mentioned in the content?
What significant factor differentiates the two drag coefficients mentioned in the content?
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What represents the empirical formulation used in the new coastal management approach discussed?
What represents the empirical formulation used in the new coastal management approach discussed?
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How many species were included in the analysis of the linear relationship within the coastal management study?
How many species were included in the analysis of the linear relationship within the coastal management study?
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Which methodology was applied for validating the tool in the context of the Scheldt estuary?
Which methodology was applied for validating the tool in the context of the Scheldt estuary?
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What is the significance of the 'biomasa' figures presented in the validation of the coastal management tool?
What is the significance of the 'biomasa' figures presented in the validation of the coastal management tool?
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What is the primary focus of 'Nature Based Solutions' in the context of coastal management discussed?
What is the primary focus of 'Nature Based Solutions' in the context of coastal management discussed?
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What does the wave attenuation coefficient ($\beta$) represent in the context of wave energy dissipation?
What does the wave attenuation coefficient ($\beta$) represent in the context of wave energy dissipation?
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Which component of the drag force calculation assumes a steady flow condition in wave energy dissipation analysis?
Which component of the drag force calculation assumes a steady flow condition in wave energy dissipation analysis?
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Which researchers first presented an energy conservation approach for regular waves in the context of wave energy dissipation?
Which researchers first presented an energy conservation approach for regular waves in the context of wave energy dissipation?
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In the equation $H_1 = H_0(1 + \beta x)$, what does $H_0$ represent?
In the equation $H_1 = H_0(1 + \beta x)$, what does $H_0$ represent?
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What approach did Méndez and Losada extend for irregular waves in the wave energy dissipation analysis?
What approach did Méndez and Losada extend for irregular waves in the wave energy dissipation analysis?
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What does the term 'energy gradient of the flow' refer to in wave energy dissipation?
What does the term 'energy gradient of the flow' refer to in wave energy dissipation?
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How do most studies in wave energy literature determine the wave attenuation coefficient?
How do most studies in wave energy literature determine the wave attenuation coefficient?
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In the formulation for wave energy attenuation, what is assumed about the drag coefficient?
In the formulation for wave energy attenuation, what is assumed about the drag coefficient?
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Study Notes
Wave Energy Attenuation
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Wave energy dissipation in coastal ecosystems traditionally used analytical formulations based on energy conservation, assuming steady flow.
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This approach calculates the energy gradient produced along the ecosystem, relating it to the dissipation induced by the flow considering the drag force exerted by the ecosystem.
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It assumes a constant drag coefficient and a representative width of the ecosystem elements per unit height along the ecosystem's height.
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Dalrymple et al. (1984) first presented this energy conservation approach for regular waves based on linear wave theory.
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Méndez and Losada (2004) extended the formulation for irregular waves.
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This approach calculates the wave height decay with distance using an attenuation coefficient, as represented by the following equation:
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- 𝐻 / 𝐻! = 1 / ( 1 + β𝑥 )**
where:
- 𝐻! is the incident wave height
- 𝐻 is the wave height at a distance x within the ecosystem
- β is the wave attenuation coefficient
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The attenuation coefficient is often determined by fitting it to experimental data.
Drag Coefficient
- Several studies have used experimental data to determine the drag coefficient for different types of coastal ecosystems and water flow conditions.
- Zostera noltii vegetation has been studied by Asano et al. (1988) and Mendez et al. (1999), reporting a drag coefficient (𝐶𝐷) varying with the vegetation diameter and Reynolds number (𝑅𝑒).
- Mendez et al. (1999) considered both stationary and moving vegetation, leading to two different drag coefficients for seagrasses.
New Approaches
- The IH Cantabria Flume, a wave-current-tsunami flume named COCOTSU, has been utilized to study the impact of mangroves on wave attenuation at a scale of 1:6.
- The flume is 26 meters wide and 156 meters long, allowing for the study of wave attenuation through a mature Rhizophora mangrove forest.
- Capacitance depth gauges are used to measure water depth variations and analyze wave attenuation through the mangrove forest.
- The study compared wave attenuation through the mangrove forest to the empty flume cases, revealing significant differences in the wave height attenuation profile.
- Research by Maza et al. (2022) found a common linear relationship for wave attenuation across various species, densities, and wave conditions.
- This research has led to the development of an empirical formulation that can be incorporated into the SWAN wave model for numerical simulations of wave attenuation in coastal ecosystems.
- The numerical tool has been validated in the Scheldt estuary, comparing simulations with field data collected by Heuner et al. (2015) and Schulze et al. (2019) for Scirpus maritimus and Spartina anglica biomas estimations.
- The validation process involved comparing the model results using the new drag coefficient formulation with available drag formulas from existing literature.
- López-Arias et al. (2023) validated the new approach using the drag formula from the literature.
Flow Energy Attenuation - Analytical Formulations
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An analytical formulation for flow energy attenuation through coastal ecosystems is presented, considering the drag force exerted by the ecosystem.
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The formulation uses the following equation:
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β = (4aNH!k sinh(kl) + 3sinh(kl)) / (9π sinh(2kh) + 2kh sinh(kh))*
Where:
- β: Wave Attenuation Coefficient
- a: Drag Coefficient
- N: Vegetation Density
- H!: Wave Height
- k: Wave Number
- l: Ecosystem Length
- h: Ecosystem Height
- C#: Wave Velocity
Wave Energy Attenuation
- Coastal ecosystems dissipate energy through waves using an analytical formulation based on the conservation of energy equation for steady flow.
- The energy gradient of the flow along the ecosystem is related to energy dissipation, considering drag force exerted on the ecosystem.
- Drag force is calculated by assuming a constant drag coefficient and a constant representative width of ecosystem elements per unit height.
- The wave height decay is a function of an attenuation coefficient:
- 𝐻/𝐻! = 1/(1+𝛽𝑥)
- where 𝐻! is the incident wave height
- 𝐻 is the wave height at a distance x within the ecosystem
- 𝛽 is the wave attenuation coefficient
- 𝐻/𝐻! = 1/(1+𝛽𝑥)
Attenuation Coefficient
- The attenuation coefficient (𝛽) is usually fitted using experimental data.
- Drag Coefficient (CD) is an important factor in calculating the 𝛽 coefficient.
Drag Coefficient (CD)
- CD values have been investigated for various vegetation types and wave conditions, with varying formulations incorporating factors like Reynolds number (Re) and vegetation diameter.
- Several studies have been conducted to measure CD for different vegetation types, including:
- Zostera noltii
- Seagrasses (artificial)
- Posidonia oceanica
- Saltmarshes
- Mangroves
- Some formulations for CD:
- Log 𝐶𝐷 = 𝛽0 + 𝛽1 𝑙𝑜𝑔 𝑐 ∗ 𝑅𝑒 (Pinsky et al., 2013)
- 𝛽0 = -1.72 and 𝛽1 =-1.67
- 𝑐 = 3*10-4
- 𝑅𝑒 is the Reynolds number considering vegetation diameter
- 𝐶𝐷 = 0.817 (Ozeren et al., 2013) for saltmarshes (J. 55.2) under regular waves
- 𝐶𝐷 = 0.08 + 2200/𝑅𝑒 (Asano et al., 1988) for Zostera noltii under regular waves
- 𝐶𝐷 = 0.40 + 4600/𝑅𝑒 (Mendez et al., 1999) for Zostera noltii under regular waves, considering vegetation movement
- Log 𝐶𝐷 = 𝛽0 + 𝛽1 𝑙𝑜𝑔 𝑐 ∗ 𝑅𝑒 (Pinsky et al., 2013)
- CD values can be different for different vegetation types and wave conditions, impacting the efficiency of wave energy attenuation.
New Approaches
- A new empirical formulation for 𝐶𝐷 emerged from a study by Maza et al. (2022) for various species, meadow densities, and wave conditions.
- The new 𝐶𝐷 formulation was implemented into the SWAN (Simulating Waves Nearshore) numerical model.
- This numerical tool was validated for the Scheldt estuary, comparing results for different vegetation types (Scirpus maritimus and Spartina anglica) and biomass distribution.
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Description
Explore the principles of wave energy dissipation in coastal ecosystems. This quiz examines the analytical formulations based on energy conservation, assumptions made about drag forces, and how wave height decays over distance. Delve into the foundational work of Dalrymple et al. (1984) and Méndez and Losada (2004) on wave attenuation.
