MANGROVE INSPIRED STRUCTURES FOR EROSION MITIGATION

Abstract

Systems and methods of coastal erosion protection are disclosed, the systems including at least one cylindrical member, wherein the at least one cylindrical member has a predetermined porosity and wherein the at least one cylindrical member has a predetermined submergence level in coastal water. The methods include identifying an area in need of coastal erosion protection; determining a strength of at least one erosion force upon the area; determining a coastal erosion risk level; positioning at least one cylindrical member in coastal water at a predetermined proximity to the area in need of coastal erosion protection; and securing the at least one cylindrical member to a sediment floor of the coastal water.

Description

BACKGROUND OF THE INVENTION

1. Field of Invention

This invention relates to systems and methods of coastal protection from erosion.

2. Description of Related Art

Coastal erosion occurs when rising sea levels, strong wave action, or flooding wear down the land along the coast. For example, coastal land subjected to the constant attack of incoming waves can experience severe erosion when rocks, soil, and sand are carried away by the strong ocean currents. In the United States alone, coastal erosion is responsible for over $500 million in property loss, including damage to ocean-front structures. [1]

Prior attempts have been made to prevent coastal erosion. For example, U.S. Pat. No. 9,644,334 (O'Neill) discloses methods and systems for controlling waterflow along waterways and coastal regions using a plurality of construction blocks to blunt tidal forces. The construction blocks may be arranged to form an impermeable wall to build structures such as river dams but may also be arranged to permit water to run past the blocks when used for controlling the force of water upon a shoreline. However, installation of the blocks is difficult because of their weight and often requires the use of hydraulic cranes.

Further, U.S. Pat. No. 10,669,684 B2 (Pierce) discloses a wave suppressor and sediment collection system that permits waterflow through the structure to carry sediment deposits toward the coastline while still breaking the force of waves upon a shoreline. However, the system disclosed by Pierce is a shelf-like system that takes up considerable space in the water and is secured only by traditional anchoring systems.

Studies have shown that mangrove trees may be effective at blunting tidal forces. [2-3] Mangrove trees are a natural interface in tropical and subtropical regions between land and coastal zones, forming a dense network of prop roots that make them resilient in this environment. The interaction of mangroves with tidal and river flows is fundamental to the preservation of estuaries and shorelines by providing a wide range of ecological ecosystem functions such as reducing coastal erosion, promoting biodiversity, and removal of nitrogen, phosphorus as well as carbon dioxide sequestrations. In particular, mitigation of erosion is highly influenced by the interaction of the flow and the intricate prop roots. The roots enhance the mangrove drag, and in tidal currents flows, the frictional effect from the drag can cause the currents to rotate and interact with the root patch. The trunk, branches, leaves, and roots of the mangrove act as an obstruction to the water flow, adding a biological dimension to the complex interactions between hydrodynamics and sediment movement in coastal area. The mangrove and hydrodynamic interaction affect the flow structure, turbulence, and waves with subsequent impact on the onset of sediment transport.

However, mangroves are only able to grow in limited environments, and may not be naturally occurring in the specific locations needed to prevent soil erosion. Thus, there is a need for systems and methods to prevent coastal erosion in a way that may be efficiently implemented in any location, have ease of installation, and take up minimal space.

All references cited herein are incorporated herein by reference in their entireties.

BRIEF SUMMARY OF THE INVENTION

A first aspect of the invention is a system for preventing coastal erosion including at least one cylindrical member, wherein the at least one cylindrical member has a predetermined porosity and wherein the at least one cylindrical member has a predetermined submergence level in coastal water.

In certain examples, the at least one cylindrical member comprises a vertical cylindrical shape.

In certain examples, the at least one cylindrical member comprises a formation of the shape of a mangrove tree root.

In certain examples, each of the at least one cylindrical members are coupled to one another in a formation of a mangrove tree root system.

In certain examples, the predetermined porosity is from 0% to 90% water-to-root volume.

In certain examples, the predetermined porosity is 47% water-to-root volume.

In certain examples, the predetermined submergence level is from 10% to 100% submergence.

In certain examples, the at least one cylindrical member comprises a material selected from the group of concrete, wood, polyethylene, steel, aluminum, copper, polyvinyl chloride (PVC), acrylic, polymethyl methacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene terephthalate (PETE or PET), and acrylonitrile-butadiene-styrene.

In certain examples, the system further includes an anchoring member.

In certain examples, they system further includes a sediment integrating member.

A second aspect of the invention includes a method of mitigating coastal erosion using the system of the invention, including identifying an area in need of coastal erosion protection; determining a strength of at least one erosion force upon the area; determining a coastal erosion risk level; positioning at least one cylindrical member in coastal water at a predetermined proximity to the area in need of coastal erosion protection; and securing the at least one cylindrical member to a sediment floor of the coastal water.

In certain examples, the area in need of coastal erosion protection is selected from the group consisting of ocean shorelines, lake shorelines, river banks, stream banks, and land in contact with water runoff.

In certain examples, the at least one erosion force includes at least one of waves, tides, running water, wind, glaciers, and gravity.

In certain examples, the coastal erosion risk level increases in parallel to the strength of the at least one erosion force.

In certain examples, the number of the at least one cylindrical member positioned in coastal water increases proportionally to the coastal erosion risk level, wherein greater numbers of the at least one cylindrical members are placed when the coastal erosion risk level increases.

In certain examples, the securing step further includes anchoring the at least one cylindrical member to the sediment floor with an anchoring member.

In certain examples, the securing step further includes inserting a sediment integrating member into the sediment floor.

In certain examples, the at least one cylindrical member is in a formation of the shape of a mangrove tree root.

In certain examples, each of the at least one cylindrical member is coupled to one another in a formation of a mangrove tree root system.

In certain examples, the predetermined proximity is selected from a group consisting of: a) a point between a shoreline and a wave breaking point, b) a point between a high tide water level and a low tide water level, c) on a shoreline, and d) a point between the location of wave formation and wave breaking point.

BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS

The invention will be described in conjunction with the following drawings:

FIG. 1(a) is a photograph showing the prop roots of red mangrove trees.

FIG. 1(b) is a schematic of mangrove roots.

FIG. 1(c) is an image showing the flow visualization behind mangrove root models of the invention.

FIG. 2(a) shows a photograph measuring sediment capture by a solid cylindrical member with 0% porosity.

FIG. 2(b) shows a photograph measuring sediment capture by an exemplary embodiment using a plurality of cylindrical members with 47% porosity.

FIG. 2(c) shows a photograph measuring sediment capture by an exemplary embodiment using a plurality of cylindrical members with 70% porosity

FIG. 2(d) shows a photograph measuring sediment capture by an exemplary embodiment using a plurality of cylindrical members with 86% porosity

FIG. 3 shows a graph of the net deposition area as a function of porosity for different flow variables.

FIG. 4(a) shows a graph of the drag coefficient versus porosity.

FIG. 4(b) shows a graph of the critical velocity versus porosity

FIG. 5 shows a graph of velocity normalized by the incoming flow velocity as a function of boundary layer thickness for cylindrical members.

FIG. 6(a) shows a graph of the spatial distribution of the momentum thickness of cylindrical members.

FIG. 6(b) shows a graph of average skin friction coefficient C_f versus porosity.

FIG. 6(c) shows a graph of skin coefficient factor versus momentum thickness.

FIGS. 7(a)-(p) show flow parameters using Particle Image Velocimetry (PIV) analysis including the spatial variation of the streamwise velocity (U), spanwise velocity (V), vorticity (w), and turbulence intensity at different porosities.

FIG. 8(a) shows a graph of viscous shear stress versus porosity.

FIG. 8 ((b) shows a graph of the profile of Reynolds Shear Stress (RSS=U′V′) for the root patches of cylindrical members at Re=2500.

FIG. 8(c) shows the variation of Reynolds shear stress as a function of spanwise distance for different porosities.

FIG. 9(a) shows a graph of the distribution of turbulence kinetic energy (TKE) downstream of the mangrove-root models.

FIG. 9(b) shows a graph illustrating local viscous dissipation that significantly exceeds the production of kinetic energy in the near-wall region.

FIG. 10 shows an exemplary embodiment of the system of the invention using three cylindrical members in a vertical formation.

FIG. 11 shows another exemplary embodiment of the system of the invention using two cylindrical members, wherein each cylindrical member is in the formation of a mangrove tree root.

FIG. 12 shows a flow chart of an exemplary method of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

Coastal areas subjected to the constant attack of waves or tidal forces may experience severe erosion. The system and method of the invention uses mangrove-inspired ocean structures to mitigate and prevent soil erosion.

In certain nonlimiting examples, the mangrove-inspired ocean structures include at least one cylindrical member used to mitigate erosion—the initiation of motion that removes sediments from the surface of land—or enhance sedimentation when particles suspended in water settle to the sediment floor. Types of erosion include wave erosion, water runoff erosion, glacial erosion, wind erosion, other tidal erosion, and gravity-based erosion. In certain examples a single cylindrical member is used, while in other examples a plurality of cylindrical members is used and each cylindrical member is positioned a predetermined distance apart from the other. Examples of formations for positioning of a plurality of cylindrical members include a straight-line formation, staggered formation, or randomized formation. Further, for cylindrical members in a formation in the shape of a mangrove tree root system, certain embodiments of the invention utilize multiple structures comprising cylindrical members in the mangrove tree root system formation.

In certain examples, the cylindrical member is made of material including but not limited to concrete, wood, polyethylene, steel, aluminum, copper, polyvinyl chloride (PVC), acrylic, polymethyl methacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene terephthalate (PETE or PET), and acrylonitrile-butadiene-styrene. In certain examples, the cylindrical member takes the form of a vertical cylindrical member. In other examples, the cylindrical member is in the form of the shape of a mangrove tree root. In certain examples where a plurality of cylindrical members is used, each cylindrical member is in the form of a mangrove tree root and is coupled to the other cylindrical members in a mangrove tree root system formation.

In certain examples, the at least one cylindrical member includes a predetermined porosity, which describes the water-to-structural volume of the cylindrical member. Porosity is determined by the number of cylindrical members and the size of said cylindrical members within a patch, or group, of the cylindrical members. Increased porosity permits greater volumes of water to flow through the cylindrical member. In certain examples, the porosity of the at least one cylindrical member may be a water-to-structural percentage of 0% (no porosity) to 90% (highly porous). In further nonlimiting examples, a porosity level of 47% water-to-structure volume is used, wherein 47% of the cylindrical member structure is open to permeation by flowing water and 53% of the structure is solid material.

In a nonlimiting example, the cylindrical member is partially submerged, with a predetermined portion of the member protruding above water level. The predetermined submergence label in a specific nonlimiting example is 50% with the remaining half of the cylindrical member protruding above water level. In other examples, the cylindrical member may be completely submerged, having only a minor portion submerged, for example, 10% of the member being submerged, or may be mostly submerged, for example, at 95% submergence level.

Certain examples of the at least one cylindrical member may be secured to the sediment floor—which may be the ocean floor, lake floor, river or stream bottom, or the land beneath a water runoff pathway—via an anchor. Other examples of the cylindrical member include a sediment anchoring member, wherein the sediment anchoring member is inserted into the sediment floor to prevent the cylindrical member from moving amidst the ocean current. In certain examples, the sediment anchoring member runs continuously with the cylindrical member, such as in a straight line, while in other examples, the sediment anchoring member includes shapes such as a hook or other similar formations to assist in gripping the surrounding sediment for stability.

Specific areas may be subject to higher risk of erosion, such as shorelines where large waves are common, riverbanks that may experience flooding, or land that frequently experiences extensive water runoff. Lakefronts may also experience such erosion with tidal forces. Areas with increased exposure to tidal forces, wind, or other environmental stressors have increased erosion risk. When the erosion risk due to water-based forces, such as running water or tidal forces, is low, fewer cylindrical member installations are necessary. However, when erosion risk is high, a greater number of cylindrical members are necessary to adequately protect the shoreline or other land area. In certain examples, cylindrical members are positioned in the coastal waters at a predetermined proximity from a shoreline. In certain examples, the cylindrical members are placed at the location between the shoreline and the point where waves break upon the shoreline to dampen the wave's strength upon reaching the shore and minimize its eroding effect.

The invention will be illustrated in more detail with reference to the following Examples, but it should be understood that the present invention is not deemed to be limited thereto.

Examples

Referring to the Figures, the interaction of mangroves with tidal and river flows is fundamental to the preservation of estuaries and shorelines by providing a wide range of ecological ecosystem functions such as reducing coastal erosion, promoting biodiversity, and removal of nitrogen, phosphorus, and carbon dioxide sequestrations. In particular, mitigation of erosion is highly influenced by the interaction of the water flow and the intricate prop roots. In an example showing the effectiveness of natural root structures, as shown in the photograph of FIG. 1(a), red mangrove (Rhizophora mangle) prop roots protrude from a shoreline, extend from the tree trunk, and form a radial, circular patch or large-scale mangrove forests. The roots enhance the mangrove drag, and in tidal currents flows, the frictional effect due to the drag can cause the currents to rotate and interact with the root patch. FIG. 1(b) shows a schematic of mangrove roots. The roots generate small-scale turbulence through the developments of vortex shedding and eddy formation. trunk, branches, leaves, and roots of the mangrove act as an obstruction to the water flow adding a biological dimension to the complex interactions between hydrodynamics and sediment movement in coastal area. This mangrove and hydrodynamic interaction affect the flow structure, turbulence, and waves with subsequent impact on the onset of sediment transport. FIG. 1(c) shows the flow visualization behind mangrove root models of the invention, wherein water flow is shown around nine cylindrical members positioned in a circular arrangement, with eight cylindrical members positioned around a central cylindrical member.

Mangrove root-models have an optimal porosity, described as the ratio between the area covered by the roots and the water, to prevent erosion. The erosion mitigation for the exemplary embodiment of the system similar to mangrove root models is better compared to a single cylindrical member or other roots configuration. The exemplary mangrove-inspired ocean structures are used to mitigate erosion (i.e. the initiation of motion of that remove sediments from the surface) and/or enhance sedimentation (particles suspend in water settled in the bottom surface). A network of submerged cylindrical members (the patch), straight or following a curve, are used to mitigate the erosion process and/or promote sedimentation. In certain examples, the patch of a plurality of cylindrical members is completely submerged in the water and in other examples, the patch protrudes outside the water. In certain examples, this technology is applied for seawalls and ocean or coastal structures (such as columns or pillars) where erosion must be minimized or sedimentation needs to be enhanced.

An exemplary study [4] was conducted of sediment capture by different exemplary models of cylindrical members with different porosity values (porosity (φ)=volume water/root volume) as examined in a flume. Particle Image Velocimetry (PIV) was used to investigate the interaction of the boundary layer with the near-bed flow using the four different cylindrical member patch porosities. PIV measurement provides direct and detailed velocity measurements over an entire flume bed. FIG. 2(a) shows a photograph of the measurements of the area of sediment capture by a solid cylindrical member with 0% porosity. FIG. 2(b) shows a photograph of the measurements of the area of sediment capture by a cylindrical member with 47% porosity. FIG. 2(c) shows a photograph of the measurements of the area of sediment capture by a cylindrical member with 70% porosity, and FIG. 2(d) shows a photograph of the measurements of the area of sediment capture by a cylindrical member with 86% porosity.

Measurements were first performed with smooth-wall conditions to establish the baseline flow structure within the unvegetated channel followed by measurements for four different patch porosities. The models were tested to develop quantitative models for prop roots effects on the bed. The parameters affecting the incipient motion were investigated to understand how spatially averaged velocity derivatives alter in the presence of the simplified mangrove root models (cylindrical members). Additionally, since the turbulence generated by the vegetation makes the flow spatially variable, a spatially-distributed flow parameter behind the root patch was presented. The sediments on the flume bed are indicated by the grayscale image of the sediment trajectories deposited on the flume bed. The flow is depicted from left to right. The black circles indicate the bottom positions of cylindrical members of the mangrove root-type models emergent in the water. The camera was positioned below the water flume in the horizontal plane. The patch with 47% porosity exhibits the minimum erosion in the near-wall mainly due to the lower turbulence and velocity in the near-wall region. This case is closer to the porosity found in natural mangroves.

After the onset of the sediment transport, it was observed that some sediments followed the streamwise direction along the flume with no indication of deposition on the bed. However, most sediments tended to deposit after the erosion took place and stayed unmoved. This trend formed a distinctive depositional region based on the area and density of the sediment accumulation. The pattern of sediment erosion posterior to the mangrove root-type cylindrical member models is shown in FIG. 2(a)-(d). For all cases, the sediment deposition region was less pronounced immediately behind the patches, however, after approximately 3 mm behind the patches, the formation of the deposition region was observed. It was also observed that most sediments were eroded for models with high porosity (less blockage). For the low porosities, a convex pattern of the deposition region was shaped and for the high porosity (case 3 and 4), the rectangular-like region was formed. However, the sediment deposition area for the high porosity models ranged from 25 to 75 cm2, the largest area among others, indicating that mangrove root porosity was related to mitigating the erosion of posterior to the patch even compared to the single solid cylindrical member. This signifies that for a fixed root configuration there was an optimal porosity to mitigate erosion.

FIG. 3 shows a graph of the net deposition area as a function of porosity for different flow variables as part of an exemplary study. In this study, the optimal porosity is 47%, and the curve fit shows variations with the velocity. The top line indicated with a vertical hash mark indicates the region between high and low net depositional areas. Optimal patch porosity for cylindrical members yields maximum energy dissipation from the water flow due to drag, with a lower erosion attributed to a higher water flow velocity required for incipient motion.

FIG. 4A shows a graph of the drag coefficient versus porosity. FIG. 4B shows a graph of the critical velocity versus porosity. Critical velocity was obtained based on Eq. (1) which indicates initiation of the sediment transport. Erosion occurs if the flow velocity over the sediments is exceeded by the critical velocity that reached the peak at φ=47%.

$\begin{array}{cc}\frac{\mathrm{Dw}}{\mathrm{Dt}}=v{\nabla }^{2}w=\underset{\mathrm{viscous}\left(w_s\right)}{\underbrace{\frac{1}{\mathrm{Re}}[\nabla \times (\frac{1}{\rho }\nabla \times \left(\tau \right)]}}& \left(1\right)\end{array}$

The key parameter is the viscous-term (w_s) with important effects owing to variation in the coefficient of viscosity in the boundary layer. The spatially averaged values of different terms at each stream-wise location are plotted for all cases. The viscous term can be further divided into two components:

$\begin{array}{cc}{w}_s=\frac{1}{\mathrm{Re}}\underbrace{\left[\nabla \times \frac{1}{\rho }\left(\frac{\partial \varphi \text{?}}{\partial x}i+\frac{\partial \varphi \text{?}}{\partial y}j\right)\right]}\text{?}+\frac{1}{\mathrm{Re}}\underbrace{\left[\nabla \times \frac{1}{\rho }\left(\frac{\partial \varphi \text{?}}{\partial y}i+\frac{\partial {\varphi }_c}{\partial x}j\right)\right]}\text{?}& \left(2\right)\end{array}$ $\text{?}\text{indicates text missing or illegible when filed}$

FIG. 4(a) shows drag coefficient, based on the patch diameter, that varies with patch porosity. FIG. 4(b) is obtained using C_f measured in the experiment and found that at φ=47%, the critical erosion velocity is much lower than the other cases, indicating a lower possibility of the sediment erosion in the near-bed. An examination of the near-bed flow structure disturbed by the mangrove root patches was then conducted. The velocity profiles of the boundary layer were acquired at stream-wise locations for four values of the porosities at U∞=2 cm/s corresponding to Reynolds number of 2500, based on the patch diameter. In FIG. 5, the normal distance is normalized by the boundary layer thickness which is defined as the value of y at which U equals 99% of the free stream velocity (U∞). For the smooth wall case (φ=100%), as the flow approached the bed, the velocity achieved zero value as dictated by the no-slip conditions. Therefore, a velocity gradient was formed in a normal direction to the flow due to the viscosity effect. The mean velocity profile revealed a parabolic trend with the mean profile for fully developed laminar flow for the smooth wall. With increasing the porosity, the mean velocity profile deviated from the laminar characteristics and became progressively flat as the flow transitions from a laminar to a turbulent flow. Specifically, the boundary layer thickness for a porosity level of 47% is approximately 10% lower than the solid cylindrical member value, and thus this results in larger velocity gradients in the region close to the wall which accounts for increased values of wall shear stress.

FIG. 6(a) shows the spatial distribution of the momentum thickness exhibited a linear change with streamwise distance from the cylindrical member patch with an insignificant porosity effect. The momentum thickness represents the loss of momentum due to the presence of a wall and increased with the distance from the patch. However, it remained almost unchanged with respect to porosity. FIG. 6(b) shows that the streamwise distribution of skin friction coefficient, C_f, measured for four cases of different porosities, indicated that the baseline case (smooth wall) skin friction coefficient ranged from 0.03 to 0.05. However, with the presence of mangrove roots, the average skin friction coefficient C_f decreased with porosity. The results show that for a constant loss in the fluid momentum, the skin friction factor opposing bed drag is high for the porosity at 47%. In addition, in FIG. 6(c), it is observed that the skin coefficient factor for a constant momentum thickness is the largest for the case indicated by the line with circular markings.

To examine the distribution of parameters in the flow structure, the spatial variation of the streamwise velocity (U), spanwise velocity (V), vorticity (w), and turbulence intensity are shown in FIG. 7(a)-(p) for different porosities. Locally, there is a small area with negative streamwise velocity, as shown in FIG. 7(a)-(d), in blue (darker shading) immediately downstream of the patches. However, by decreasing the porosity, the positive streamwise region increases. It is noted that for the φ=47% the elevated streamwise and spanwise velocity is mainly due to the augmented flow constraints by the neighboring cylindrical members in the patch with 47% porosity as shown in FIG. 7(e),(f). The difference between the maximum and minimum local streamwise and spanwise velocities can also be seen to decrease significantly with patch porosity, as shown in FIG. 7(g),(h). This decrease in velocity change has also been observed in flow through random cylindrical member configurations. Therefore, an area with positive vorticity emerged downstream of the patch due to the recirculation in the wake region. As the patch porosity decreases, the flow that is channeled between cylindrical members follows an increasingly tortuous path. Vorticity change in the middle of the wall region is relatively small because the fluid particles can acquire rotation only by viscous diffusion which is the low value at the end of the buffer layer. During the time fluid traveled downstream of the patch, it was observed that the sediments diffused only a small distance away from the boundary layer. Similarly, the fluctuation of streamwise velocity indicated by turbulence intensity (FIG. 7(m)-(p)) was around 0.001 for the least porous patch and decayed with porosity increase. The patch with φ=47% exhibited the nearly zero value for the vorticity and turbulence intensity compared to the impermeable cylindrical member and other patches (FIG. 7(j)-(n)). This deficiency in velocity fluctuation elevated the possibility of sediment deposition in the near-wall region for the case where porosity is 47%.

Even though the viscous shear stress has a low value for the high porous patch, it is relatively unchanged with porosity increase in farther distance from the patch (FIG. 8(a)). Importantly, for the case where porosity is 47%, sediments most likely experienced high resistance forces as the normalized viscous shear stress was around one, which contributes to a lower erosion in the near-wall region. FIG. 8(b) presents the profile of Reynolds Shear Stress (RSS=U′V′) for the root patches at Re=2500. Furthermore, at a fixed y, excellent collapse of the RSS profile for all cases is noted, where the profile exhibits a linear region from the centerline to the peak location. This linear behavior confirms the characteristics of transitional and turbulent flow and shows the dominance of turbulent (inertial) effect over viscous stress. As the wall is approached, deviation from the patch was noted for the rough patches as the magnitude of the peak in the RSS increases with increasing porosity, coupled with a slight shift in the peak location close to the wall. FIG. 8(c) indicates that the streamwise velocity fluctuations were sufficient for all cases (U′ U>10%) to grow the instability in the near-wall region and Tollmien-Schlichting (T-S) waves emerge in the boundary layer. The T-S waves are formed when the disturbance interacts with the roughness in a process also known as receptivity. These waves are gradually augmented as they move downstream until they may eventually grow large enough that nonlinearities conquest and the flow transitions to turbulence.

It is also important to note that for the higher porosities, the vorticity is higher and thus the velocity gradient in the near-wall is lower compared to the lower porosity. Therefore, the boundary layer is similar to the unvegetated channel with a low near-wall velocity gradient and consequently low C_f values (FIG. 6(b),(c)). Turbulent Kinetic Energy (TKE) rises steadily from almost zero at the wall to a peak value at y+≈12 and then declines through the upper part of the buffer region as it proceeds towards the downstream. The distribution of TKE downstream of the mangrove-root models is characterized by a noticeable peak (FIG. 9(a)) suggesting the turbulent region behind the case where porosity is 47% is less than y+<10. It is mainly due to the local viscous dissipation that significantly exceeds the production of kinetic energy in the near-wall region (FIG. 9(b)). Thus, there is strong cross-stream diffusion of energy both towards the wall and towards the core flow. The energy balance of the mean motion can be rewritten as:

$\begin{array}{cc}\frac{{\mathrm{du}}^{+}}{{\mathrm{dy}}^{+}}={\left(\frac{{\mathrm{du}}^{+}}{{\mathrm{dy}}^{+}}\right)}^2+{\tau }_l^{+}\frac{{\mathrm{du}}^{+}}{{\mathrm{dy}}^{+}}& \left(3\right)\end{array}$

where the first term on the left-hand side is related to the energy supply, the second term is viscous dissipation, transformed into internal energy and the third term is turbulence production which is used to generate turbulent fluctuations energy. This term would eventually transform into internal energy. The turbulence has a maxim of 0.25 at y+=10.6 (FIG. 9b). At this distance from the wall, the viscous dissipation and turbulence production are equal. For y+<10.6 the viscous dissipation dominates whereas for y+>10.6 the turbulence production dominates. This is mainly due to the Reynolds stress works against the mean velocity gradient to remove energy from the mean flow, just as the viscous stress works against the velocity gradients. However, the energy removed by the viscous stress is directly dissipated, reappearing as heat, but the action of the Reynolds stress provides energy for turbulence fluctuations. The loss of mean flow energy to turbulence is large compared with the viscous dissipation. Consequently, the exemplary study shows that for the case where porosity is 47%, the turbulence production is not sufficient to exceed the viscous dissipation and discourage the initiation of sediment transport.

FIG. 10 shows an exemplary embodiment of the system of the invention using the at least one cylindrical member 2 in a vertical formation 4. In this example, a plurality of cylindrical members 2 is used and is positioned at the point 6 within the coastal waters 18 between the shoreline 8 and the point at which waves break 10. Each cylindrical member includes an anchoring member 12 to anchor the cylindrical member 2 to the sediment floor 14 and avoid movement of the cylindrical member when encountered by wind or current. The cylindrical members 2 in this example assist in dampening the eroding effect of a wave 16 upon the shoreline 8.

FIG. 11 shows another exemplary embodiment of the system of the invention using the at least one cylindrical member 2, wherein each cylindrical member is in the formation of a mangrove tree root 24. When a plurality of cylindrical members 2 are coupled together, they are coupled in the formation of a mangrove tree root system 22. In certain examples, a plurality of mangrove tree root system formations 22 are used. Additionally, the each of the cylindrical members 2 includes an anchoring member 12. In certain examples, instead of an anchoring member, the cylindrical member uses a sediment integrating member in the shape of a hook which burrows into the sediment floor 14 to anchors the cylindrical members. The cylindrical members 2 are placed in coastal waters 18 and may protrude from the water to dampen the eroding effect of a crashing wave 16 upon the shoreline 8. However, in other examples, the cylindrical members 2 are positioned in rivers, streams, areas experiencing common water runoff, lakes, or other bodies of water near land that experiences frequent erosion.

FIG. 12 shows a flow chart of an exemplary method of the invention, wherein the method includes identifying an area in need of coastal erosion protection; determining a strength of at least one erosion force upon the area; determining a coastal erosion risk level; positioning at least one cylindrical member 2 in coastal water 18 at a predetermined proximity to the area in need of coastal erosion protection; and securing the at least one cylindrical member to a sediment floor 14 of the coastal water. In certain examples, the area in need of coastal protection is a shoreline 8. In other examples, the area in need of coastal protection may be a lakefront, riverbank, streambank, or area experiencing frequent water runoff. As stated above, the stronger the erosion force upon the area, the higher the coastal erosion risk level. When coastal erosion risk levels increase, a higher number of cylindrical members 2 is necessary. In certain examples, the at least one cylindrical member 2 is secured by means including an anchoring member 12 and sediment integrating member 20.

While the invention has been described in detail and with reference to specific examples thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof.

REFERENCES

• [1] United States Government (Apr. 1, 2021). Coastal Erosion, U.S. Climate Resilience Toolkit, https://toolkit.climate.gov/topics/coastal-flood-risk/coastal-erosion.
• [2] Murdiyarso, D. et al. The potential of Indonesian mangrove forests for global climate change mitigation. Nat. Clim. Chang. 5, 1089-1092. https://doi.org/10.1038/s41467-018-04692-w2 (2015).
• [3] Kazemi, A., Bocanegra Evans, H., Curet, O. & Castillo, L. On the role of mangrove root flexibility and porosity in sediment deposition and erosion control. Bull. Am. Phys. Soc. 63 (2018).
• [4] Amirkhosro Kazemi1, Luciano Castillo, & Oscar M. Curet. Mangrove roots model suggest an optimal porosity to prevent erosion. Nature Scientific Reports. 11:9969. https://doi.org/10.1038/s41598-021-88119-5 (2021).

Claims

1. A system for mitigating coastal erosion, the system comprising at least one cylindrical member, wherein the at least one cylindrical member has a predetermined porosity and wherein the at least one cylindrical member has a predetermined submergence level in coastal water.

2. The system of claim 1, wherein the at least one cylindrical member comprises a vertical cylindrical shape.

3. The system of claim 1, wherein the at least one cylindrical member comprises a formation of the shape of a mangrove tree root.

4. The system of claim 3, wherein each of the at least one cylindrical members are coupled to one another in a formation of a mangrove tree root system.

5. The system of claim 1, wherein the predetermined porosity is from 0% to 90% water-to-root volume.

6. The system of claim 1, wherein the predetermined porosity is 47% water-to-root volume.

7. The system of claim 1, wherein the predetermined submergence level is from 10% to 100% submergence.

8. The system of claim 1, wherein the at least one cylindrical member comprises a material selected from the group of concrete, wood, polyethylene, steel, aluminum, copper, polyvinyl chloride (PVC), acrylic, polymethyl methacrylate (PMMA), polycarbonate (PC), polypropylene (PP), polyethylene terephthalate (PETE or PET), and acrylonitrile-butadiene-styrene.

9. The system of claim 1, further comprising an anchoring member.

10. The system of claim 1, further comprising a sediment integrating member.

11. A method of mitigating coastal erosion using the system of claim 1, the method comprising: a) identifying an area in need of coastal erosion protection;b) determining a strength of at least one erosion force upon the area;c) determining a coastal erosion risk level;d) positioning at least one cylindrical member in coastal water at a predetermined proximity to the area in need of coastal erosion protection; ande) securing the at least one cylindrical member to a sediment floor of the coastal water.

12. The method of claim 11, wherein the area in need of coastal erosion protection is selected from the group consisting of ocean shorelines, lake shorelines, river banks, stream banks, and land in contact with water runoff.

13. The method of claim 11, wherein the at least one erosion force includes at least one of waves, tides, running water, wind, glaciers, and gravity.

14. The method of claim 11, wherein the coastal erosion risk level increases in parallel to the strength of the at least one erosion force.

15. The method of claim 11, wherein the number of the at least one cylindrical members positioned in coastal water increases proportionally to the coastal erosion risk level, wherein greater numbers of the at least one cylindrical members are placed when the coastal erosion risk level increases.

16. The method of claim 11, wherein the securing step further comprises anchoring the at least one cylindrical member to the sediment floor with an anchoring member.

17. The method of claim 11, wherein the securing step further comprises inserting a sediment integrating member into the sediment floor.

18. The method of claim 11, wherein the at least one cylindrical member comprises a formation of the shape of a mangrove tree root.

19. The method of claim 11, wherein each of the at least one cylindrical members are coupled to one another in a formation of a mangrove tree root system.

20. The method of claim 11, wherein the predetermined proximity is selected from a group consisting of: a) a point between a shoreline and a wave breaking point, b) a point between a high tide water level and a low tide water level, c) on a shoreline, and d) a point between the location of wave formation and wave breaking point.