#
Protecting the Coast:

A Simulation of Artificial Reefs

**David Carvalho**Author

**Fábio Cruz**Reviewer

In Perspectives on the Sea, we look into how simulation can help us face societal challenges, particularly those related with the ocean.

We have detailed here how coral reefs are *more* than a thriving ecosystem.

They provide *natural* protection to the coastline against harsh sea conditions.

**Artificial reefs** *can* recreate this protection profile.
However, estimating how well these structures fare requires **intense modeling and computation**.

But there can be other ways to get the job done.

In this post, we showcase how this assessment can be made not only with the aid of simulation but also with real data from hydraulic experiments and Machine Learning models.

# Protecting the Coast:

A Simulation of Artificial Reefs

We saw
that natural coral reefs are incredibly efficient structures in protecting the coastline.
So much so that about **200 million** people worldwide rely on the protection they provide.

*Regrettably, they are facing a truly existential threat.*

Inventive solutions to recreate their features are becoming widespread.

For instance, **custom-designed** shapes can now be 3D-printed — providing crevices, refuges and shelter spots to altogether new ecosystems:

Video 1: 3D-printed reef for ecological protection. A whole new ecosystem was born after 3 years. Credits Seaboost Ecological Engineering

*But what if reef components were used to protect the coastline?*

For that, a more analytical approach is needed.

## Simulating reef components:

a laborious computational task

The effect of arbitrary structures on complex environments can lead to setups which tend to be **intensive to simulate** because they rely on the **geometry** of the specific piece as well as on the **materials** used.

Fig. 1: Simulation of the flow field around two different stacking reefs structures, respectively in the inset of (a) and (b). This computation suggests that stacking reefs longitudinally to increase the influence area of the slow-flow zone is not particularly functional. Credits: [1]

To make matters more challenging, the behavior of the structure can vary wildly depending on the incoming **fluid conditions**, such as its viscosity or velocity [2].

With both reef and flow parameters to consider, the number of simulations needed to be run increases **prohibitively**.

Another challenge in simulating arises mostly because the currents formed inside and around the structure are oftentimes **turbulent** [3], requiring refined computationally-intensive frameworks to solve notoriously hard equations of fluid dynamics [3, 4].

Take the simple example of a stack of hollow tubes, shown in Fig. 2.

Using *Fluent*, a Computational Fluid Dynamics (CFD) simulator, and real data from tank experiments, the flow around the reef can be estimated and contrasted [3].

The velocity components of the fluid show turbulent features and can be seen occurring in the region shielded by the 3-tube reef as the water flows from left to right.

Fig. 2: (top) 3D depiction of the reef for various tube arrangements. (bottom) By fixing one coordinate and setting incoming flow conditions, the velocity vector of the fluid can be seen in the two remaining coordinates through (left) *Particle Image Velocimetry* experiments and (right) the CFD simulation package *Fluent*. Credits: [3]

This example illustrates an important point when modelling any intervention on a coastal scenario: for a simulation to be consequential, the properties of each component must be properly estimated.

Needless to say, this is yet another challenge coming our way.

### Dragging along

Wave overtopping is easier to mitigate if incoming waves move slower.

The kinetic energy they carry can be **transferred** from the water to the rough surface of the reef component.

As fluid moves along it a **drag force** \(F_D\) in the direction of the fluid at each point of the object boundary is generated:

where \(\rho\) is the fluid density and \(\mathbf{u}\) its velocity at that point. The object response is quantified through the **drag coefficient** \(C_D\).

This coefficient is **challenging** to quantify since it depends not only on the object geometry but also on the fluid properties [2].

Fig. 3: Estimation of the drag coefficient \(C_D\) for various reef geometries for a fixed fluid regime [5] as done in [6].

One way out is to abstract the geometrical properties of each structure (such as their *porosity* and *permeability*) into classes and then estimate the drag coefficient of each class.

In the context of providing coastal protection for the South Korean coastline, this is done in [6], where a total of 24 reef components are proposed and their response *benchmarked*.

Fig. 4: 3D geometries of 24 different reef components considered for a South Korean Coastal Protection study. Credits: [6].

The upshot coming from this optimization task can be **very substantial**.

For instance, the geometrical variations from component AR17 to component AR20 (shown in Fig. 4) can lead to drag coefficients **6 times** larger [6].

*But the space of all shapes and materials seems huge.*

We must start somewhere.

## An actual artificial reef component in action

Instead of aiming at generalizations, we can focus on a **particular** reef component geometry — ideally one easy to manufacture — and fine-tune it with the aid of a handful of *parametric* features in order to ensure *optimal* wave attenuation.

Take the rooftop tile-like piece studied for this task in [7, 8].

This shape was chosen so it can both **dampen** the incoming waves and **collect** sand.

Fig. 5: Depiction of the reef component from (a) the side and (b) from the top. Credits: [8]

The response of the reef is then studied in a controlled tank environment where hydraulic experiments are conducted [8]. This allows to ascertain which reef properties are **optimal** in attenuating incoming waves.

*How?* From Fig. 6, it is a simple idea.

From the right, many incoming wave conditions can be generated by means of a paddle, of varying wave height \(H_0\) and wavelength \(L_0\). These can be lumped into a single parameter, the **wave steepness** \(H_0/L_0\).

As the wave propagates and moves over the reef, it will *dampen*.

At a point right after the reef, measurements of the transmitted wave height \(H_t\) lead to a **transmission coefficient** \(C_t = H_t/H_0\), which quantifies the reef protective power.

Fig. 6: Sketch of how the transmission coefficient \(C_t\) is measured. The reef design parameters, which are meant to be optimized, are also depicted. Credits: [8]

For this geometry, only two design parameters are needed:

**Crown width**\(x/B\), where \(B\) is the*crest width*i.e. the reef length across the channel and \(x\) the*cross-shore*size where sediments are deposited.**(Local) submergence ratio**\(l_s/h\), a measure of how tall the structure is (\(l_s\)) with respect to the channel baseline water level \(h\).

The transmission coefficients \(C_t\) are assessed from a multitude of incoming wave conditions by taking a series of 9 measurements along the neighborhood of the reef (depicted and numbered in Fig. 7)

Fig. 7: Hydraulic experiment setup. Waves are generated on the right and propagated toward the reef flat. Credits: [8].

Costal protection entails more than wave attenuation.
Reefs can help mitigate **erosion** and this process can also be studied in this type of experiments.

The reef slope (shown in the setup of Fig. 7) is made with gravel and sand grains to scale.
Precise measures of their displacement allow for *morphological* changes to be tracked in time.

Fig. 8: (top) Preparation setup outlining the composition of the reef slope; (bottom) changes to ramp morphology for different time intervals. Credits: [7]

### Machine-learning the wave attenuation

The relationship between so many parameters is highly nontrivial.
**Neural Networks** are particularly well suited for this sort of task.

By supervising the model with high-quality hydraulic data, the transmission coefficients are **learned** for each wave and reef parameters.

To achieve this, a dataset with 192 configurations, comprised of 7 physically-relevant quantities measured along the channel around the reef are used.

After successfully training, the model **infers** how the coefficient change with respect to those 3 characteristic ratios of the reef, allowing **optimal design parameters combinations** to be found.

Fig. 9: Relationship between the transmission coefficient \(H/H_0\) and the reef design parameters, with respect to: (top) wave steepness; (middle) submergence ratio; (bottom) crown width. Credits: [8]

## Data & Simulation:

A Symbiosis for the Future

Simulating the response to many wave conditions of artificial reef components of arbitrary shapes and materials is a **computationally-intensive** endeavor.

But successful and alternative optimization steps can be taken **incrementally**.

With the aid of hydraulic experiments, high-quality data can be used to train Neural Networks, allowing the behavior on appropriate **reef design features** to be understood and optimal combinations **fine-tuned**.

The symbiosis between simulation and experiments is extremely important and will guide our understanding into more complex domains.

Reefs are truly **multi-functional** structures.

In the next post, we look into how artificial reefs can be used close to beaches… to enhance their surfing conditions

### 🌊 *Hang loose and stay tuned!* 🌊

## References

[2] - Reynolds Number
A standard way to characterize flow regimes is with the aid of the *Reynolds number* \(Re\).

[4] - Reynolds-averaged Navier-Stokes Equations (RANS) In this context, the RANS are used to capture finer, small-scale flow features.

[5] - For the estimates of the coefficients in Fig. 3, a Reynolds number \(Re \approx 10^2\) was used.

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