# Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations

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## Abstract

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## 1. Introduction

- Instrument measurement uncertainties are reasonably small and well understood if best practices are followed during instrument deployment and data analysis.
- Extrapolation procedures for tidal energy data are established, but the correct evaluation in site conditions with asymmetric tidal flows is challenging. Incorporating and quantifying wave–current interactions when measuring and predicting the tidal resource is a key uncertainty factor for wave exposed sites.

## 2. Modeling

Site | Description |
---|---|

PTEC, Isle of Wight | Located 2.5 km off the southern tip of the Isle of Wight the site runs east–west for approximately 5 km and is approximately 1 km across. Spring peak flows are up to 4 ms${}^{-1}$. As of 2021, a 30 MW tidal array demonstration project is currently in the planning stages. The site has a potential capacity of 300 MW [26,27]. The mean water depth at the model output point used in this study is 65 m. |

Alderney | Le Raz Blanchard is the highly energetic race between the island of Alderney and the Normandy coast. With spring peak flows of over 5 ms${}^{-1}$ [28]. It is one of the most powerful tidal stream sites in Europe. An initial 7–20 MW array is planned to begin in 2021-2022 with up to 2–3 GW of tidal turbines are planned in the future [29]. It is estimated in [5] that the potential resource is as high as 5.10 GW. The mean water depth at the model output point used in this study is 38 m. |

Guernsey | There are several areas around Guernsey with fast flows that could be suitable for tidal energy extraction. This study looks at Big Roussel, the race between the two small islands of Sark and Herm. It has peak flows of up to 3 ms${}^{-1}$ [30]. Coles et al. [5] estimated that there is a maximum capacity of 0.12–0.24 GW. The mean water depth at the model output point used in this study is 40 m. |

#### 2.1. Effects of Waves on Currents

#### 2.1.1. Stokes Drift and Mass Flux

#### 2.1.2. Streaming

#### 2.1.3. Wave Induced Turbulence

#### 2.1.4. Forcing by Radiation Stress Gradients

#### 2.1.5. Enhancement of the Bed Shear Stresses

## 3. Results and Analysis

#### 3.1. General Characterization

#### 3.2. Difference in Flow between Coupled and Uncoupled Runs

## 4. Analysis

#### 4.1. Stokes Drift

#### 4.2. Enhancement of the Bed Shear Stresses

#### 4.3. Forcing by Radiation Stress Gradients

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The D-Flow FM computational mesh: (

**top**) the entire grid; and (

**bottom**) a subsection of the domain showing the location of the three points of interest: 1, :PTEC; 2, Alderney Race; 3, Guernsey. The extent of the SWAN model domain is shown as the yellow box.

**Figure 3.**Example of the harmonic constituents used to calculate the water level forcing at the boundary. The plot represents the southwest corner of the grid.

**Figure 4.**Summary of wave and current conditions: (

**Top row**) scatter plots of significant wave height, ${H}_{s}$, against mean absolute wave period (as measured in a fixed frame of reference); (

**Middle row**) wave rose; and (

**Bottom row**) current speed versus direction. Note that wave directions are ‘coming from’ and current directions are ‘going to’.

**Figure 5.**Difference in flow power from uncoupled and coupled models against flow power from uncoupled model. Blue points indicate positive easterly components while green points indicate negative easterly components.

**Figure 6.**Difference in current speed from uncoupled and coupled models against current speed from the coupled model (positive when easterly component is positive). The color of points indicates concurrent significant wave height.

**Figure 7.**Difference in current speed from uncoupled and coupled models against relative significant wave height. The color of points indicates concurrent current speed from coupled model.

**Figure 8.**Contours of normalized Stokes drift current ${u}^{S}/{H}_{s}^{2}$ (m${}^{-1}$s${}^{-1}$) as a function of water depth and wave period.

**Figure 9.**Depth-averaged Stokes drift current speeds derived from the wave model for the three sites.

**Table 2.**Mean values of flow power density from uncoupled model, ${P}_{u}$, and percentage difference in flower power density from coupled model, ${P}_{c}$, relative to uncoupled model.

Easterly | Westerly | Overall | ||||
---|---|---|---|---|---|---|

${\mathit{P}}_{\mathit{u}}$ | $({\mathit{P}}_{\mathit{c}}-{\mathit{P}}_{\mathit{u}})/{\mathit{P}}_{\mathit{u}}$ | ${\mathit{P}}_{\mathit{u}}$ | $({\mathit{P}}_{\mathit{c}}-{\mathit{P}}_{\mathit{u}})/{\mathit{P}}_{\mathit{u}}$ | ${\mathit{P}}_{\mathit{u}}$ | $({\mathit{P}}_{\mathit{c}}-{\mathit{P}}_{\mathit{u}})/{\mathit{P}}_{\mathit{u}}$ | |

[kW/m${}^{\mathbf{2}}$] | [kW/m${}^{\mathbf{2}}$] | [kW/m${}^{\mathbf{2}}$] | ||||

PTEC | 4.7 | +7.0% | 3.5 | −8.4% | 4.1 | +0.7% |

Alderney | 5.9 | +7.0% | 8.4 | −9.6% | 7.1 | −2.5% |

Guernsey | 2.0 | +2.6% | 1.5 | −9.0% | 1.8 | −1.5% |

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**MDPI and ACS Style**

Hardwick, J.; Mackay, E.B.L.; Ashton, I.G.C.; Smith, H.C.M.; Thies, P.R.
Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations. *Energies* **2021**, *14*, 3625.
https://doi.org/10.3390/en14123625

**AMA Style**

Hardwick J, Mackay EBL, Ashton IGC, Smith HCM, Thies PR.
Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations. *Energies*. 2021; 14(12):3625.
https://doi.org/10.3390/en14123625

**Chicago/Turabian Style**

Hardwick, Jon, Ed B. L. Mackay, Ian G. C. Ashton, Helen C. M. Smith, and Philipp R. Thies.
2021. "Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations" *Energies* 14, no. 12: 3625.
https://doi.org/10.3390/en14123625