# Development of a Kelp-Type Structure Module in a Coastal Ocean Model to Assess the Hydrodynamic Impact of Seawater Uranium Extraction Technology

^{*}

## Abstract

**:**

^{2}). There is concern however that the large scale deployment of adsorbent farms could result in potential impacts to the hydrodynamic flow field in an oceanic setting. In this study, a kelp-type structure module based on the classic momentum sink approach was incorporated into a coastal ocean model to simulate the blockage effect of a farm of passive uranium extraction devices on the flow field. The module was quantitatively validated against laboratory flume experiments for both velocity and turbulence profiles.Model results suggest that the reduction in ambient currents could range from 4% to 10% using adsorbent farm dimensions and mooring densities previously described in the literature and with typical drag coefficients.

## 1. Introduction

^{2}[4].

^{2}. The submerged farm closely resembles a kelp forest, which is known to exert a substantial drag on coastal currents [6]. Hence, there is concern that the large scale deployment of adsorbent farms could result in potential impact to the hydrodynamic flow field in an oceanic setting.

## 2. Methodology

#### 2.1. Kelp-Type Structure Module Development

^{3}), C

_{d}= drag coefficient of the equivalent (cylindrical) braid or kelp structure, A = flow-facing area of the adsorbent braid or kelp frond (m

^{2}), A = diameter × length for cylinders, and = velocity vector (m/s).

_{x}, F

_{v}) are the horizontal momentum diffusivity terms in the x and y directions, respectively; K

_{m}is the vertical eddy viscosity coefficient; ρ is water density; p is pressure; and f is the Coriolis parameter. F

_{x}

^{M}and f

_{y}

^{M}are the momentum sink term (m/s

^{2}) induced by the uranium adsorbent device that was added to the original FVCOM governing equations [10,14], and is defined as the following general form:

_{c}= momentum control volume in which the adsorbent device is deployed (m

^{3}), N = the number of adsorbent braids deployed within the same momentum control volume, and the rest terms were defined previously in Equation (1).

_{e}= triangular element surface area (m

^{2}), Δ

_{σ}D = σ-layer thickness (m), R

_{u}and R

_{v}= all the remaining momentum terms including advection, diffusion, and pressure gradient. The right hand side of Equations (5) and (6) represents the volumetric momentum sink rate (m

^{4}/s

^{2}) contributed by the adsorbent braid or kelp frond defined in Equation (1), and A

_{σ}= flow-facing area of braid adsorbent within the σ-layer.

#### 2.2. Module Validation

**Figure 1.**Schematic of the experimental flume setup (adapted from Plew [15], with permission from © 2011 American Society of Civil Engineers). Cylinders were arranged in rows with a spacing of L (m) in the direction of flow, and a transverse spacing of B (m) between cylinders. Velocity measurements were taken at a distance of 4 m from the inlet. H (m) is the total water depth in the flume, h

_{c}(m) is the canopy height, and h

_{g}(m) is the distance between the canopy and the flume bed.

Validation Run | H (mm) | h_{g} (mm) | L (mm) | B (mm) | a (m^{−1}) | Q (L/s) |
---|---|---|---|---|---|---|

A | 200 | 100 | 100 | 50 | 1.908 | 10.5 |

B | 200 | 100 | 150 | 50 | 1.272 | 10.1 |

C | 200 | 100 | 200 | 50 | 0.954 | 10.1 |

D | 200 | 100 | 200 | 100 | 0.477 | 10.3 |

_{d}) of the canopy was treated as spatially uniform but its value for each validation run was calibrated based on model-data comparisons. Figure 2b shows the spatial distribution of the cylinder array in Validation Run D. The corresponding model predicted surface velocity field during the baseline condition (without cylinder array) and Run D are presented in Figure 2c,d, respectively. The presence of cylinders significantly altered the flow field. Surface velocity was generally reduced within the cylinder canopy compared to the baseline condition.

**Figure 2.**(

**a**) Finite Volume Coastal Ocean Model (FVCOM) model grid (in the horizontal plane) for the flume experiment. (

**b**) Spatial distribution of cylinders in Run D. (

**c**) Surface velocity field in the baseline condition without the cylinder array. (

**d**) Surface velocity field in Run D.

## 3. Results and Discussion

#### 3.1. Kelp-Type Module Validation

_{d}) of 1.75 was found to provide good model-data comparison in this validation run.

**Figure 3.**(

**a**) FVCOM predicted vertical velocity profiles for Validation Run A. (

**b**) Normalized velocity profiles for validation Run A compared to the experimental measurements.

^{2}/s

^{2}), and K

_{m}= vertical eddy viscosity (m

^{2}/s).

**Table 2.**Error statistics for kelp-type structure module validation runs (R

^{2}denotes the coefficient of determination and RE stands for relative error defined by , where η

^{m}and η° stand for model predictions and laboratory observations, respectively, η

^{o}is the mean of observations).

Validation Run | Velocity | Turbulent Stress | ||
---|---|---|---|---|

R^{2} | RE (%) | R^{2} | RE (%) | |

A | 0.98 | 1.2 | 0.94 | 6.0 |

B | 0.98 | 1.4 | 0.98 | 3.6 |

C | 0.98 | 1.7 | 0.94 | 5.5 |

D | 0.97 | 2.5 | 0.93 | 5.0 |

**Figure 4.**(

**a**–

**d**) Model-data comparisons of normalized mean vertical velocity profiles for Validation Runs A, B, C, and D, respectively. (

**e**–

**h**) Model-data comparisons of normalized mean turbulent stress profiles for Validation Runs A, B, C, and D, respectively.

^{2}) and low relative error (RE) between predicted and measured velocity and turbulent stress values (Table 2). In general, the model captures the vertical structure for both velocity and turbulent stress. For instance, the velocities were significantly attenuated for flows through the cylinders and the maximum turbulence was generated near the middle depth of the water column at the interface between the bottom of the cylinder canopy and the flow immediately below. In addition, as evident from model predictions and laboratory data, higher cylinder density (Parameter a in Table 1) tends to exert a stronger impact on flows. The maximum differences between the model and data occurred in the middle depths of the water column. A better parameterization may be needed at canopy-water interfaces to account for this difference. For example, additional skin friction contributed by the bottom of the cylinder may be considered. This discrepancy could also be contributed by the inadequate characterization of the canopy’s effects on turbulence in the current module, as suggested by other studies [16,17].

_{d}) is a function of canopy density and increases with higher density. For example, the calibrated C

_{d}values for Runs A, B, C and D are 1.75, 1.5, 1.25, and 1.0, respectively. This is also consistent with the findings in other similar studies [9,15,18]. Wu and Wang [18] and Struve et al. [9] reported that C

_{d}values greater than 3.0 were needed to reach a good agreement between model and data. As discussed by Wu and Wang [18], this is presumably due to the inherent dependency of C

_{d}on the Reynolds number (Re). At higher canopy densities, reduced flow velocity and Reynolds number in the model domain lead to larger drag coefficients according to the relationship between C

_{d}and Re for a single cylinder [19]. The validation tests also suggest this. Although the actual C

_{d}values varied with canopy density, a spatially uniform C

_{d}represented the major conditions reasonably well.

#### 3.2. Module Applications—Kelp Forest and Braid Adsorbent Farm Simulation

_{d}) used for this numerical experiment was 0.08 fronds/m

^{2}, which is the average of the observed kelp density range of 0.02 to 0.14 fronds/m

^{2}.

_{d}) of 0.00178 moorings/m

^{2}, much less dense than the kelp forest (0.08 fronds/m

^{2}). The model results suggest that with typical drag coefficient values of 0.2 to 0.5, the reduction in ambient currents by braid adsorbent farms could range from 4% to 10%.

**Figure 5.**(

**a**) Map of the Point Loma kelp forest offshore of the California coast. The dotted line represents a general outline of the kelp canopy (map adapted from Tegner et al. [22] with permission from Elsevier). (

**b**) Predicted potential reductions in ambient currents by the kelp forest and braid adsorbent farm with typical canopy/mooring densities.

## 4. Conclusions

## Acknowledgments

## Conflicts of Interest

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**MDPI and ACS Style**

Wang, T.; Khangaonkar, T.; Long, W.; Gill, G.
Development of a Kelp-Type Structure Module in a Coastal Ocean Model to Assess the Hydrodynamic Impact of Seawater Uranium Extraction Technology. *J. Mar. Sci. Eng.* **2014**, *2*, 81-92.
https://doi.org/10.3390/jmse2010081

**AMA Style**

Wang T, Khangaonkar T, Long W, Gill G.
Development of a Kelp-Type Structure Module in a Coastal Ocean Model to Assess the Hydrodynamic Impact of Seawater Uranium Extraction Technology. *Journal of Marine Science and Engineering*. 2014; 2(1):81-92.
https://doi.org/10.3390/jmse2010081

**Chicago/Turabian Style**

Wang, Taiping, Tarang Khangaonkar, Wen Long, and Gary Gill.
2014. "Development of a Kelp-Type Structure Module in a Coastal Ocean Model to Assess the Hydrodynamic Impact of Seawater Uranium Extraction Technology" *Journal of Marine Science and Engineering* 2, no. 1: 81-92.
https://doi.org/10.3390/jmse2010081