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Article

Hydrodynamic Modification in Channels Densely Populated with Aquaculture Farms

by
Pablo Cornejo
1,2,*,
Nicolás Guerrero
2,
Marcus Sobarzo
2,3 and
Héctor H. Sepúlveda
4
1
Mechanical Engineering Department, University of Concepcion, Concepcion 4070409, Chile
2
Interdisciplinary Center for Aquaculture Research (INCAR), Concepcion 4070386, Chile
3
Department of Oceanography, Faculty of Natural and Oceanographic Sciences, University of Concepcion, P.O. Box 160-C, Concepcion 4030000, Chile
4
Geophysics Department, Faculty of Physical and Mathematical Sciences, University of Concepcion, Concepcion 4030000, Chile
*
Author to whom correspondence should be addressed.
Submission received: 29 May 2023 / Revised: 19 June 2023 / Accepted: 20 June 2023 / Published: 30 June 2023
(This article belongs to the Special Issue Intensifying and Expanding Sustainable Aquaculture Industry)

Abstract

:

Featured Application

To strengthen the productive and environmental management of the aquaculture industry and serve as a basis for a methodological approach to the estimation of carrying capacity.

Abstract

We predicted small-scale hydrodynamics, including the effect of the aquaculture farming infrastructure, for a region within the group of salmon farm concessions identified in the Chilean regulation as ACS-7. The geographical region corresponds to the Caucahue Channel, composed of two branches connected by a constriction on Caucahue Island, Inland Sea of Chiloe, Chilean Patagonia. The prediction methodology considers the interaction of a regional ocean model and a high-resolution local CFD model. The model prediction was validated using available data from ADCP. We find that the Caucahue Channel is characterized by a complex circulation and hydrodynamics, including an unstable shear flow, with meanders and turbulent structures, and retention zones. Results show the aquaculture infrastructure has a non-local hydrodynamic effect. Differences in horizontal and vertical velocity can be quite significant even far from aquaculture centers, reaching up to 300% and 170%, respectively, in simulations without taking its effects into account. The useful characteristics of this predictive approach and its potential use in particle tracking and species diffusion prediction allow for the use of projecting as a tool for strengthening the environmental and productive management of this industry.

1. Introduction

Over the last 30 years, the Chilean aquaculture industry has experienced sustained growth, positioning the country as the second-largest producer of salmonids and one of the 10 world leaders in aquaculture production [1]. This is in part due to good environmental conditions, low labor costs, and a public and private ecosystem that has encouraged and permitted its development [2]. Thus, the fisheries and aquaculture macro-export sector is the third most important in Chile, with a value that represents 9.5% of all exports (January 2020) [3]. In addition, it is estimated that in Chile, where the number of indirect jobs could be highly underestimated [4], the salmon industry provides some 30,000 direct jobs and 14,500 indirect jobs [5].
The growth of this productive sector has not been free of sanitary and environmental problems. Currently, there is evidence of local eutrophication and changes in biodiversity in areas surrounding farms [6]. In addition, there is record of some negative impacts on the ecosystem [7,8,9], such as habitat loss [10], pollution [11], escapes, genetic interaction with non-native species and wild populations [12,13,14], disease transmission [15,16], and dissolved inorganic wastes that increase the risk of algal blooms [17].
Salmon farms discharge nutrients, chemicals, and pharmaceuticals into the environment, whose ecological and biological impacts can potentially be long-lasting [11]. Different types of antibiotics have been found in native fish near the farm cages [18], where different antibiotic-laden biological wastes could modify the resistance of benthic bacteria [19,20,21,22].
In 2007, a sanitary crisis interrupted the growth of this industry and forced a normative restructuring around new regulations, as it became evident that the Chilean salmon industry was not sustainable [2]. The most substantial innovation resulting from this crisis was the designation of groups of salmon concessions known as salmon neighborhoods in the 2010 reform [23]. The neighborhoods or salmon concession groups are intended to organize and separate production areas to manage pathogens through controlled monitoring and control the spread of disease [24]. Neighborhoods are intended to maintain the biosecurity of a set of facilities; however, there is no evidence to support the fact that one neighborhood is not connected to another one. For example, the residual circulation given by non-linear tidal current effects in the Caucahue Channel (ACS-7, Chiloe Inland Sea, Chilean Patagonia) could become a non-trivial connection and a source of pathogen transport to other neighborhoods [25].
In the last decade, some significant advances were made in the application of new techniques to determine the environmental impacts of aquaculture: geospatial technology to measure the evolution of water bodies and the extent of areas used for aquaculture [26,27], geographic information systems (GIS), and remote sensing for maintaining water resources and controlling pollution in an area [28]. On the other hand, predictive models based on numerical simulation have become important tools for assessing the impacts and interactions of open-water aquaculture systems [29,30,31,32,33]. In the same way, tools such as DEPOMOD have been integrated into the administration and management systems of this industry [34].
While Eulerian measurements of currents for short periods of time may be useful for sizing anchorages, they are insufficient to characterize the dispersion of diluted elements in fish farms, which are immersed in a complex environment that requires a complete hydrodynamic characterization of the site condition [35,36], which contrasts with the requirements of current Chilean regulations [37].
Regarding current simulation tools, black box local models, such as Depomod [34], do not consider the hydrodynamic effect of the nets that confine the fish in the farming cages and do not account for the transport of dilute nutrients available in the water column discharged from the aquaculture farms. Another class of models employed in aquaculture is one based on regional oceanography [38,39,40,41]. Although the application of this class of models in the hydrodynamic prediction of fjords and channels seemed quite straightforward, in practice, their implementation considers low resolutions that significantly filter out the coastline and bathymetry and do not include the hydrodynamic effect of aquaculture farms. Some of these models resolve submesoscale processes (resolution of a few kilometers), and a higher level of detail has been achieved through the use of nested domains reaching horizontal resolutions of hundreds of meters [42]. This leads to an inadequate representation of the circulation, characterizing the hydrodynamic behavior with a typical length scale an order of magnitude larger (order of kilometers) than the characteristic scale length of the local environmental impacts of this industry, which include regions affected by dilution, transport, sedimentation and diffusion of uneaten food, and feces and the excretion of fish (order of meters [43]), making the results from ocean models incompatible with the information requirements for the environmental management of this productive activity.
As an alternative to the limitations found in regional ocean models and black box models, advanced simulation tools based on Computational Fluid Dynamics were adopted in the last decade to predict the hydrodynamics of aquaculture centers immersed in sites with small-scale topographic and bathymetric characteristics [44,45,46,47,48,49,50,51,52]. This approach has shown important advantages over traditional simulation methods, such as high resolution, realism in the representation of bathymetry and coastline, explicit representation of the hydrodynamic effect of cages and mussel lines, and ability to predict sedimentation of solids and diffusion of dissolved elements, among others. The characterization of the small-scale circulation of channels and fjords and the predictions of hydrodynamic characteristics of aquaculture centers allow for the evaluation of environmental impacts and strengthening of environmental management, contributing to the sustainable growth of this activity. The objective of this work is to apply a simulation approach based on Computational Fluid Dynamics for a region of the Chiloe Inland Sea at Chilean Patagonia, which is recognized by the massive installation of aquaculture centers for salmon grow-out and mussel production. According to Chilean regulations, this area (Caucahue Channel) corresponds to the association of salmonid concessions (ACS) 7; it is formed by two branches connected through a constriction in Caucahue Island. In the first manuscript, the predictions resulting from the simulation will be compared with in situ ADCP data in order to evaluate the model performance and predict the hydrodynamic effects of aquaculture centers over small-scale hydrodynamics. In a second manuscript, the approach will be complemented with a Lagrangian model for particle tracking in order to study some environmental impacts and sanitary connections between fish and mussel farms.

2. Methods

2.1. Simulation Methodology

Figure 1 shows the simulation methodology flowchart followed for the hydrodynamic simulation of the Caucahue Channel. The methodology is based on the interaction of two simulation frameworks: the first one is based on a Regional Oceanic model (CROCO) wherein the resolution is of the order of hundreds of meters, oriented to predict the large-scale circulation to force a second local modeling approach, based on a Large Eddy Simulation (LES) model implemented in a Computational Fluid Dynamics (CFD) framework, with a resolution of the order of meters, focused on predicting the small-scale circulation characteristics of the channel and the local hydrodynamic behavior of aquaculture farms.
The CROCO model corresponds to a new version of the ROMS AGRIF model [39]. It is a three-dimensional, non-hydrostatic, free-surface numerical model that solves the primitive equations of ocean fluid dynamics on vertical coordinates that follow the bathymetry [38]. This model is used to describe the large-scale circulation of the Chilean Inland Sea (CIS), considering several nested domains. This model has been used in many CIS simulations, such as [47,50,51,53], validating its good performance compared to ADCP data.
To implement the communication between the regional ocean model and local CFD model, we used user-defined functions (UDF) in order to force the hydrodynamic variables at boundary conditions and define the fluid properties.

2.2. Local CFD Model: Small-Scale Circulation of Channel and Hydrodynamics of Aquaculture Farms

Advanced simulation tools based on Computational Fluid Dynamics were adapted for the implementation of the local hydrodynamic model. The characteristics of this adaptation have been reported in previous works [47,50,51,54]. The model solves the governing equations corresponding to the conservation laws of mass, momentum, and energy, plus an equation for salinity conservation and the equation of state or seawater that links density to a number of state variables: temperature, pressure, and salinity. The turbulent character is described through a modified Large Eddy Simulation (LES) formulation proposed in the works of [55], which combines a mixing length model with a modified Smagorinsky model [56] with the wall-damping function of Piomelli [57]. Thus, the version of the modeling LES approximation corresponds to the algebraic Wall Modeled LES (WMLES). This model is forced using results from the regional model, including currents and wind stress.

2.3. Fish Farm Modelling

Several fish farms are massively installed in the Caucahue Channel. All these farms are made up of cages of different sizes and shapes. In the local CFD model, the hydrodynamic effect of these cages is explicitly described [47]. The cage nets are considered as a semi-permeable porous membrane characterized by a known relationship between the pressure drop or the drag force and the incident velocity [58]. This relationship was determined experimentally for nets of different geometries and drag levels [59]. The hydrodynamic effect of cages over the currents is represented physically as a sink in the momentum conservation equation. This sink is described by a porous medium following Darcy’s law plus an additional inertial term. The porous medium and, therefore, the hydrodynamic effect of the cages is determined by the porosity of the nets, the netting characteristics, the thickness, and the level of biofouling. The latter was previously studied and characterized [60].

2.4. Modelling Mussel Drop Farms

Mussel farming in the Caucahue Channel is carried out on long lines of buoys, which in some cases extend for more than 100 m. On these lines, ropes with mussels are kept suspended up to a depth of 8 m. Physically, mussel droppers are modeled following the same modelling approach considered for the fish farms. They are considered vertical semi-permeable membranes described as a porous medium, where the characteristics of this porous medium are defined by a known relationship between drag coefficient and incident velocity. This experimental characterization was obtained previously by Xu and Dong [61].

3. Simulation

3.1. Case Description

The Caucahue Channel is situated in the northeastern region of Chiloe Island (42°08′30″ S, 73°28′00″ W), at the westside boundary of the Gulf of Ancud, 32 km south of the Chacao Channel (41°47′00″ S, 73°35′00″ W). The Caucahue Channel is 1 of the 2 connections between the CIS and the open ocean. This channel forms two branches connected to the CIS through its north and south mouths. In this zone, maximum depths reach 120 m. The north and south branches extend for 7.5 and 11 km, respectively, and the width at the connection point with CIS reaches 3.8 km and 2.9 km for the north–south entrances, respectively. Both branches connect at the Quemchi constriction, the shallowest (<40 m) channel zone. The Caucahue Channel houses 13 salmonids farm concessions, including Atlantic salmon, Pacific salmon, and rainbow trout. Besides salmonids farms, there are 38 concessions installed for mussel farms and 6 for seaweed farms. The size of these aquaculture production centers fluctuates between 0.1 and 0.3 km, and the distance between them can be less than 1 km. According to [62], during the last ISAV Chilean epidemic, in the period 2007–2009, only the southern branch of the channel suffered infections. The layout of the salmon and mussel production concessions are shown in Figure 2 in green and red boxes, respectively.

3.2. ADCP Measurements

Current measurements were carried out using an RDI Workhose 300 kHz Acoustic Doppler Current Profiler (ADCP). The sensor was installed at the Quemchi constriction (42°8′31.91″ S; 73°27′52.07″ W) (Figure 2) between 6 June and 4 July 2014. The sampling time interval was 600 s.

3.3. Regional Model

The regional ocean simulations were run by employing the Coastal and Regional Ocean Community model. The domain extends meridionally between 41° S to 47° S and zonally from 79° W to 72° W, as shown in Figure 3. This model has a horizontal resolution of 1/72° and considers 32 vertical levels. The bathymetry was built upon a mixture of data from GEBCO08 [62] and data provided by the Chilean Hydrographic and Oceanographic Service (SHOA). The minimum depth considered reached 10 m, and the shoreline was enhanced to include the main fjords and channels of the CIS based on topographic information from SHOA. For initial conditions, the World Ocean Atlas 2009 [63,64] was used. Tide forcing was considered using surface elevation and barotropic velocity components from the TOPEX/Poseidon global tide inverse solution (TPXO8 [65]). The free surface was considered by forcing heat and wind fluxes from NCEP2 [66]. Ten tidal constituents were employed simultaneously: four semi-diurnal components (M2, S2, N2, K2); four diurnal components (K1, O1, P1, Q1); and the long lunar period tides Mf and monthly Mm. The simulation period chosen was June–July 2014 due to the availability of ADCP data.

3.4. Local CFD Model

The local CFD model was implemented within the framework of the multipurpose code for CFD ANSYS FLUENT modified to describe geophysical fluids dynamics [50,51,54]. For the open boundaries, we used outputs from regional ocean simulations. The fish farms and mussel lines were described using a porous medium approximation. Several UDFs were written to communicate regional and local models, adding the Earth’s rotation effect and calculating density using an equation of state. The simulation was run using a pressure-based solver with a transient formulation. The spatial discretization was set up using Cell-Based Least Squares for gradients calculations, second-order terms for pressure, a Bounded Central Differencing and second-order upwind schemes for momentum equation and energy equation, and the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method for the coupling of continuity and momentum equations. We used a second-order implicit scheme with a time-step of t = 60 s, and we considered 0.001 for the residuals of all the equations for each time step. Simulations were run using a CPU Intel Core i9 10900F 10 cores 2.8 GHz/Ram 16GB 2666MHz × 2/GeForce GTX 1660 6GB. The region under analysis is shown in Figure 4. The computational representation of this region is shown in Figure 5. In this local model, bathymetry and coastline were built upon information provided by the Chilean Hydrographic and Oceanographic Service (SHOA). The depth in the local CFD model varies between 0 and 120 m.
Control volume was discretized using a computational grid of 2.1 million cells. Figure 6, Figure 7, Figure 8 and Figure 9 show different views of the grid. The horizontal resolution was considered between 1 m and 30 m, where the highest resolution is found within the fish and mussel farms. Depth was discretized with 16 non-uniformly spaced levels.

4. Results

Using the simulation methodology described in the previous sections, we simulated three days of the small-scale circulation considering successive floods and ebb tide corresponding to semi-diurnal variability in the period between 19 and 21 June 2014. In order to investigate the hydrodynamic effects associated with the presence of massively installed aquaculture infrastructure in the Caucahue Channel, two simulations were run: one considering the hydrodynamic effect of fish and mussel farms and the other without considering its effect. Model predictions from the simulated period are in good agreement with data from ADCP measurements. Figure 10 shows the comparison of the velocity magnitude predicted by the local CFD model and the ADCP data measured in situ in the constriction of the Caucahue Channel. Figure 11 shows this comparison in the form of a scatter plot. The dotted red line shows the level of correlation associated with R∼0.81.
Figure 12 and Figure 13 show the predicted circulation at the northern and southern branches of the constriction for the simulation considering the hydrodynamic effect of aquaculture infrastructure. Figures show the velocity vector field colored by velocity magnitude. Both the northern and southern branches of the Caucahue Channel develop a complex circulation, which is characterized by a highly unstable shear flow involving the interaction of meanders and turbulent structures associated with recirculation and retention zones. The presence of these turbulent structures is more significant in the southern branch, while the northern branch shows a more uniform circulation. At 30 m depth, the southern branch shows a large semi-permanent recirculation, present in both flood and ebb tide conditions.
The southern branch of the Caucahue Channel contains the most fish and mussel farming concessions; at the time, this region developed the most complex circulation, and in the history of sanitary conflicts, this region was affected by the large 2007–2009 ISAV outbreak [67].
Figure 14 shows transect AB axially crossing the southern branch of the Caucahue Channel. Figure 15, Figure 16, Figure 17 and Figure 18 show the comparison of simulations considering the fish and mussel farms installed and simulation without considering its hydrodynamic effect for the horizontal velocity magnitude, vertical velocity, turbulent viscosity, and z-vorticity and for the flood and ebb tide at 15 m and 30 m depth, which follow the ABA transect. Results show the hydrodynamic effect of the aquaculture infrastructure over the channel’s hydrodynamics is not local but spreads far from them, showing significant differences between the distribution of hydrodynamic variables obtained in the simulations considering the installation of farming centers compared with the simulations that do not consider its effect. In the case of turbulent viscosity, associated with the diffusion of dissolved elements, this difference is more significant in shallower waters. Regarding the horizontal velocity magnitude, the installation of farming centers implies differences that can generate a decrease of 81% for flood tide and 30 m depth and an increase of 300% for ebb tide and 30 m depth. In the case of vertical velocity, the presence of centers can decrease its magnitude up to 13% at 30 m depth and flood tide or increase by 170% at 30 m depth and ebb tide. On the other hand, for vertical vorticity, the presence of farming centers can decrease its magnitude by 20% at a 15 m depth and a flood tide, while at an ebb tide and 30 m depth, it can increase by 700%.

5. Discussion

The growth of the current aquaculture industry is stressed by the increase in protein demand and the need to significantly reduce environmental impacts, and this in a context where current concepts, methods, and technology are saturated; that is, in recent decades, the progress in improving efficiency [68] and decreasing environmental impacts is stalled. This reality has an obvious significance: new concepts, methods, and technologies need to be developed and introduced that imply paradigmatic changes and significant improvements in productive efficiency and environmental impacts.
Results allowed a complex characterization of the small-scale circulation, predicting an unstable shear flow, including the interactions of meanders and turbulent structures. This characterization moves away from the preconceived visions that oversimplify hydrodynamics and circulation, assuming uniform currents and considering the fish and mussel farms are installed in zones with homogeneous conditions where a single Eulerian measurement of currents of a short period of time can characterize their hydrodynamic behavior (for Chilean regulation [37]). Knowing the characteristics of the small-scale circulation in channels and fjords as well as the hydrodynamic behavior of farming centers for the complete production cycle is a necessary and fundamental condition to effectively and realistically determine the main environmental impacts of this activity on the ecosystem, i.e., whether an area is ecologically affected by the transport of dissolved elements available in the water column such as nutrients, drugs, and cleaning chemicals or whether an area is affected by the sedimentation of organic matter [43,69]. The results presented in the previous section showed certain significant non-local hydrodynamic effects. This hydrodynamic modification should impact the vertical transport and diffusion of substances transported by currents. Therefore, a methodology that aims to predict environmental impacts should necessarily consider the hydrodynamic effect of aquaculture infrastructure. The territorial management of aquaculture concessions, as well as the strengthening of environmental management, demands the ability to predict the environmental impacts of aquaculture realistically and accurately. The proposed methodology has several advantages over standard approaches based on black box models such as Depomod [34] or regional oceanography models like Roms, Croco, Fvcom, Mike, etc. [38,39,40,41]: small-scale bathymetry and coastline, high resolution, explicit representation of the hydrodynamic effect of fish and mussel farms, and possible direct match with particle dispersion models and diffusion of dissolved elements [44,45,46,47,48,49]. In this sense, the application of regional models by themselves does not seem to be adequate to account for the environmental impacts of aquaculture centers because their resolution is not compatible with the scale length of these environmental impacts. The proposed simulation approach is based on the adaptation of CFD simulation tools to the description of geophysical fluids dynamics that feels Earth’s rotation and stratification [47,50]. A hydrodynamic model implemented in the framework of a CFD code can be extended for the prediction of the lagrangian trajectory of particles and the diffusion of species transported by currents; in this sense, the simulation approach described in the present manuscript constitutes the base for a potential predictive tool to address the environmental impacts of the aquaculture industry and identify the interconnection between centers of a neighborhood whose link is related to the spread of caligus and bacterial diseases (SRS) in complex channels and fjord systems. The extension of the CFD model in the solution of an additional conservation equation to account for oxygen transport would also allow us to predict its distribution inside fish and mussel farms, with potential use as a tool to design, size, and test the performance of continuous oxygen injection systems. This implementation would be quite straightforward in state-of-the-art CFD packages like ANSYS FLUENT, Flow3D, OpenFOAM, etc.
The present simulations results, together with previously reported evidence that confirms the link between the velocity magnitude inside fish farms and the growth rate and FCR [70,71,72], allow for the projection of the foundations for the consideration of farms with a differentiated number of fish according to the distribution of the velocity magnitude within each cage during the productive cycle, i.e., the aquaculture industry can enhance its productivity by the proper use of hydrodynamics predictions.
This type of numerical tool is oriented towards the description of representative scenarios of the main modes of circulation. It is possible to study representative scenarios of different times of the year or scenarios describing extreme events that have some utility for productive or environmental management. However, its high spatial and temporal resolution and consequent high computational cost do not allow simulation for long periods of time.

6. Summary and Conclusions

We describe the small-scale circulation, including the hydrodynamic effect of the aquaculture farms located in a part of the group of salmonid concessions identified in the Chilean regulation as ACS-7, which is composed of two channels connected by an island constriction, Caucahue Channel, Inland Sea of Chiloe, Chilean Patagonia. For such purposes, we used a simulation methodology that considers the interaction of a regional oceanography model and a high-resolution local CFD model. Results show a complex circulation in both branches of the Caucahue Channel, predicting an unstable shear flow, including interacting meanders and turbulent structures associated with recirculation and retention zones. The southern branch presented semi-permanent turbulent structures, which made the circulation less ventilated, which is consistent with the history of sanitary conflicts, including the large 2007–2009 ISAV outbreak, which affected this branch.
This hydrodynamic characterization moves away from preconceived visions that oversimplify circulation and hydrodynamics of channels and fjord systems. This is important, provided the hypothesis of oversimplifying circulation and hydrodynamics is based the productive and environmental management.
We found a non-local hydrodynamic effect of the aquaculture infrastructure; the modification over currents spreads far from them, manifesting in some areas with significant differences between the distribution of hydrodynamic variables obtained in the simulation considering the installation of fish and mussel farms.
Coupling the local CFD model with a Lagrangian model for particle tracking and a diffusion model for the species transport would enable this simulation approach to be used as a potential tool to predict the environmental impacts of the aquaculture industry and help to strengthen the productive and environmental management of this productive activity.

Author Contributions

Conceptualization, P.C.; methodology, P.C.; software, N.G.; validation, P.C., M.S., and H.H.S.; formal analysis, P.C.; investigation, N.G.; resources, M.S. and H.H.S.; data curation, M.S. and H.H.S.; writing—original draft preparation, P.C.; writing—review and editing, P.C. and N.G.; visualization, N.G.; supervision, P.C.; project administration, P.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Interdisciplinary Center for Aquaculture Research, INCAR (ANID; FONDAP 5110027).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data from the numerical simulations can be obtained from the authors upon request.

Acknowledgments

P. Cornejo, N. Guerrero and M. Sobarzo acknowledge the Interdisciplinary Center for Aquaculture Research, INCAR (ANID; FONDAP# No 15110027 and 1522A0004).

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Simulation methodology.
Figure 1. Simulation methodology.
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Figure 2. Caucahue Channel. Position of the ADCP is indicated by a blue dot. Salmon and mussel concessions are shown in green and red boxes.
Figure 2. Caucahue Channel. Position of the ADCP is indicated by a blue dot. Salmon and mussel concessions are shown in green and red boxes.
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Figure 3. Regional ocean model of CIS, source [52].
Figure 3. Regional ocean model of CIS, source [52].
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Figure 4. Region under analysis for Caucahue channel (A) 1st area (B) 2nd area (C) 3rd area, and (D) 4th area.
Figure 4. Region under analysis for Caucahue channel (A) 1st area (B) 2nd area (C) 3rd area, and (D) 4th area.
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Figure 5. Computational representation of Caucahue Channel; (A) view to the northern branch of the channel, (B) view to the southern branch of the channel.
Figure 5. Computational representation of Caucahue Channel; (A) view to the northern branch of the channel, (B) view to the southern branch of the channel.
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Figure 6. Discretization of fish and mussel farms.
Figure 6. Discretization of fish and mussel farms.
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Figure 7. Computational grid 3D view.
Figure 7. Computational grid 3D view.
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Figure 8. Computational grid top view.
Figure 8. Computational grid top view.
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Figure 9. Computational grid, discretization near fish and mussel farms.
Figure 9. Computational grid, discretization near fish and mussel farms.
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Figure 10. Velocity magnitude at Caucahue Channel’s constriction: model predictions vs. ADCP data.
Figure 10. Velocity magnitude at Caucahue Channel’s constriction: model predictions vs. ADCP data.
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Figure 11. Velocity magnitude at Caucahue Channel’s constriction: scatter plot, R∼0.81.
Figure 11. Velocity magnitude at Caucahue Channel’s constriction: scatter plot, R∼0.81.
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Figure 12. Small-scale circulation at northern branch of Caucahue Channel: (a,b) flood and ebb tide, 15 m depth; (c,d) flood and ebb tide, 30 m depth.
Figure 12. Small-scale circulation at northern branch of Caucahue Channel: (a,b) flood and ebb tide, 15 m depth; (c,d) flood and ebb tide, 30 m depth.
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Figure 13. Small-scale circulation at southern branch of Caucahue Channel: (a,b) flood and ebb tide, 15 m depth; (c,d) flood and ebb tide, 30 m depth.
Figure 13. Small-scale circulation at southern branch of Caucahue Channel: (a,b) flood and ebb tide, 15 m depth; (c,d) flood and ebb tide, 30 m depth.
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Figure 14. AB transect.
Figure 14. AB transect.
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Figure 15. Hydrodynamic effect of fish and mussel farms: horizontal velocity magnitude.
Figure 15. Hydrodynamic effect of fish and mussel farms: horizontal velocity magnitude.
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Figure 16. Hydrodynamic effect of fish and mussel farms: vertical velocity.
Figure 16. Hydrodynamic effect of fish and mussel farms: vertical velocity.
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Figure 17. Hydrodynamic effect of fish and mussel farms: turbulent diffusion.
Figure 17. Hydrodynamic effect of fish and mussel farms: turbulent diffusion.
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Figure 18. Hydrodynamic effect of fish and mussel farms: z vorticity.
Figure 18. Hydrodynamic effect of fish and mussel farms: z vorticity.
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Cornejo, P.; Guerrero, N.; Sobarzo, M.; Sepúlveda, H.H. Hydrodynamic Modification in Channels Densely Populated with Aquaculture Farms. Appl. Sci. 2023, 13, 7750. https://0-doi-org.brum.beds.ac.uk/10.3390/app13137750

AMA Style

Cornejo P, Guerrero N, Sobarzo M, Sepúlveda HH. Hydrodynamic Modification in Channels Densely Populated with Aquaculture Farms. Applied Sciences. 2023; 13(13):7750. https://0-doi-org.brum.beds.ac.uk/10.3390/app13137750

Chicago/Turabian Style

Cornejo, Pablo, Nicolás Guerrero, Marcus Sobarzo, and Héctor H. Sepúlveda. 2023. "Hydrodynamic Modification in Channels Densely Populated with Aquaculture Farms" Applied Sciences 13, no. 13: 7750. https://0-doi-org.brum.beds.ac.uk/10.3390/app13137750

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