A Numerical Simulation Study on the Distribution Pattern of the Habitat Suitability Index near the New Eco-Revetment Structure for Grass Carp with Different Life Cycles

Abstract

Fish are an important criterion for evaluating the quality of river ecosystems, and water flow characteristics may be the main factor affecting the living environment of fish. As the main component of a river, the topography of the bank slope has a significant impact on the characteristics of nearshore water flow. At the same time, eco-revetment structure has the functions of smoothing water flow, maintaining stable bank slopes, and improving river ecology. It can reset the distribution of nearshore water flow and provide a stable living environment for fish. This study focuses on the middle and lower reaches of the Yangtze River as the research area, with the main research object being grass carp. We construct a generalized model based on river morphology and flow characteristics. A new eco-revetment structure is proposed with the main research area of nearshore waters, aiming to improve the flow state of nearshore water and enhance its ecology. A suitability evaluation model for grass carp habitat was constructed based on Large Eddy Simulation and fuzzy mathematics theory, with water flow as the main habitat influencing factor. We study the distribution pattern of suitability for grass carp habitats near nearshore waters. The results indicate that the nitrogen phosphorus ratio near the top of the revetment structure is close to the Redfield value and can be used as a stable foraging area for fish. The flow rate is the dominant factor for the habitat of juvenile grass carp. When there is no vegetation, the suitability of region A is 0–0.4, the suitability of region B is 0.2–0.6, and the area proportion of the high suitability area (0.4–0.6) is maintained at 10–30% with the increase in the flow rate. Region C is not suitable for the long-term survival of juvenile grass carp. When there is vegetation, the suitability of region A ranges from 0 to 0.6, and the proportion of low-suitability areas decreases. The suitability of region B ranges from 0.4 to 0.6, and the proportion of suitable areas is positively correlated with flow velocity. The suitability of region C is consistent with the absence of vegetation. The dominant factors for fish spawning habitat are flow velocity, vorticity, and kinetic energy gradient. The spawning suitability zone (HSI ≥ 0.6) is located between the spanwise structures, with a proportion positively correlated with flow velocity and higher suitability on the deep-water side. The existence of fish has little impact on the habitat. In the juvenile fish habitat area, the proportion of areas suitable for juvenile fish in region A has slightly decreased, and the suitability of region B has increased. In spawning grounds, an HSI ≥ 0.6 accounts for about 5% of the decrease compared to no-fish conditions, and overall can meet the needs of fish habitat, foraging, and spawning. This article provides ideas and foundations for the design of future new eco-revetment structures and a suitability analysis of living environments for fish.

1. Introduction

Fish, as an important component of river ecosystems, can serve as a crucial indicator for evaluating the quality of river ecosystems. The habitat environment is an important condition for ensuring the integrity of river ecosystems and is an important component of river ecosystems [1]. The main functions of fish habitats are foraging, spawning, daily survival, and emergency shelter. Wintering grounds, spawning grounds, feeding grounds, and migration channels are mainly summarized as the “three fields and one channel” of fish habitats [2].

There are many factors that affect the survival of fish, and environmental factors mainly include food, temperature, oxygen content, pH value, and hydraulic characteristics [3,4,5,6]. Researchers explore the intrinsic relationships among various ecological factors, providing theoretical basis and technical support for fish habitat protection [7,8,9,10,11,12]. With fish habitat requirements as the core ecological constraint factor, a scientifically reasonable ecological scheduling process has been constructed [13]. Hydraulic characteristics, as a key environmental factor affecting fish habitats, mainly include parameters such as flow velocity, water depth, turbulence intensity, and flow velocity gradient. Their spatial distribution characteristics directly determine the habitat and aggregation areas of fish, and are the core entry point for studying fish behavior response mechanisms [14,15]. Winger [16] et al. found that velocity gradients in habitats are important water flow characteristics that affect the survival of Atlantic cod. Sanagiotto [17] predicted the existence of a suitable water flow characteristic standard for migratory fish survival by quantitatively analyzing the water flow characteristics in the fishway. Liao [18] found through literature review and theoretical analysis that the direction of vortices plays a crucial role in maintaining stability for fish, such as trout and Atlantic salmon. Cai [19] and others summarized and analyzed the swimming ability of Chinese cyprinid fish and established an estimation formula, providing a reference for the construction of fish passage facilities in the future. Cao [20] analyzed the response of grass carp swimming behavior to rapidly changing water flow velocity through physical experiments.

Bank slope is an important component of river channel, serving as a link for material information energy exchange between aquatic organisms and water flow, and is the primary habitat for fish. Human activities restrict the development of natural river channels, leading to a decrease in ecological water demand for habitats and causing serious damage to fish habitats, disrupting the original stability of fish habitats and affecting their survival [21,22,23,24]. Eco-revetment, in the construction of river bank slopes, radiates to the bank slope and its surrounding waters, providing a stable living environment for aquatic organisms while ensuring smooth nearshore water flow and stable bank slopes.

The black carp, grass carp, silver carp and bighead carp, as the “the four famous domestic fishes”, are the most important economic fish species in the Yangtze River and play a very important role in freshwater fisheries. They have the habits of growing in lakes, spawning in rivers, and migrating between rivers and lakes. They are typical semi-migratory fish in rivers and lakes. Grass carp is the most famous of the four famous domestic fishes. Grass carp is a typical herbivorous fish. It lives in rivers and lakes in the plain area, and generally prefers to live in the middle and lower layers of the water and near shore areas with many aquatic plants. Grass carp have strong reproductive ability, and laying eggs requires a certain flow rate and turbulence. They cannot reproduce under still water conditions [25].

Based on the above, this study focuses on the middle and lower reaches of the Yangtze River as the research area, with the main research object being grass carp. We construct a generalized model based on river morphology and flow characteristics. A new eco-revetment structure is proposed with the main research area of nearshore waters, aiming to improve the flow state of nearshore water and enhance its ecology. A suitability evaluation model for grass carp habitat was constructed based on Large Eddy Simulation and fuzzy mathematics theory, with water flow as the main habitat-influencing factor. We study the distribution pattern of suitability for grass carp habitats near nearshore waters.

Compared with previous studies, the innovation of this study lies in combining the design of a new eco-revetment structure with the study of fish habitats based on Large Eddy Simulation and fuzzy mathematics theory. The revetment structure improves water flow diversity by changing the water flow characteristics near the shore, creating a living environment for fish. The fish habitat evaluation model and new eco-revetment structure proposed in this study provide a scientific basis for the fish living environment and ecological river construction.

2. Materials and Methods

2.1. Design of New Eco-Revetment Structure

The design idea of the new bank protection structure proposed in this study is to smooth the flow, prevent bank slope erosion, provide a stable living environment for aquatic organisms, and promote energy material information exchange. The actual dimensions of the structure are shown in Figure 1a. The bottom dimension of the eco-revetment block is 230 mm, the top dimension is 150 mm, and the height is 200 mm. The top is perforated, and the interior of the structure is designed as a cavity. The circular arc surface connects the upper and lower parts. The upper circular arc design ensures the smooth flow of water and increases the contact surface between the water flow and the outer wall of the structure, so as to increase the living space of aquatic organisms. The circular arc design at the bottom ensures that the arrangement of the revetment structure generates gaps that can be used as drainage channels. The side-wall circular opening design increases the material information energy exchange between structures and improves the richness of flow characteristics, as shown in Figure 1b. In this study, the new eco-revetment structure will be placed on both sides of the straight river section, mainly on the bank slope of the water level fluctuation zone.

2.2. Large Eddy Simulation

In the study of hydraulic characteristics of nearshore water flow and sediment transport on bank slopes, numerical models have greater degrees of freedom. They can more accurately and intuitively observe the complex instantaneous flow state of water flow and sediment transport.

This study is based on the CFD software ANAYS Fluent 19.0 and mainly uses the Large Eddy Simulation (LES) turbulence model. The working principle of the LES turbulence model is to divide fluid flow into large-scale flow and small-scale flow. Large-scale flow is sensitive to boundaries, and currently there is no suitable universal turbulence model to simulate large-scale flow under different boundary conditions. It mainly simulates and solves directly based on Navier–Stokes (N-S) equations. The turbulence model directly filters small-scale flows through filtering. For small-scale flows, it has isotropic properties and is less affected by boundary conditions. By establishing a subgrid scale model for simulation, the subgrid scale model has universality for small-scale flows.

2.2.1. Flow Control Equation

The basic equation of the turbulence model is the classical Navier–Stokes equation. This section simulates incompressible fluid, and the equations are as follows:

Continuity equation:

$${\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}=0$$

(1)

Momentum equation:

$${\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}}{\partial \mathrm{t}}}+{\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{j}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}=-{\displaystyle \frac{1}{{\rho }_{\mathrm{t}}}}{\displaystyle \frac{\partial \mathrm{p}}{\partial {\mathrm{x}}_{\mathrm{i}}}}+\upsilon {\displaystyle \frac{{\partial }^2{\mathrm{u}}_{\mathrm{i}}}{\partial {\mathrm{x}}_{\mathrm{j}}{\partial }_{{\mathrm{x}}_{\mathrm{j}}}}}+{\mathrm{f}}_{\mathrm{i}}$$

(2)

where u_i represents instantaneous velocity in x_i (i represents x, y and z).

f_i represents the mass force component in the x_i direction.

Υ stands for viscosity coefficient.

p is the instantaneous pressure on the computational grid.

The filtered N-S equations are as follows:

Continuity equation:

$${\displaystyle \frac{\partial \overline{{\mathrm{u}}_{\mathrm{i}}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}=0$$

(3)

Momentum equation:

$${\displaystyle \frac{\partial \overline{{\mathrm{u}}_{\mathrm{i}}}}{\partial \mathrm{t}}}+{\displaystyle \frac{\partial \overline{{\mathrm{u}}_{\mathrm{i}}}\overline{{\mathrm{u}}_{\mathrm{j}}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}=-{\displaystyle \frac{1}{{\rho }_{\mathrm{t}}}}{\displaystyle \frac{\partial \overline{\mathrm{p}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}+\upsilon {\displaystyle \frac{{\partial }^2\overline{{\mathrm{u}}_{\mathrm{i}}}}{\partial {\mathrm{x}}_{\mathrm{j}}{\partial }_{{\mathrm{x}}_{\mathrm{j}}}}}-{\displaystyle \frac{\partial {\tau }_{\mathrm{ij}}^{\mathrm{SGS}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}$$

(4)

where the subgrid stress is expressed as ${\tau }_{\mathrm{ij}}^{\mathrm{SGS}}=\overline{{\mathrm{u}}_{\mathrm{i}}{\mathrm{u}}_{\mathrm{j}}}-\overline{{\mathrm{u}}_{\mathrm{i}}}\overline{{\mathrm{u}}_{\mathrm{j}}}$.

2.2.2. Subgrid Stress Model

In LES simulation, the subgrid stress model affects the accuracy of the calculation results; so, selecting an appropriate subgrid stress model can accurately simulate the energy transfer process between large and small scales. The research area is located near the nearshore eco-revetment structure of the bank slope; therefore, the WMLES model based on the evolution of the Smagorinsky model is adopted.

The Smagorinsky model has the advantages of simple form, good stability, and convenient calculation [26]. The Smagorinsky model is similar to viscous stress in laminar flow, and the subgrid stress term ${\tau }_{\mathrm{ij}}^{\mathrm{SGS}}$ is obtained by solving the strain rate tensor $\overline{{\mathrm{S}}_{\mathrm{ij}}}$ and viscous coefficient ${\upsilon }_{\mathrm{t}}$.

$${\mathrm{S}}_{\mathrm{ij}}={\displaystyle \frac{1}{2}}({\displaystyle \frac{\partial \overline{{\mathrm{u}}_{\mathrm{i}}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}+{\displaystyle \frac{\partial \overline{{\mathrm{u}}_{\mathrm{j}}}}{\partial {\mathrm{x}}_{\mathrm{i}}}})$$

$$\left|{\overline{\mathrm{S}}}_{\mathrm{ij}}\right|=\sqrt{\overline{{\mathrm{S}}_{\mathrm{ij}}} \overline{{\mathrm{S}}_{\mathrm{ij}}}}$$

(5)

${\upsilon }_{\mathrm{t}}$ is not a unique property of fluids, but a parameter based on the modeled flow field.

$${\upsilon }_{\mathrm{t}}\propto \mathrm{lq}$$

(6)

Among them, l represents the mixing length; q represents the flow velocity at the subgrid scale. Compared to the RANS model, the calculation of mixing length in LES is relatively simple and requires modeling the maximum scale to be similar to the filtering scale.

$$\mathrm{l}={\mathrm{C}}_{\mathrm{s}}\Delta$$

(7)

${\mathrm{C}}_{\mathrm{s}}$ represents the Smagorinsky constant. $\Delta$ represents grid scale. Based on the Prandtl mixing assumption, the flow velocity at the subgrid scale is as follows:

$$\mathrm{q}=\mathrm{l}\left|{\overline{\mathrm{S}}}_{\mathrm{ij}}\right|={\mathrm{C}}_{\mathrm{s}}\Delta \left|{\overline{\mathrm{S}}}_{\mathrm{ij}}\right|$$

(8)

Substitute Equations (7) and (8) into Equation (6):

$${\upsilon }_{\mathrm{t}}=\mathrm{lq}=\mathrm{l}2\left|{\overline{\mathrm{S}}}_{\mathrm{ij}}\right|=({\mathrm{C}}_{\mathrm{s}}\Delta )2\left|{\overline{\mathrm{S}}}_{\mathrm{ij}}\right|$$

(9)

The Smagorinsky subgrid model has irreversible transfer, which means that the subgrid model can only simulate the process of energy transfer from a large scale to a small scale. Meanwhile, in complex three-dimensional flows, ${\mathrm{C}}_{\mathrm{s}}$ varies with position, and the Smagorinsky subgrid model cannot accurately simulate it.

Based on the Smagorinsky subgrid stress model, Shur et al. [27] proposed a Large Eddy Simulation for wall modeling. The WMLES model overcomes the scale limitation of the Reynolds number and allows for the simulation of high-Reynolds-number conditions.

$${\upsilon }_{\mathrm{t}}=\min [{\left(\mathrm{k}{\mathrm{d}}_{\mathrm{w}}\right)}^2,{\left({\mathrm{C}}_{\mathrm{smag}}\Delta \right)}^2] \mathrm{S} \{1-\exp [-{({\mathrm{y}}^{+}/25)}^3\left]\right\}$$

(10)

In the formula, S is the strain rate; d_w is the distance from the point to the wall; k is a constant, 0.41; C_smag = 0.2; $\Delta$ represents the subgrid scale size:$\Delta =\min (\max \left({\mathrm{C}}_{\mathrm{w}}·{\mathrm{d}}_{\mathrm{w}},{\mathrm{C}}_{\mathrm{w}}·{\mathrm{h}}_{\max },{\mathrm{h}}_{\mathrm{uw}}\right),{\mathrm{h}}_{\max })$.

2.3. Fuzzy Mathematics Theory

Fuzzy set theory is an extension of the classical set theory with fuzzy set or membership function as the central concept. The fuzzy logic method uses fuzzy sets and fuzzy rules to infer unknown models, uncertain system descriptions, and control objects with strong nonlinearity and large delay through the judgment of uncertain concepts and reasoning thinking mode, and expresses transitional boundaries or qualitative knowledge and experience by simulating a human brain. At this stage, the key hydraulic factors suitable for fish habitat have not been determined, so the establishment of fuzzy mathematical model is very useful to express the distribution of fish habitat suitability.

For the regular fuzzy information problem, which conventional methods find difficult to sole, fuzzy comprehensive judgment is adopted. According to the above analysis, fuzzy logic reasoning is divided into three steps:

① The membership function is used to fuzzify the explicit value input: Compared to traditional sets where the characteristic function can only take two values, 0 or 1, the range of values for fuzzy set characteristic functions can be continuously within the interval of [0, 1]. To distinguish between the two, the feature function established by the fuzzy set is called the membership function. The membership function can be used to convert between ordinary sets and fuzzy sets described by membership degrees. Fuzziness is the process of converting explicit values into linguistic variable values with a certain degree of membership through membership functions, providing input for fuzzy reasoning.

② Using fuzzy rules for fuzzy logic reasoning: Generally, fuzzy reasoning is based on expert experience and existing conclusions to formulate fuzzy rules, and fuzzy input is transformed into fuzzy output.

③ The output result is defuzzified to obtain a definite value: The output result of fuzzy logic reasoning is defuzzified to convert it into a definite value. Defuzzification methods: barycenter method, area integral method, maximum method, etc. The center of gravity method is the most commonly used, and the center of gravity (cog) calculation method is as follows:

$$\mathrm{Vcog}={\int }_{\mathrm{z}1}^{\mathrm{z}2}\mathrm{z}\mathsf{\mu }(\mathrm{z})\mathrm{dz}/{\int }_{\mathrm{z}1}^{\mathrm{z}2}\mathsf{\mu }(\mathrm{z})\mathrm{dz}$$

(11)

where z represents the explicit value of the language variable. z1 and z2 represent the minimum and maximum values of z. μ(z) represents the membership function of the language variable C. V_cog represents the explicit value of the final output after defuzzification.

2.4. Index of Spatial Characteristics of Fish Habitats

2.4.1. Habitat Suitability Index

The Habitat Suitability Index (HSI) represents the degree to which the habitat requirements of the target species in the study area are met [28]. It is calculated using a grid as the smallest unit and directly output from the habitat model. The range of values for the Habitat Suitability Index is between 0 (completely not meeting the target species’ habitat needs) and 1 (fully meeting the target species’ habitat needs).

2.4.2. Weighted Usable Area

Weighted Usable Area (WUA) is the most commonly used habitat evaluation indicator and has a positive correlation with fish biomass [29]. Many studies use WUA as a key indicator to evaluate whether fish biomass has recovered. This article will use WUA as a key indicator to evaluate the biomass of grass carp in spawning grounds.

$$\mathrm{W}\mathrm{U}\mathrm{A}=\sum _{\mathrm{i}=0}^{\mathrm{n}}({\mathrm{A}}_{\mathrm{i}}{\times \mathrm{HSI}}_{\mathrm{i}})$$

(12)

A_i represents the area of unit i, m².

HSI_i represents the Habitat Suitability Index for calculating unit i.

n represents the number of grids.

2.5. Experimental Design

2.5.1. Selection of Grid Size, Initial and Boundary Conditions

This study used Large Eddy Simulation and, considering the cost of the experimental site and time, chose a model scale of 1:3. In the LES calculation process, selecting an appropriate grid can enhance the convergence and accuracy of numerical simulation. In this study, the computational domain is chosen as a structured grid with a regular hexahedral mesh, which possesses advantages such as high generation quality, simple data structure, and convenient information storage. To accurately reflect the hydraulic characteristics near the eco-revetment structure, the grid division near the structure is as shown in Figure 2a. The grid thickness near the wall is y+ = 1, which is 2 × 10⁻⁵ m, with a paving thickness of 30 layers. The grid is densely paved in the area near the revetment structure, accounting for 70% of the total grid. Due to the stable boundary conditions at the far water end and transition section, the grid scale is appropriately increased.

The model boundary conditions are set as shown in Figure 2b. The water inlet is set as a velocity inlet boundary (Velocity-inlet), using the fully developed water flow UDF file written above. The water outlet is set as a pressure outlet boundary condition (Pressure-out). The top region of the computational domain, where the water surface fluctuates slightly, is set as a rigid lid boundary. The bottom and both sides of the computational domain are set as wall boundary conditions (Wall), satisfying the no-slip condition. The solution time is as follows: a time step length of 1 × 10⁻⁴ s. The convergence criterion is the residual set to 1 × 10⁻⁶.

In this study, the length of the computational domain will be shortened to 2 m in length, 1 m in width, and 0.2 m in height. The hollowed-out eco-revetment structure of the square platform is placed on the inclined bank slope of the river bank, and the top of the structure is flush with the bank slope. In this study, tall grass cover plants were selected, such as miscanthus that is a perennial reed-like herbaceous plant in the Poaceae family, with a stem height of over 50 cm and a diameter of over 2 mm. Due to the uniform morphology of the vegetation studied in this study in the vertical direction, an equivalent representation of an equal diameter cylinder can be used, ignoring subtle morphological differences such as the sharp top and sparse bottom of the canopy, as shown in Figure 2c. Aquatic plants have a small diameter and are concentrated in the cavities of the revetment structure, with a concentrated planting area. Therefore, three to five small plants are summarized as one large plant for analysis.

2.5.2. Design Test Conditions

Based on data analysis, the common bank slope gradient in the middle and lower reaches of the Yangtze River Basin is generally between 15° and 40°. Therefore, the experimental bank slope gradient in this article is selected to be around 20°, with a gradient of 1:3. According to hydrological data, the average water flow velocity in the middle and lower reaches of the Yangtze River is between 0.5 and 3.0 m/s. The experiment simulated different conditions and selected a speed of 1.2 to 1.7 m/s as the average speed for the experiment. Due to limitations in experimental conditions and model computational capabilities, a water depth of 0.2 m was chosen as the experimental depth.

Hydraulic characteristics are decisive factors affecting the survival of fish. We studied the distribution of suitable living environments for fish with different life cycles near the new eco-revetment structure. The experimental plan is shown in

Table 1. Test scheme design.

Test Conditions	Water Depth (m)	Gradient	Side Wall Opening Rate (%)	Velocity (m/s)	Plants	Plant Diameter (mm)	Fish
Case 1	0.2	1:3	50	0.7	×	×	×
Case 2				0.9			×
Case 3				1			×
Case 4				0.7	√	8	×
Case 5				0.9			×
Case 6				1			×
Case ※				0.9	√	8	√

Side-wall opening rate = (Top opening area/upper half area of the side wall of the revetment structure) × 100%. Due to the influence of sequence order, 7 calculation schemes were considered, but only 3 schemes were effective for each factor. For the absence of plant factors, Case 1, 2, and 3 are the same, and for the presence of plant factors, Case 4, 5, and 6 are the same. And for the factors affecting fish, Case 5 and ※ are the same. “√” indicates the presence of the research parameter in the operating conditions, while “×” indicates the absence of the research parameter in the operating conditions. In the process of analyzing the suitability of fish habitats, all calculated data are restored to the prototype data according to the model scale for analysis.

.

2.5.3. Grid Independence Verification and Numerical Model Validation

LES has stringent requirements for grid size division. To ensure the accuracy of the experimental results and prevent them from being influenced by grid division, appropriate grid sizes are selected through grid independence verification. This ensures experimental accuracy while also reducing computational costs. In this paper, three types of grids with different levels of accuracy are designed for the experiment, and the parameters are shown in

Table 2. Comparison of grid parameters.

Test Conditions	Number of Grids in Each Direction (X, Y, Z)	Maximum Dimensionless Grid Spacing (Δx+, Δy+, Δz)	Total Number of Grids
Case I	510 × 320 × 540	30, 30, 20	80,000,000
Case II	420 × 270 × 450	40, 40, 30	55,000,000
Case III	330 × 230 × 360	50, 50, 30	30,000,000

.

We selected three different grid spacing options, with grid numbers of approximately 80 million, 55 million, and 30 million. By comparing the calculation results, the mesh size parameters of Case 2 are applied to actual cases.

Figure 3 illustrates the variation in flow velocity near the eco-revetment structure with water depth y/H (dimensionless). Through verification of the flow velocity distribution, the physical model and numerical simulation exhibit a high degree of data fitting. By verifying the flow velocity distribution, the fitting results of Case 2 and Case 3 both meet the experimental requirements. Finally, apply the grid size parameters of Case 2 to the numerical simulation research. Overall, the mathematical model constructed in this study is reasonable and can be used for this research.

3. Results

The area near the revetment structure is spatially divided into three parts: the fully enclosed side-wall region A (0 < y/H ≤ 0.43) around the bottom to the side-wall opening, side-wall region B (0.43 < y/H ≤ 1) with the opening, and top near-wall region C (y/H > 1), where h represents the height of the revetment structure, as shown in Figure 4.

As shown in Figure 5, near the new eco-revetment structure, the water flow characteristics are complex, and there are differences in flow velocity distribution in different regions and under different conditions. Under the condition of no plants, the water blocking effect of the structure in region A is significant, and the flow velocity value in this area is relatively low, basically maintained at 0–0.15 m/s. Region B, the side-wall opening, increases the flow of water, with a velocity distribution of −0.15–0.15 m/s. In region C, the water flow velocity near the top of the revetment structure rapidly increases to the same level as the mainstream flow velocity. Plants exist under certain conditions, and the turbulence of water flow is enhanced, especially in the structures along the water flow, where the water flow fluctuates greatly, as shown in Figure 5b. Therefore, the rich water flow characteristics enhance the diversity of fish living environments.

3.1. Analysis of the Suitability of Plankton Distribution

We consider the eco-revetment structure and nearby waters as an ecosystem, with phytoplankton serving as producers to provide food for planktonic animals and juvenile fish. Therefore, the survival suitability of phytoplankton directly affects the stability of the ecological system of the revetment structure. The purpose of this section is to conduct preliminary feasibility studies on the suitability of fish habitats, ensuring that the area can be used as a foraging area for grass carp.

Phytoplankton are autotrophic organisms, and diatoms, green algae, and blue–green algae in the Yangtze River Basin feed on dissolved nitrogen, phosphorus, and other trace element nutrients in water. At the same time, nitrogen and phosphorus nutrients, as the material basis of primary productivity in river ecosystems, can directly affect algal reproduction and indirectly affect the distribution of nutrients in water and the structure of water stability layers. As a limiting resource, in addition to absolute concentration, the nitrogen-to-phosphorus ratio (TN/TP) is also an important factor affecting phytoplankton biomass and algal community structure [30,31,32,33]. Generally speaking, the TN/TP value required for the growth and physiological balance of phytoplankton is 16, which is the Redfield value [34], indicating optimal growth of phytoplankton.

There is a high correlation between nitrogen and phosphorus transport patterns and water flow characteristics. Based on Large Eddy Simulation, we use the discrete phase model (DPM) for nitrogen and phosphorus transport analysis. The DPM is a particle tracking method based on Lagrange, which simplifies moving particles into stationary particles and models their shape and volume. During the calculation process, the flow details around the particles (such as vortex shedding, flow separation, boundary layer, etc.) are ignored.

The initial conditions for nitrogen and phosphorus in this study were selected as follows: nitrogen content of 0.5–1.5 mg/L and phosphorus content of 0.1–0.2 mg/L [35]. Analysis of the vertical TN/TP distribution shows that y/H ≤ 1 indicates that the TN/TP values in region A are relatively low, generally less than 5. The TN/TP ratio between the side-wall opening and top region B increases, reaching 15 in the absence of plants near the top and 20 in the presence of plants. The TN/TP value approaches the Redfield value, stimulating rapid growth of phytoplankton. The remote TN/TP ratio fluctuates around 5. As shown in Figure 6, the nitrogen–phosphorus ratio in the water area near the top of the eco-revetment structure provides a stable living environment for primary producers of phytoplankton to store nutrients and can also serve as a feeding ground for fish.

3.2. Habitat Suitability Analysis of Juvenile Fish

3.2.1. Characteristic Factors and Classification of Habitat Suitability for Juvenile Fish

Taking velocity as a characteristic factor, the important velocity indexes that can reflect the swimming behavior of fish include induced velocity, critical velocity and burst velocity. This study focuses on juvenile grass carp as the research object. In order to better reflect the relationship between flow velocity and suitability, the classification is based on the habitat index threshold of juvenile fish. The induced flow velocity range for juvenile fish is 0.03–0.1 m/s. When the flow velocity is below 0.03 m/s, juvenile fish lose their ability to distinguish direction. The critical velocity range for juvenile fish is 0.39–0.94 m/s. When the speed is greater than 0.94 m/s, it is not conducive to the long-term survival of fish. The threshold and suitability level of habitat indicators for juvenile fish are shown in

Table 3. Threshold grade and suitability grade classification of juvenile grass carp habitat index.

Velocity (m/s)	Suitability Index	Level
0 ≤ V ≤ 0.03	Unsuitable	0–0.2
0.03 < V ≤ 0.1	Suitable	0.2–0.4
0.1 < V ≤ 0.39	Extremely suitable	0.4–0.6
0.39 < V ≤ 0.94	Suitable	0.6–0.8
V > 0.94	Unsuitable	0.8–1.0

According to the living habits of young fish, the flow velocity is divided into three levels: unsuitable, suitable and extremely suitable.

.

3.2.2. Vertical Distribution of Habitat Suitability of Juvenile Fish

As shown in Figure 7a–c, in region A, there are no plant conditions, and the habitat suitability of juvenile fish is basically distributed between 0 and 0.4, accounting for more than 90%. When the flow rate increases, the proportion of the area a suitability of 0–0.2 decreases.

With plants, region A is more suitable for the survival of juvenile fish, and the habitat suitability for juvenile fish is basically distributed between 0 and 0.6. Under the same conditions, the region with a suitability between 0 and 0.2 decreases. The suitability is distributed between 0.4 and 0.6 near the plants, and the proportion of the distribution area is positively correlated with the incoming flow, with the highest proportion being about 20%, as shown in Figure 7d–f. Therefore, the flow velocity in region A is basically maintained in the range of induced flow velocity, providing a stable area for young fish to rest.

In region B, the side-wall opening ensures the flow of water between structures, and the habitat suitability is between 0 and 0.6. Compared with region A, the proportion of areas with a suitability of 0–0.2 is reduced, ranging from 5% to 15%, and mainly distributed in the area near the spanwise side-wall opening. Under the condition of no plants, the suitability is distributed in the range of 0.2–0.6. With the increase in flow velocity, the proportion of areas with a 0.4–0.6 suitability gradually increases and remains between 10% and 30%, as shown in Figure 8a–c.

The existence of plants increased the turbulence of water flow, and the proportion of 0–0.2 area decreased. The dissipation of flow velocity along the flow direction leads to a suitability of 0.2–0.4, accounting for about 90% of the area. A suitability of 0.4–0.6 only exists among the revetment structures along the flow direction, and there is a positive correlation between the area proportion and the inflow, as shown in Figure 8d–f. In conclusion, region B meets the feeding and survival needs of juvenile fish.

In region C at the top of the revetment structure, the velocity is greatly affected by the upstream inflow. When the mainstream velocity is 1.2 m/s, the habitat suitability near the wall is between 0.6 and 0.8, which is suitable for the survival of young fish. With the increase in inflow, when the mainstream velocity is greater than 1.5 m/s, the habitat suitability of the top area is between 0.6 and 1.0, and the proportion of habitat suitability of 0.6–0.8 is negatively correlated with the inflow. The existence of plants has little effect on the suitability distribution. Therefore, under the condition of large flow, the top area cannot meet the needs of fish for long-term survival, as shown in Figure 9.

3.2.3. Spanwise Distribution of Habitat Suitability for Juvenile Fish

As shown in Figure 10a, under no-plant conditions, a suitability of 0–0.2 is mainly distributed in region A and the area with openings along the spanwise side wall. The habitat suitability at the side-wall opening along the flow direction of region B is 0.4–0.6, and the habitat suitability at other locations is 0.2–0.4.

Under the condition of plants, the proportion of area with a suitability of 0–0.2 in region A decreases. In region B, plants increase the dissipation of water flow inside the structure, and the proportion of area with a habitat suitability of 0.4–0.6 decreases, which is distributed around plants. The external influence of the structure is small, and its distribution rule is similar to that without plants, as shown in Figure 10b.

Through the above analysis, functional zoning can be carried out near the revetment structure. In region A, the flow velocity is generally less than 0.1 m/s and the habitat suitability is 0.2–0.4; the flow velocity basically meets the needs of the juvenile fish’s sensing direction. The closed design around the structure provides an independent and stable resting area for juvenile fish. In region B, the flow velocity is not more than 0.3 m/s, the flow velocity is higher than the induced flow velocity and lower than the maximum critical flow velocity, and the habitat suitability is concentrated in 0.2–0.6. The side-wall opening design promotes the foraging of juvenile fish and the exchange of aquatic biomass information energy, which can be used as the foraging and exchange area for juvenile fish. When the inflow is greater than 1.5 m/s, the velocity in the top area exceeds the maximum value of the velocity limit of juvenile fish, which is not suitable for the long-term survival of juvenile fish. The deep-water side is more suitable for the survival of young fish than the shallow-water side.

3.3. Analysis of Suitability of Spawning Ground

Egg laying is the most important part of fish life. For pelagic fish eggs, after fertilization, the eggs absorb water and expand, sinking to the bottom of the water, which can affect development and lead to death, thereby reducing survival rates.

Externally, the water flow conditions are complex, and there are vortex structures near the plants, which follow the distribution pattern of cylindrical flow. There is a negative pressure gradient zone on the back side of the vegetation. After the water flows through the vegetation, there are wake vortices behind the plants, with two parallel wake vortices alternately generated. Due to the high flow velocity, axial force is generated along the axis of the vortex tube, resulting in a phase difference in the axial position of the vortex tube, as shown in Figure 11.

Therefore, the external water flow conditions of the structure are complex, and whether they meet the spawning needs of fish is the focus of this section.

3.3.1. Construction of Fuzzy Mathematical Model

The exterior of the new eco-revetment structure has strong turbulence in water flow. This paper mainly considers the velocity, vorticity and kinetic energy gradient. The researchers determined the subsection curve function of the flow velocity suitability index through physical model testing and field surveying [36,37,38,39], as shown in Figure 12a. By obtaining the vorticity ranges of different spawning grounds, the piecewise curve function of the absolute value suitability index of vorticity is determined, as shown in Figure 12b. By summarizing the hydraulic characteristics of different types of spawning grounds, the piecewise curve function of the kinetic energy gradient suitability index is determined, as shown in Figure 12c.

Based on relevant research and expert knowledge [7,40], we set language variable values for flow velocity, vorticity, kinetic energy gradient, and sustainability and determined their corresponding membership functions. Due to the complexity of Gaussian membership functions in computation, triangular and trapezoidal membership functions are used for description. The triangular and trapezoidal membership functions are used to describe the flow velocity variables, including extremely slow (TM), slow (M), moderate (Z), fast (K), and extremely fast (TK). Vorticity variable values are extremely small (TM), small (M), moderate (Z), large (K), or extremely large (T). Kinetic energy gradient variable values are extremely small (TM), small (M), moderate (Z), large (K), or extremely large (TK). The sustainability index variable values are extremely unsuitable (TM), unsuitable (M), moderate (Z), suitable (K), or extremely suitable (TK). The membership diagram is shown in Figure 13.

Among them, the suitability fuzzy reasoning rule is based on expert experience, and the weight values of flow velocity, vorticity, and kinetic energy gradient are 50%, 25%, and 25%, respectively. Therefore, the fuzzy mathematical model established by the key factors of multiple habitats can determine the distribution of fish spawning grounds and obtain more accurate and suitable spawning areas for fish.

Based on the flow mathematics and fuzzy mathematics model, this paper establishes the fish spawning suitability evaluation model and determines the fish spawning site suitability index. The threshold level and suitability level of habitat indicators for fish spawning grounds are shown in

Table 4. Threshold and suitability levels of habitat indicators for grass carp spawning grounds.

Level	Suitability Index
Extremely unsuitable	0–0.2
Unsuitable	0.2–0.4
Moderate	0.4–0.6
Suitable	0.6–0.8
Extremely suitable	0.8–1.0

.

3.3.2. Suitability Distribution of Fish Spawning Ground

In this study, the average flow rate is 1.2–1.7 m/s, and the HSI of spawning ground inside the revetment structure is 0–0.2, which does not meet the survival needs of fish eggs. With a cross-section z/Z = 0.5, flow disturbance leads to the disturbance of hydraulic characteristics near plants, the HSI value of the suitability index is small, and there is a negative correlation with water depth, as shown in Figure 14(a-1–c-1). With a cross-section y/Y = 0.6, the spanwise suitability index and HSI distribution have obvious stratification phenomena, the HSI gradually decreases along the X direction, and the HSI value near the mainstream of the river is higher than that near the shore, which is caused by the reduction in water depth and the effect of the near bottom on the water flow. The proportion of the low-HSI area near the plants is negatively correlated with the incoming flow and is mainly concentrated between the downstream structures. The suitable fish survival area is located between the spanwise structures, as shown in Figure 14(a-2–c-2).

As shown in Figure 15, the distribution of the area with an oviposition suitability index HS ≥ 0.6 between plants is positively correlated with the incoming flow. Analyzing the proportion of this area in Case 4 with an HSI < 0.6 between plants in the spanwise and downstream directions showed that it accounted for more than 95%, and the area with an HSI ≥ 0.6 almost did not exist and was distributed dispersedly. With the increase in flow rate, the area with an HSI ≥ 0.6 in Case 5 and Case 6 increased, accounting for 20–35%.

3.3.3. Analysis of the Impact of Fish Existence on Habitat Suitability

Through the above analysis, the internal structure can provide a suitable living environment for young fish, and the external plants can provide a suitable environment for fish spawning. This section mainly analyzes the impact on fish habitat suitability under the condition of containing fish. The distribution of fish is shown in Figure 16, and the operating parameters are shown in Table 1 (Case ※).

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Habitat suitability analysis for juvenile fish

There are fishes inside the eco-revetment structure, and the distribution of flow velocity and suitability is shown in Figure 17. In region A, the proportion of the area with a suitability of 0–0.2 increased slightly due to the presence of fish, but the suitability was still mainly concentrated in 0.2–0.4, as shown in Figure 17a. In region B, fish exist at the side-wall opening, and the proportion of the area with a suitability index of 0.4–0.6 increases significantly, as shown in Figure 17b.

Through the analysis of spanwise velocity distribution and suitability, it can be seen that the existence of fish in region A leads to a decrease in the suitability index, but the proportion is relatively small, so it is still suitable for young fish to survive in when considered comprehensively. Fish have a positive impact on region B, and the habitat suitability for nearby juvenile fish has been improved, as shown in Figure 17c. In conclusion, the eco-revetment structure with a square platform hollow body can provide a good living environment for juvenile fish.

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Habitat suitability analysis of fish spawning ground

As shown in Figure 18a,b, through the calculation of the fuzzy mathematics model, under the condition of the existence of fish, the distribution of the fitness index is basically the same as that of Case 5; only the fitness index around the fish will change, resulting in a reduction of about 5% in the area with an HSI ≥ 0.6 and an increase in the area with fitness between 0.2 and 0.4, as shown in Figure 18c.

4. Conclusions

This article takes nearshore waters as the research area and proposes a new type of eco-revetment structure to improve nearshore water flow and reset the living environment of fish. Based on the characteristics of water flow as a key habitat factor affecting fish survival, a fish habitat suitability evaluation model is constructed using Large Eddy Simulation technology and fuzzy mathematics theory. We conducted a feasibility study and analysis of grass carp habitats near structures based on evaluation models. The main conclusions are as follows:

The distribution of the nitrogen–phosphorus ratio near the eco-revetment structure and the nitrogen–phosphorus ratio near the top of the structure is close to the Redfield value, which is conducive to the rapid growth of plankton. This area can be used as a stable foraging area for fish.

The spatial distribution characteristics of habitat suitability in the waters near the new eco-revetment structure were analyzed by taking flow velocity as the dominant factor of habitat suitability for juvenile grass carp. Under the condition of no vegetation, the habitat suitability range for juvenile fish in region A is 0–0.4. Region B, with side-wall openings to improve water connectivity between structures, has a suitability distribution of 0.2–0.6. As the flow velocity increases, the proportion of high-suitability areas gradually increases, and the overall level remains at 10–30%. Region C, with a fitness index of 0.6–0.8, is not suitable for the long-term survival of juvenile fish as the flow velocity increases. In the presence of plants, areas with a suitability index of 0–0.6 are found in region A, while the proportion of areas with a low suitability index of 0–0.2 has decreased. Vegetation enhances water flow turbulence. In region B, the suitability along the water flow direction is mainly between 0.2 and 0.4, and the proportion of areas between structures with a suitability index between 0.4 and 0.6 is positively correlated with the inflow. The distribution pattern of suitability in region C is basically consistent with the absence of vegetation conditions.

The distribution pattern of habitat suitability for grass carp near structures was analyzed using flow velocity as the dominant factor. The water flow velocity in region A meets the requirements for juvenile fish induction velocity and can be used as a resting area. In region B, the side-wall openings allow juvenile fish to exchange material information and energy, making it a foraging area. The flow velocity in the top area and river channel is too high for fish to survive for a long time. The unique design of the revetment structure can also be used as an emergency shelter.

The spawning environment of fish requires high water flow conditions, and the presence of external plants leads to complex water flow conditions. In this study, indicators such as water flow velocity, vorticity, and kinetic energy gradient were selected as the main reference factors affecting fish spawning. Based on fuzzy mathematics theory, a suitability evaluation model for fish spawning plants was established. It can be inferred that the spawning suitability index (HSI) ≥ 0.6 is located between wingspan structures, and its area ratio is positively correlated with inflow. Moreover, the suitability index on the deep-water side is greater than that on the shallow-water side, making it more suitable for fish to lay eggs.

Near the eco-revetment structure, the presence of fish has a relatively small impact on the distribution of fish habitat suitability. In the area with Y/H ≤ 1 and A, the proportion of the area suitable for the survival of young fish is slightly reduced, but this area is still suitable for the survival of young fish. The presence of fish has had a positive impact on region B, and the habitat suitability for nearby juvenile fish has been improved. In areas where Y/H > 1, fish only have an impact on the surrounding water flow, and the suitability index changes. The impact on other areas is weaker, and the proportion of areas with an HSI ≥ 0.6 is reduced by about 5% compared to areas without fish.

Through the fish habitat evaluation model, it was found that the new eco-revetment structure can provide a stable living environment for young fish inside the structure and can serve as a stable spawning ground for fish under the presence of plants outside the structure. The fish habitat evaluation model constructed based on Large Eddy Simulation and fuzzy mathematical theory in this study can provide ideas for future research on aquatic organism habitat evaluation systems. The proposed eco-revetment structure provides a basis for fundamental research on the construction of ecological rivers. Meanwhile, this study has certain limitations, lacking direct biological validation, and the connection between TN/TP analysis and hydraulic models is still in the exploratory stage. In future research, we will continue to strengthen exploration and research in the fields of biology, ecology, and hydrodynamics to ensure the feasibility and universality of our conclusions.