Torquigener albomaculosus, also known as the white-spotted pufferfish, is known for creating circular nests in the underwater sand as part of the mating ritual. The nests are built by the males to attract females through the nest’s impressive design and related ability to gather fine sand particles. As the fluid-dynamic processes associated with these unique nests are still almost completely unknown, in the present study, an analysis has been conducted to investigate how the geometric parameters related to the nest design influence the fluid velocity in its center. For this reason, a geometric model of the nest consisting of 24 channels, where each unit channel can be described by three strips of broken lines, has been introduced, and a multivariate analysis has been implemented to determine the relative weight of each considered parameter. In particular, the “optimal” combination of parameters has been obtained by means of an orthogonal design approach. We show that these bio-nest structures also display a potential for significant application in marine litter collection, or for use as a buffer against the waves in offshore areas.

The emergence of bionics has led to new levels of scientific research, technological development, and engineering capabilities for applications in human lives [

For thousands of years, humans have continued to observe and study nature, the habits, and the habitats of many different organisms. Different kinds of tools and machines have been invented to effectively solve various technological development problems. This paper is a study of the habitat of Torquigener albomaculosus. Torquigener is a species of fish in the family Tetraodontidae [

Bionic structural studies are often carried out with the help of computers [

Torquigener albomaculosus builds the mystery circles as their nests. The nest can attract female fish and allows ocean currents to deliver sand into the center of the nest. However, studies focused on the fluid behaviors of these mystery circles are rare. To study these mystery circle nests, firstly, a geometric model of the fish nest is built to ensure maximum consistency with the nests built by the pufferfish. Then, the fluid behavior of the fish’s nest is studied using a univariate fluid analysis method. Only the relative height of a point in the boundary line or median line of the nest is varied to observe the flow characteristics. Finally, the flow characteristics of the nest are studied by multivariate analysis, and the optimal solution of the nest model is obtained by the orthogonal test method. It is verified that it has the lowest average speed in the living area. The bio-nest structures show a significant potential for a possible application for reducing the impact of ocean currents in offshore areas or the flushing of quicksand in the desert.

The model was derived from the nest of Torquigener albomaculosus, a kind of fish living in the Pacific Ocean. The geometric model of the constructed nest is ensured to be maximally consistent with that built by Torquigener albomaculosus, as shown in

Three critical broken lines describe one channel unit (_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}_{i}

Upon observing the established geometric models of the nest, first, we consider that for fluid analysis, the shapes of the boundary lines (_{1}_{1}_{2}_{2}_{1}_{1}_{2}_{2}

_{1}_{1}_{1}_{1}_{1}_{1}

Similarly, the changing rule of the middle lines (_{2}_{2}_{2}_{2}_{2}_{2}_{2}

Based on the results of the fluid analysis of the stated geometric models, a group of orthogonal experiments were conducted to study the fluid behaviors of the nest, while the shapes of the boundary lines (_{1}_{1}_{2}_{2}_{1}_{1}_{2}_{2}_{1}_{1}_{2}_{2}_{1}_{1}_{1}_{2}_{2}_{2}_{1}_{1}_{2}_{2}

The commercial finite element software, HyperWorks (Version 2017, Altair Engineering, Inc., Troy, Michigan), was used to analyze the nest’s fluid behaviors. The finite element (FE) models of the nest were established in the CFD module of Hypermesh, a pre-processor of HyperWorks (

The governing equations of stable, incompressible fluids generally consist of the conservation equations of mass (continuity equation) and momentum conservation equation. The specific governing equation is as follows:

Mass conservation equation (continuity equation):

Momentum conservation equation (Reynolds-Averaged Navier-Stokes equation):

where _{u}_{v}_{w}

The convergence of the mesh directly affects the accuracy of the calculated results, and it is essential to reduce the errors in CFD simulations [

Mesh type | The total number of mesh cells (million) | Experimental results (m/s) |
---|---|---|

Mesh 1 | 1.64 | 1.173 |

Mesh 2 | 3.14 | 1.268 |

Mesh 3 | 5.65 | 1.251 |

Mesh 4 | 6.20 | 1.270 |

Corresponding to _{1}_{1}_{1}_{1}_{1}_{1}

While the shapes of the boundary lines (_{1}_{1}_{1}

The living area of the nest is of significant importance for Torquigener albomaculosus, and the average velocity of the living area in the geometric model is calculated and compared in _{1}_{1}_{1}

The fluid behaviors of the nest and the shapes of the middle line (_{2}_{2}_{2}_{2}

As depicted in _{2}

The velocity of the living area is calculated and compared in _{2}_{2}_{2}_{2}

Based on the above univariate fluid analysis, a group of orthogonal experiments were designed and conducted for multivariate fluid analysis in this section. As discussed in _{1}_{1}_{1}_{1}_{2}_{2}_{2}_{2}_{1}_{2}_{1}_{2}

Experimental factors (_{i} |
Description | Experimental values (m) | ||
---|---|---|---|---|

1 | 2 | 3 | ||

_{1} |
Height of _{1} |
0.30 | 0.35 | 0.40 |

_{2} |
Height of _{2} |
0.20 | 0.25 | 0.30 |

_{3} |
Height of _{1} |
0.15 | 0.20 | 0.25 |

_{4} |
Height of _{2} |
0.05 | 0.10 | 0.15 |

As presented in ^{4} = 81 experiments in the designed orthogonal experiment. It is similar to the earlier detailed univariate fluid analysis. The fluid behaviors of the nest models from these 9 experiments are compared in _{i1}_{i2}_{i3}_{1}_{1}_{1}_{3}_{31}H_{21}H_{33}H_{41}_{31}H_{21}H_{33}H_{41}

Experiment lists | Experimental factors (_{i} |
Combination | Experimental results (m/s) | |||
---|---|---|---|---|---|---|

_{1} |
_{2} |
_{3} |
_{4} |
|||

1 | 1 | 1 | 1 | 1 | _{11}H_{21}H_{31}H_{41} |
2.062 |

2 | 1 | 2 | 2 | 2 | _{11}H_{22}H_{32}H_{42} |
2.430 |

3 | 1 | 3 | 3 | 3 | _{11}H_{23}H_{33}H_{43} |
2.363 |

4 | 2 | 1 | 2 | 3 | _{12}H_{21}H_{32}H_{43} |
1.618 |

5 | 2 | 2 | 3 | 1 | _{12}H_{22}H_{33}H_{41} |
1.553 |

6 | 2 | 3 | 1 | 2 | _{12}H_{23}H_{31}H_{42} |
2.089 |

7 | 3 | 1 | 3 | 2 | _{13}H_{21}H_{33}H_{42} |
1.268 |

8 | 3 | 2 | 1 | 3 | _{13}H_{22}H_{31}H_{43} |
1.585 |

9 | 3 | 3 | 2 | 1 | _{13}H_{23}H_{32}H_{41} |
1.330 |

Results average of _{i1} |
2.285 | 1.649 | 1.912 | 1.648 | N/A | N/A |

Results average of _{i2} |
1.753 | 1.856 | 1.793 | 1.929 | ||

Results average of _{i3} |
1.395 | 1.927 | 1.728 | 1.855 | ||

Range | 0.890 | 0.278 | 0.184 | 0.281 | ||

Optimum solution | 3 | 1 | 3 | 1 | _{31}H_{21}H_{33}H_{41} |
1.215 |

In this paper, we constructed a geometric model of the nest that Torquigener albomaculosus builds. Three critical broken lines describe the channel unit of the nest. Firstly, we considered that the shapes of the boundary lines (_{1}_{1}_{2}_{2}_{1}_{1}_{2}_{2}

In the section of the univariate fluid analysis, it can be concluded that the average velocity of the living area decreases when the relative height of point _{1}_{1}_{1}_{1}

In the univariate analysis, it is also obtained that the average velocity of the living area increases with the relative height increasing from 0.20 to 0.29 m compared to the fixed point _{2}_{2}_{2}

In the section on multivariate fluid analysis, a group of orthogonal experiments for fluid analysis were designed and conducted. It can be concluded that the relative height of _{1}_{1}_{1}_{3}_{31}H_{21}H_{33}H_{41}

In this paper, we revealed that the nests of Torquigener albomaculosus can effectively reduce the ocean current’s velocity in their living area. In future research, this structure can potentially be used in intercepting plastic waste moving with ocean currents. In addition, this structure has a further potential application as a buffer device against the incoming waves in offshore areas.

We thank Prof. Biczo for his linguistic assistance during theoreparation of this manuscript.

This work is supported by the

Zhimin Zhao: Methodology, Writing-review & editing, Supervision. Shangbin Wang: Writing-original draft, Methodology, Conceptualization. Yuanhao Tie: Data curation. Ning Feng: Validation, Writing-review & editing, Supervision.

The authors declare that they have no conflicts of interest to report regarding the present study.