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Numerical study of complex modal characteristics in anguilliform mode of fish swimming

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Abstract

In nature, anguilliform fish swim fast and efficiently by undulating their elongate body in a specific way, which is generally described as a travelling wave. In present work, the undulatory motions of anguilliform fish are analyzed by the method of complex orthogonal decomposition (COD), and these particular motions are decomposed into two parts: the travelling component and standing component. The relative ratio between the travelling and standing components is defined as the travelling index, and the biological data show that anguilliform fish prefer to the undulatory motions with high travelling index (0.74–0.90). To study this phenomenon, a two-dimensional numerical model of anguilliform fish is developed by our proposed LS-IB numerical method, in which the shape of fish body is described by level-set (LS) function, and the interactive force is demonstrated by the immersed boundary (IB) method. The results show that the net force is decreased slightly with the travelling index, but the efficiency is increased with the travelling index until it reached to 0.8, which is consistent with the biological observations. Besides, the influences of the oscillating amplitude, tail-beat frequency and Strouhal number are also discussed. Overall, the results in present study can be used to explain why anguilliform fish would like to select the swimming gaits with high travelling index.

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Abbreviations

A :

The maximum amplitude

C f :

The net force coefficient

C p :

The propulsive coefficient

f i :

The interactive force at the forcing point

f b :

The interactive force of solid body

F :

The average net force (ANF)

F 0 :

The ANF of tethered fish without any motions

h (x, t):

The midline motions

h i :

The lateral velocity

H (x):

The amplitude envelope

K a :

The amplitude coefficient

k :

The wave number

L :

The length of fish body

\(\vec n\) :

The unit normal vector

N :

The total number of forcing points.

p :

The pressure

P s :

The loss power acting on fish body

Re:

Reynolds number

St :

Strouhal number

t n :

Time instants in one tail-beat period

T :

The tail-beat period

u i :

The velocity components

U ∞ :

The velocity of incoming flow

V :

The kinematic viscosity

V :

The wave speed

w :

The tail-beat frequency

(w)(x):

The half width of fish body

x i :

The Cartesian coordinates (x, y, z)

x m :

Positions along the midline of fish body

Δx :

Uniform grid size in x-direction

Δy :

Uniform grid size in x-direction

\(\phi \left( {\vec x,t} \right)\) :

The LS function

α :

The amplitude growth rate

λ :

The wave length

γ :

The traveling index

ρ :

The density

τ ij :

Subgrid-scale (SGS) stress

ϵ :

Three times of the minimal grid size

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 12002097), the Natural Science Foundation of Guizhou Provice (No. ZK[2021]-266, No. [2017]5789-20), and the Scientific Start-up Project of GuiZhou Institute of Technology (XJGC20190956).

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Authors and Affiliations

  1. School of Aerospace Engineering, Guizhou Institute of Technology, Guiyang, 150003, China

    Zuo Cui

  2. School of Mechatronic Engineering, Harbin Institute of Technology, Harbin, 550003, China

    Hongzhou Jiang

Authors
  1. Zuo Cui
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  2. Hongzhou Jiang
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Correspondence to Zuo Cui.

Additional information

Zuo Cui received his Ph.D. degree in Mechanical Engineering from Harbin Institute of Technology, in 2017. Currently, he is an Associate Professor in the School of Aerospace Engineering, Guizhou Institute of Technology, China. His research interest covers biofluid mechanics, bionic robotics, computational fluid dynamics.

Hongzhou Jiang received his Ph.D. degree in Mechanical Engineering from Harbin Institute of Technology, in 2001. Currently, he is a Professor in the Department of Mechanical Engineering at Harbin Institute of Technology, China, and a member of Chinese Society of Astronautics. He has published about 70 refereed journal and conference papers. His research interest covers parallel robotics, control systems, and hydrodynamic control system.

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Cui, Z., Jiang, H. Numerical study of complex modal characteristics in anguilliform mode of fish swimming. J Mech Sci Technol 35, 4511–4521 (2021). https://doi.org/10.1007/s12206-021-0921-5

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  • DOI: https://doi.org/10.1007/s12206-021-0921-5

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