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. 2013 Feb 13;280(1756):20122071.
doi: 10.1098/rspb.2012.2071. Print 2013 Apr 7.

The fish tail motion forms an attached leading edge vortex

Iman Borazjani  1 , Mohsen Daghooghi
Affiliations

The fish tail motion forms an attached leading edge vortex

Iman Borazjani et al. Proc Biol Sci. .

Abstract

The tail (caudal fin) is one of the most prominent characteristics of fishes, and the analysis of the flow pattern it creates is fundamental to understanding how its motion generates locomotor forces. A mechanism that is known to greatly enhance locomotor forces in insect and bird flight is the leading edge vortex (LEV) reattachment, i.e. a vortex (separation bubble) that stays attached at the leading edge of a wing. However, this mechanism has not been reported in fish-like swimming probably owing to the overemphasis on the trailing wake, and the fact that the flow does not separate along the body of undulating swimmers. We provide, to our knowledge, the first evidence of the vortex reattachment at the leading edge of the fish tail using three-dimensional high-resolution numerical simulations of self-propelled virtual swimmers with different tail shapes. We show that at Strouhal numbers (a measure of lateral velocity to the axial velocity) at which most fish swim in nature (approx. 0.25) an attached LEV is formed, whereas at a higher Strouhal number of approximately 0.6 the LEV does not reattach. We show that the evolution of the LEV drastically alters the pressure distribution on the tail and the force it generates. We also show that the tail's delta shape is not necessary for the LEV reattachment and fish-like kinematics is capable of stabilising the LEV. Our results suggest the need for a paradigm shift in fish-like swimming research to turn the focus from the trailing edge to the leading edge of the tail.

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Figures

Figure 1.
Figure 1.
Different virtual swimmers tested in this study are built by attaching different tail geometries to a mackerel body and meshed with triangular elements required by the curvilinear, immersed boundary method [25,26]. We test three different tail geometries: a homocercal forked tail, e.g. mackerel; a heterocercal with larger top lobe, e.g. shark tail; and a homocercal unforked tail, e.g. bull trout.
Figure 2.
Figure 2.
The flow near the tail in the inertial regime (St ∼ 0.25) visualized by streamlines coloured by the vorticity magnitude at phase angle φ = 2πft = π/3 (f is frequency and t is time). A stable, leading edge vortex with spiralling flow around it is visible. See the electronic supplementary material, movie S1 for the evolution of the streamline during one cycle. (Online version in colour.)
Figure 3.
Figure 3.
The flow near the tail in the transitional regime (St ∼ 0.6) visualized by streamlines coloured by the vorticity magnitude at phase angle φ = 2πft = π/3 (f is frequency and t is time). Owing to a high lateral velocity of the tail relative to the axial velocity, the vortex at the leading edge grows and becomes unstable. See the electronic supplementary material, movie S2 for the evolution of the streamline during one cycle. (Online version in colour.)
Figure 4.
Figure 4.
The leading edge vortex on the rectangular tail in the inertial regime (St ∼ 0.25) is visualized using streamlines coloured by vorticity magnitude, which demonstrates that the fish-like kinematics without the delta shape is capable of stabilizing the LEV. (Online version in colour.)
See this image and copyright information in PMC

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