How to Tune a Tuna: Resonance of Locomotor Structure and Hydrodynamic Wake

Team Members

• Marina Dimitrov

 

General Objectives

• Further understand the mechanism of energy transfer between the tuna’s internal locomotor structure and the surrounding fluid medium.
• Explore the interesting phenomenon that tuna control their swimming speed predominantly through tailbeat frequency rather than tailbeat amplitude or “stride length” – unlike kangaroos, for example.
  • Cost of transport remains fairly constant over a range of speeds (1-2 bodylengths/second), while tailbeat frequency changes significantly (almost doubles) – inconsistent with theory of forcing an oscillator at close to its natural frequency for minimum energy expenditure.

 

Research Questions

• What is the “natural frequency” of the tuna locomotor system – specifically, the arrangement of red muscle myomeres, ribs, posterior oblique tendons (POTs), and great lateral tendon (GLT) that power cruising (Figure 3)?
  • [later, summer research maybe] Is a more sophisticated model of “natural frequency” necessary, to incorporate interaction with the surrounding fluid?
• Is this frequency comparable to the tailbeat frequencies and swimming speeds most commonly observed in wild tuna?
• [later, summer research maybe] Is this frequency comparable to that of vortex shedding from a tuna’s body at cruising speeds?
• [another relevant bio study to do] Is a tuna muscle fiber’s force-velocity curve more forgiving than its force-length curve (hence the constant amplitude, variable frequency swimming style)?

 

Plan for Success

• I am already well-informed in tuna biomechanics (literature and personal experience).
• Start with the simplest possible model and increase complexity until it adequately represents the situation.

1. One pin joint for tail fin, pulled by one tendon on either side (GLT equivalent, also representative of force generated by muscles earlier in body).
2. Maybe need to represent bending of spine (although it is not as significant in tuna as it is in other fish) – progressively add more degrees of freedom and representative actuators as needed.
3. If interested in complete POT system of anatomical complexity, can extend Matt Millard’s kinematic MATLAB model (Figure 3, left) by adding tendon properties Melinda Cromie had measured, etc.
4. Maybe measuring impulse response of passive system is not enough – then need to include muscle actuation.

• Compare frequency of model/simulation to tailbeat frequencies and swimming speeds most commonly observed in wild tuna – presumably similar. If not, reevaluate model assumptions.
• Support from experienced collaborators (Melinda Cromie, Matt Millard, John Dabiri).

 

Progress

 

 

 

 

Tuna, one of the top predators in the ocean, swim with an incredible mix of power, speed, and efficiency. In this “thunniform” swimming, the front part of the body remains fairly straight. Bending the last part of the spine swings the stiff tail region right before the fin, called the peduncle, back and forth. The tail fin, in turn, bends relative to this peduncle, adding a characteristic flick to the tail strokes. Figure 1 shows this combined mode of oscillation.

 

(sorry, not published yet)

Figure 1 – Tail motion of a swimming tuna (Dimitrov et al. in preparation). Note the two primary motions of interest: that of the peduncle at the end of the spine, and that of the tail fin relative to the peduncle.

(but here is a video where you can get the idea)

 

This gives the tuna fine control over the interaction between vortices coming off the body and those generated by the tail, as modeled with computational fluid dynamics (CFD).^1,2 Vortices are rotational patterns of fluid motion that a fish creates while swimming, generating force and leaving the equivalent of footprints in the water (Fig. 2).

 

    

Figure 2 – 3D fluid structure behind an oscillating tuna tail fin modeled using CFD (left), and a 2D slice of that (right), showing how the vortices form almost like “footprints”.²

 

During cruising, tuna swim by almost exclusively using a system of red muscle myomeres, ribs, and posterior oblique tendons (POTs), shown in Figure 3, which transmit muscle forces to the spine.³ The horizontal ribs coming out of each vertebra act as struts, allowing the muscle attached to each tendon to pull on a vertebra farther down the spine. Figure 4 shows how these muscles contract along the body throughout the swimming “stride.”

 

(sorry, not published yet)

Figure 3 – A 2D engineering model (left) of the red muscle and posterior oblique tendon (POT) system in tuna (right), with the normally stacked muscles separated and folded out (Cromie et al. in preparation).

(but here is a figure mashup from another paper that illustrates it)³

 

 

Figure 4 – Muscle activation patterns of a swimming yellowfin tuna. From the head towards the tail, the muscles on one side start contracting, until they are all contracted. This then repeats on the other side of the body.⁴

 

Posterior to this POT system, a bony keel jutting out horizontally from the vertebrae acts to increase the moment arm of the great lateral tendon (GLT), which attaches to the tail fin (Fig. 5). Passing over the keel rather than lying close to the backbone provides the GLT and associated muscle myomeres with greater mechanical advantage as they pull on the tail. The GLT also attaches to the skin at various points on the way back to the tail.

 

 (sorry, not published yet)

Figure 5 – The great lateral tendon (GLT, blue) and associated muscle myomeres (red) of a yellowfin tuna (Dimitrov et al. in preparation).

(but here is a photo from another paper illustrating the anatomy)³

 

1. Yang, L. & Su, Y. CFD simulation of flow features and vorticity structures in tuna-like swimming. China Ocean Eng. 25, 73–82 (2011).
2. Zhou, K., Liu, J. & Chen, W. Numerical Study on Hydrodynamic Performance of Bionic Caudal Fin. Appl. Sci. 6, 15 (2016).
3. Westneat, M. W., Hoese, W., Pell, C. A. & Wainwright, S. A. The horizontal septum: Mechanisms of force transfer in locomotion of scombrid fishes (Scombridae, Perciformes). J. Morphol. 217, 183–204 (1993).
4. Altringham, J. D. & Shadwick, R. E. in Fish Physiology (ed. Stevens, B. B. and E.) 19, 313–344 (Academic Press, 2001).