Decoding the Relationships between Body Shape, Tail Beat Frequency, and Stability for Swimming Fish

Round 1

Reviewer 1 Report

The manuscript presents a numerical study of fish using caudal fin propulsion. Its main result, the technique of assessing the stability by computing the corrective torques, is a valuable contribution. I think that the manuscript should be published, but there are a few pints that require further clarification or correction.

 

1. I found the explanation of the driving torque and the discussion of equations (9) – (11) difficult to follow. A much clearer explanation is in the end of the paper (page 8): “We also actuate the model at one vertical axis, as if it was being twisted back and forth on a stick”. I suggest that move this sentence to section 2.3 where they introduce the driving torque. Besides that, it may be helpful to add a sentence in the end of section 2.3 reminding that the result of (14) is substituted in (4) in the simulation.

 

2. What were the initial conditions in the simulations? In particular, are the results and the conclusions sensitive to the initial phase in (9)? Is it justified to always start from zero phase? Again, this is partly answered in section 4 (If we mirror the fish…), but I am curious about arbitrary initial phase.

 

 

3. Why the authors are so sure that the initial transient is shorter than 10 cycles? Maybe, after 100 cycles, the fish model will no longer require stabilizing force? What happens if the fish is released from a stabilized condition?

 

4. The last sentence in section 2.4: “access” - > axes.

 

 

5. I did not find any information about the size of the fish. It would be nice to see it in Table 1. Also, in section 3.3, “…25% taller and shorter than the original body”, but how tall was the original?

 

6. 2nd paragraph in 3.1: “with respect to the driving torque frequency” - > with the driving torque frequency?

 

7. 3rd paragraph in 3.1: “we plotted the trajectory”. I do not see any trajectory in figure 4, but only the initial position/posture and 6 end positions/postures.

 

 

8. 1st paragraph in 3.2: “are consistent over three cycles”. Why does figure 5 show only two cycles?

 

9. 2nd paragraph in 3.2: “the pitch torque amplitude has a peak”. I cannot see it with a naked eye. Maybe add an inset with amplitude versus frequency?

 

 

10. Figure 4 caption. I do not see any transparent snapshot, but, instead, there are 6 different frequency labels.

 

11. Figure 5 caption. “to 0.25 Hz” -> to 2.0 Hz?

 

Author Response

We have included our response to reviewer in the attached file.

Reviewer 2 Report

This paper studies the stability of fish movement by computing a compensating torque required to maintain an upright forward motion.  The novelty of the work mainly centers around proposing a new way to quantify instability in fish movement using a computational approach. Previous studies using simulation-based analysis of fish stability are scare.  Results are well presented and reasonable, supported by the authors' strong experience in publishing in this field. Overall, I find this paper acceptable for publication in Fluids. I have one conceptual comment and a few more minor points, however, which I would strongly suggest to be addressed in a revision.

1. Can there be any discussion or at least some insights that can be provided regarding the possible relation between short vs. medium vs. tall fish body and positions of center of mass, buoyancy and pressure with respect to each other?
2. Line 5 of the abstract: `` the role of unconstrained on the fish model…” A word seems to be missing here, “unconstrained motion”?
3. Line 6 of the abstract: `` The resulting kinematics a product of the passive …”  the verb is missing here.
4. Line 7 of the abstract:`` We then examine a constrained model understand the role that …”…``to’’ understand?
5. Line 42 Sec. 1: The reference is missing.
6. Line 53 Sec.1 : Replace “means’’ should be “mean”
7. Line 57 Sec. 2: Replace “describe” with “describes”
8. Eq(4) Sec. 2: Shouldn’t a portion of F be the transmission forces on $\partial \mathcal U$?
9. Line 68 Sec. 2: Suggest mentioning that the three-dimensional delta function here is $\delta(\vec{x})=\prod_{i=1}^{3}\delta(\vec{x}_{i})$.
10. Fig 1: Can you show the xyz triad on the figure for clarification?
11. Sec 2 Line 79: “0 2mm radius’’ ??
12. Sec 2.5: Any word on FE discretization/mesh of the fish body?
13. Suggest stating clearly at the beginning of the Results section (Sec 3.) how you define and quantify stability in your analysis.

 

Author Response

Please see attachment.

Author Response File: Author Response.pdf