Hydrodynamic Interaction of Two Self-Propelled Fish Swimming in a Tandem Arrangement
Round 1
Reviewer 1 Report
The authors simulated different scenarios to explore the hydrodynamic interactions of two fish swimming in a tandem arrangement. Overall the results are interesting.
Here are my comments to help the authors improve the manuscript.
1. Even though the "abbreviations" were added at the end of the manuscript, I think it would be better if the authors change this to a full table of abbreviations of the parameters, their values, and units. There are a lot of parameters to keep track in the simulations/results.
2. It's unclear how the fish model was discretized. Is it just a collection of points connected by springs on the centerline? Or is it a collection of points connected by springs along the boundary of the body? It would be good to add a visualization of the model discretization.
3. There should be an algorithm subsection where the authors present a flow chart or a list of steps for the simulations. When reading through the manuscript, it's not clear what forces were used, etc. Even though the authors use the software IBAMR, the overall ideas of the IBM developed by Peskin and all the forces in use should be stated clearly.
4. Is there any experimental work to support the analysis? For example, in the paper "Role of body stiffness in undulatory swimming: Insights from robotic and computational models" (Phys. Rev. Fluids 1, 2016), both physical and computational models of the lamprey were developed and compared side by side.
5. The convergence test might be moved to the Supplementary Information (SI) to leave space for more detailed explanations of the numerical method. Also, some snapshots of the fluid flow in the surroundings of the two fish could be added to the SI to help illustrate the wake regions in different scenarios.
6. Another interesting measure for the comparison could have been the pressure at the end of each fish throughout a traveling wave cycle.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper studies the hydrodynamic interaction of two fish swimming in a tandem arrangement. The study is based on numerical simulations, addresses a wide range of parameters in a tandem swimming and focuses in a possibility to save energy when swimming in a tandem or swarm, compared to swimming alone. Fish swimming in general as well as swimming in schools is widely studied topic. This paper contributes by experimenting with various parameters to study the effectiveness of swimming in swarms. The topic is relevant as it allows us to understand fish better and also could benefit into building swarms of underwater robots or other vessels.
In general the paper is well organized but few things could be improved.
Section 3:
In lines 189-192 the authors write:
For the cases of δϕ=0 and π/4, the extreme values of u/us occur at the same wavelength, i.e., the maximum and minimum u/us appear at λ=4L and λ=1.4L,respectively
What is meant by the "same wavelength" here?
Figure 4:
What is the d0 in those figures? If it is the distance between fish 1 and fish 2 as in Figure 1 then the fish positions in Figure 4 do not seem to match the description.
Figure 5:
The four individual graphs are not marked with a, b, c, and d.
Figures 4 and 5:
Can you please elaborate why are those parameters chosen T=1, λ=1.0L ?
In lines 312 - 314 the authors write: Meanwhile, when 0.05L<A<0.2L, the mean work done by the rear fish is greater than that of the upstream fish, as plotted in Fig. 8a. This may explain why the rear fish is more energy-saving efficient than the upstream fish in most cases.
In lines 322 - 324 the authors write: Meanwhile, the mean work done by rear fish is greater than that of the isolated fish under some situations, as given in Fig. 8b. This may explain why the rear fish is higher energy consumption than the isolated fish in some cases.
These two statements seem to be contradicting in terms of energy consumption/energy saving.
Section 3 would benefit from an overview table with all studied parameters and results. As this paper presents a lot of data and it is often difficult to search for a specific parameter from a plain text.
Conclusion summarizes the findings from this study. Do the findings agree with other similar studies? The authors should provide examples and comparison of their findings with other studies.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
In this paper, the hydrodynamic interaction of two swimming fishes in a tandem arrangement is computationally studied. The authors have performed the grid convergence and parametric studies. However, the methodology and discussion may need some improvements.
First of all, the simulation set-up is not clear. I presume that the simulation of fish swimming is done in a fluid-structure interaction fashion while the swimming motion is prescribed, but the detailed procedure is not described. The authors may need to explain: i) how the swimming motion (body) motion is prescribed with the immersed boundary method, ii) how the bulk fish motion is updated. Are the fishes allowed to move in both x and y directions? iii) If the equation of the motion is being solved, how the force term is computed, iv) The fluid and body solvers are coupled implicitly or explicitly? v) how the power is computed.
If the fishes are allowed to move in x-direction, the distance between two fishes at the equilibrium would be another important output parameter, and this may need to be discussed. There should be a relation between the streamwise distance, wavelength, and the tail-beat phase difference.
Although it makes sense that the rear fish obtains the speed gain by the interaction with the wake of the front fish, it is still not clear that how the front fish gets the same speed gain while there is no wake interaction. The authors may need to explain this more clearly.
Other minor comments:
1) Page 3, line 96: The kinematic viscosity of the water is 1e-3 in MKS unit?
2) Page 4, line 105: What was the time scale used to normalize the period T?
3) The authors can show the transient time histories of u1 and u2 along with the streamwise distance to demonstrate that how two fishes obtain the speed gain at the equilibrium state.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
I think the equations for F and P shown in the authors' response have to be included in the manuscript for the completeness of the methodology.
If possible, show the definition of F_c as well.
Other than that the revised manuscript looks good.
Author Response
Please see the attachment.Author Response File: 
Author Response.docx
