Pressure Field Estimation from 2D-PIV Measurements: A Case Study of Fish Suction-Feeding
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsI feel the experiments are good but the analysis is very simple.
1. Though the focus is on pressure measurement, the discussion on how it is computed and validated is not there. This has be elaborated.
2. In my opinion, Number of samples looks very less for any conclusions. Please whether results are repeatable.
3. I am not sure if I missed it, if the fish survived the laser flashes - 200 mJ/flash could be high assuming they are short pulse duration in the order of ns. State the laser power used in the work.
4. Flow is 3D due to complex movements of the fish but the authors have take 2D flow assumption. How is 2D analysis justified ?
5. Please check Sign of equations (4) and (5)
6. Define the non-dimensional numbers when first used: For example Womersley Number in line 159
7. How did the authors ensure that the laser sheet in the plane through mid of fish every time. This question is related to repeatability.
8. In figure 4, denote where the location of fish mouth which will add clarity.
9. The scatter in figure 5 for various fish sample is high. Is this because of the orientation of measurement plane or due to the flow being 3D ?
Author Response
Response to Reviewer 1
The attached PDF is similar to the text herein.
I feel the experiments are good but the analysis is very simple.
Reply: Thank-you for your review and valuable feedback. We have addressed the concerns point-by-point below.
- Though the focus is on pressure measurement, the discussion on how it is computed and validated is not there. This has to be elaborated.
Reply: Thank you for your comment. The method used to compute the pressure gradient field has been explained and validated in prior studies including the numerical method used, which are referenced in the manuscript; thus, we provided a brief review of those methods in the introduction. We have elaborated a bit more in the revised manuscript to further clarify this point as well as re-organized the sections so the technique is better highlighted. The novel aspect of the paper is in how the boundary conditions are determined for a flow with a flexible, moving boundary that was measured with 2D PIV. The mathematical expressions used for implementing these boundary conditions with 2D PIV data are described in Eq. 3-5. The method is being evaluated via analysis of fish suction feeding to verify that the method provides reasonable results in a complex flow. Further validation of the method using these boundary conditions should be part of further research and this point was added to the concluding remarks in the revised manuscript.
- In my opinion, Number of samples looks very less for any conclusions. Please whether results are repeatable.
Reply: When performing flow measurements using in-vivo animals, especially where the focus is on the measurement technique, small sample sizes are typical (i.e., Higham et al., 2005; Day et al., 2007; Pekkan et al, 2016). The small sample size may limit the extent to which the suction feeding results can be extended to other species or fish populations, but it does not impact demonstration of the method to determine boundary conditions on an instantaneous flow field for the purposes of estimating the pressure field. The method could be performed on any 2D PIV frames collected. We use suction feeding as a test case because we expect noticeable differences in the pressure field to occur during suction feeding making it a good test case.
Higham, T.E., Day, S.W. and Wainwright, P.C. (2006). The pressures of suction feeding: the relation between buccal pressure and induced fluid speed in centrarchid fishes. Journal of Experimental Biology, 209(17), 3281-3287.
Day, S.W., Higham, T.E. and Wainwright, P.C. (2007). Time resolved measurements of the flow generated by suction feeding fish. Experiments in Fluids, 43(5), 713-724.
Pekkan, K., Chang, B., Uslu, F., Mani, K., Chen, C.Y. and Holzman, R. (2016). Characterization of zebrafish larvae suction feeding flow using μPIV and optical coherence tomography. Experiments in Fluids, 57(7), 112.
- I am not sure if I missed it, if the fish survived the laser flashes - 200 mJ/flash could be high assuming they are short pulse duration in the order of ns. State the laser power used in the work.
Reply: Thanks for your comment. The laser is an Nd:YAG type. The laser pulses contain high energy, yet this energy is spread through set of optical lenses to form a light sheet. The energy distribution across the light sheet is not high when scaled by the area and do not pose any risks to the fish. The laser power spec is about 3W/s, which is relatively low as the laser operates at 15Hz.
- Flow is 3D due to complex movements of the fish but the authors have take 2D flow assumption. How is 2D analysis justified?
Reply: We agree with the reviewer that the flow is 3D by nature. Although, given the relatively symmetrical body shape of this fish species and the notion that the fish was moving relatively slow in respect to the quiescent medium, we assume that the three-dimensional aspects within the flow field are not substantial. Here, we used suction-feeding as a test case to demonstrate the feasibility of the proposed technique to estimate the boundary conditions to estimate the pressure field in a non-intrusive manner with moving boundaries. We did not attempt to fully characterize the physical-biological interactions. The next step is to perform a similar analysis on 3D data. It is also important to note that, currently, 2D PIV systems are more common than 3D PIV, especially in non-engineering fields such as biology. Thus, demonstrating this technique with 2D PIV data first will be useful to many researchers whom utilize 2D PIV systems in their biologically-focused research. We have added a statement in the conclusions that indicates that the method should be further validated with 3D PIV data: “Further validation of the method in other similarly complex flows is needed as well as application of the technique to time-resolved 3D PIV data.”
- Please check Sign of equations (4) and (5)
Reply: Thank you for your comment. We have re-checked the signs of both equations and verified them. The signs follow equation 3. The pressure term has a minus sign as it is a force acting on a control volume and has a dot product with the normal outward in respect to the control volume; thus, the normal vector and pressure-force vector are in opposite directions, so their dot product is negative. Hence, the pressure term is positive. The viscous term has moved to the left-hand side, thus, its negative (here, we swap the locations and place the pressure at the left hand-side and the other terms on the right-hand side for clarity). In the y-direction, the same applies where the gravity term is negative (due to the vector in Eq. 3) and thus, once moved to the other side will become positive.
- Define the non-dimensional numbers when first used: For example Womersley Number in line 159
Reply: Thanks for your comment. We have revised the text accordingly and it now reads:
“The Reynolds number Re is 1420 defined as: where u is the ram speed (the fish speed in respect to the flow), and L1 is the characteristic length, defined as the distance from the snout to the base of the tail fin, respectively, of the swimming fish, and ν is the kinematic viscosity of the fluid. The Womersley number is 10.8 defined as: where ω is the angular frequency of the pulse, and L2 a characteristic length associated with ω. Following Krishnan et al. (2020), we consider suction as a single-pulse event, in which the angular frequency is the time it takes for the fish to fully open its mouth (time to peak gape, TTPG), , and the characteristic length is the peak gape diameter (PG) (Olsson et al., 2022).”
Krishnan, K., Nafi, A. S., Gurka, R. and Holzman, R. (2020). The hydrodynamic regime drives flow reversals in suction-feeding larval fishes during early ontogeny. Journal of Experimental Biology, 223(9), jeb214734.
Olsson, K. H., Gurka, R. and Holzman, R. (2022). Trophic guilds of suction-feeding fishes are distinguished by their characteristic hydrodynamics of swimming and feeding. Proceedings of the Royal Society B, 289(1966), 20211968.
- How did the authors ensure that the laser sheet in the plane through mid of fish every time. This question is related to repeatability.
Reply: The light sheet was stationary whist the fish was swimming towards the prey. The light sheet was located in-line with the center of the prey. This setup ensured that when the fish approached the prey and performed suction-feeding of the prey, the light sheet was aligned with the fish’s mouth. Therefore, it is plausible to assume that the light sheet was in line with the center region of the buccal. We have revised the text to better clarify this ambiguity: “The laser was a dual-head Nd:YAG Quantel Evergreen …cylindrical lens that were used to form a ~1 mm light sheet through the center of the experimental section of the tank that intersected with the threaded rod holding the bait (Ferry-Graham et al., 2003; figure 1). This rod setup ensured that when the fish approached the bait and performed suction-feeding, the light sheet was aligned with the fish’s mouth.” Furthermore, the trap door or divider was just large enough for the fish to swim through it (Fig. 1). As a result, the fish must orient itself straight and perpendicular to the light sheet in order to move through the trap door and the prey was just far enough from the door that as soon as the fish was through the door then it was approaching/at the prey. This divider/trap door setup also helped ensure the fish’s mouth was aligned with the light sheet as best as possible. The manuscript was revised to clarify this point.
- In figure 4, denote where the location of fish mouth which will add clarity.
Reply: Thanks for the comment. The location of the center of the mouth of the fish is denoted with a black dashed line in Figure 4, and is described in the figure caption in the last sentence. We have revised the last sentence to better clarify this point due to your misunderstanding in the original draft: ‘In A-I, the horizontal dashed line marks the center of the mouth of the fish.”
- The scatter in figure 5 for various fish sample is high. Is this because of the orientation of measurement plane or due to the flow being 3D?
Reply: The scatter is high because we are measuring the pressure field in the vicinity of a live organism, where we have no control on their positioning, kinematics, and morphology. The scatter factors depend on multiple variables including the orientation of the fish with respect to the measurement plane and 3D flow (see responses to #7 and #4), but is also impacted due to variations in the fish, such as their adult stage, male/female, size, etc. This manuscript presents a technique for estimating boundary conditions to estimate pressure in complex flows such as this one; it is less focused on the biological or ecological aspects of suction-feeding. We agree with the reviewer that the scatter is high but such scatter is typical when doing experiments with live organisms; we do not have sufficient statistics in terms of fish specimens to interpret the scatter.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsMy comments are listed in the attached report
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 2:
The attached PDF is similar to the response herein.
The paper presents a method for estimating pressure and its gradients from 2D-PIV measurements. This method was applied to investigate pressure variations around the mouth of Bluegill fish during the different phases of suction feeding.
Reply: Thank you for your review and the valuable feedback. We have revised the text according to your comments.
Before this article can be accepted for publication, the authors must address the following points:
A validation of this method is missing. For example, the results can be compared with a classical pressure measurement technique (e.g. pitot tube). I understand that the pitot tube is an intrusive measurement technique. However, there is already an obstacle (threaded rod) inserted in the water tank, which can be replaced by a pitot tube.
Reply: Thanks for your comment. The novelty of the paper is not in the computation of the pressure field from 2D PIV but in the application of boundary conditions for a pre-existing method to estimate pressure from 2D flow measurements, specifically when the boundaries are dynamic such as when making flow measurements around live organisms. Specifically, we propose to define the boundary conditions for the pressure field from the integral momentum equation. The technique to estimate the pressure from 2D PIV measurements has been applied and validated for 20 years since it was proposed by Gurka et al. (1999). Gurka et al. (1999) validated the technique using pressure transducers for an impinging jet case and demonstrated its validity. To validate the boundary conditions, we independently compute the corner points in both the x and y directions and obtain the same value at these overlapping locations, which indicates the validity of the methodology of the boundary conditions. Because this validation is mentioned early in the paper, it may have been difficult to connect it. Thus, we have added some text to emphasize that matching values at the corners were obtained and act as a validation on the boundary condition methodology: “…same; in all cases (see Sections 2.1 and 3), the values at the corners matched when computed independently from x and y components, which provides a partial validation on the boundary condition methodology.”
As stated in the manuscript, the accuracy of the proposed method depends on the experimental noise. However, the experimental noise of the performed experiments has not been discussed.
Reply: Thanks. We have added some discussion on experimental uncertainties in the Material and Methods section (section 2.1.3): “There are several sources of uncertainty when estimating pressure from PIV data, the accuracy depends on the numerical scheme, the quality of the PIV images, the PIV correlation analysis, and the experimental uncertainties. The estimated error for the PIV velocity measurements is about 2% (Raffel et al., 2018). The error associated with the numerical scheme used to compute the pressure field was estimated by Gurka et al. (1999) to be about 2% assuming a sufficient sample size, which is not fully achieved here due to the limitation of working with live organisms. The error resulting from the fish motion, and associated misalignments, is challenging to quantify. However, because the fish motion manifests itself into the PIV measurements, these experimental uncertainties are largely accounted for in the error associated with the PIV velocity measurements, which accounts for the correlation analysis, outliers, sub-pixel interpolation, large gradients, and 3D effects (Haung et al., 1997).”
Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T. and Kompenhans, J. (2018). PIV uncertainty and measurement accuracy. In Particle Image Velocimetry: A Practical Guide. Springer.
Huang, H., Dabiri, D. and Gharib, M. (1997). On errors of digital particle image velocimetry. Measurement Science and Technology, 8(12), 1427.
Gurka, R., Liberzon, A., Hefetz, D., Rubinstein, D. and Shavit, U. (1999). Computation of pressure distribution using PIV velocity data. 3rd International Workshop on PIV'99, Santa Barbara, CA, USA.
The suction-feeding cycle is divided into three phases. Although the flow changes rapidly during phase 2, all the analyses of this phase are based on an instantaneous flow velocity field. As the velocity changes during this phase (frequency of about 30 Hz), time-resolved measurements would be more appropriate to capture the flow dynamics and hence a correct estimation of the pressure variations. It would be useful if you highlight this issue and discuss it in the manuscript.
Reply: Thanks for your comment. We agree that this phenomenon is time dependent and would be better characterized with time-resolved PIV. Unfortunately, we do not have a PIV system that can acquire at such a fast rate. We have added that further validation with time-resolved 3D PIV data would be advantageous. We would also like to point out that we have used our proposed technique on suction-feeding as a test case and we did not aim to provide new insight on the transport phenomena. We added the following text in the conclusion: “Further validation of the method in other similarly complex flows is needed as well as application of the technique to time-resolved 3D PIV data.”
I have some specific comments/remarks:
Line 103, the first term represents the change of the momentum within the CV, and this term cannot be the mass flow rate.
Reply: Thank you for the valuable comment. We fully agree and have revised the text accordingly: ‘where is the rate of change of momentum within the control volume, is the momentum flux…’
Equation 5, please define ? in the gravity term.
Reply: ? stands for volume. We have revised the text to add a definition of this symbol.
Line 158/159, please define both Reynolds and Womersley numbers (how they are calculated?)
Reply: Thanks for your comment. We have revised the text accordingly and it now reads:
“The Reynolds number, Re, is 1420 defined as: where u is the ram speed (the fish speed in respect to the flow, which was estimated to be in the order of 10 mm/sec), and L1 is the characteristic length, defined as the distance from the snout to the base of the tail fin, respectively, of the swimming fish, and ν is the kinematic viscosity of the fluid. The Womersley number is 10.8 defined as: where ω is the angular frequency of the pulse, and L2 a characteristic length associated with ω. Following Krishnan et al. (2020), we consider suction as a single-pulse event, in which the angular frequency is the time it takes for the fish to fully open its mouth (time to peak gape, TTPG), , and the characteristic length is the peak gape diameter (PG) (Olsson et al., 2022).”
Krishnan, K., Nafi, A. S., Gurka, R. and Holzman, R. (2020). The hydrodynamic regime drives flow reversals in suction-feeding larval fishes during early ontogeny. Journal of Experimental Biology, 223(9), jeb214734.
Olsson, K. H., Gurka, R. and Holzman, R. (2022). Trophic guilds of suction-feeding fishes are distinguished by their characteristic hydrodynamics of swimming and feeding. Proceedings of the Royal Society B, 289(1966), 20211968.
Line 206, the feeding cycle is 0.065 s. This value contradicts the value mentioned in line 188 (0.032s).
Reply: Thank you for pointing out this inconsistency. The full cycle (from open to close is 0.065 s), and we mistakenly wrote the half-cycle number. This oversight has been revised to reflect the entire cycle: “…and the average duration of the suction-feeding cycle was 0.065 s.”
Line 214, a 5x5 local median validation filter is used. Did the authors check the effects of the filter size on the results, especially in the zones that have high velocity gradients? Because with this filter, you consider that the velocity changes are less than 3? over a distance of about 5 mm (the size of the interrogation window is about 1 mm).
Reply: Thanks, we tried several filter sizes and examine the impact on the results. No significant differences were observed between the smallest filter size (3x3) and 5x5. Given this result, we chose 5x5 because it is a commonly used filter size for PIV error analysis and vector validation (Nogueira et al., 1997). The 3? filter is the global filter and is not applicable to this local median filter.
Nogueira, J., Lecuona, A. and Rodriguez, P.A. (1997). Data validation, false vectors correction and derived magnitudes calculation on PIV data. Measurement Science and Technology, 8(12), 1493.
Line 222, the provided value of Re is calculated based on the speed of the buccal cavity. Reynolds number is usually calculated based on the flow velocity, not the object velocity. Also, the flow velocity varies between zero and a maximum value with a frequency of about 30 Hz. For such oscillating flow, the root mean square value (rms) of the velocity is used.
Reply: Thank you for the valuable comment. We have re-calculated the Reynolds number to better align with previous studies done in the field of fish suction-feeding to allow comparison with previous work. The Reynolds number is based on the fish speed with respect to the flow (i.e.: ram speed), the fish length, and the water kinematic viscosity (see for example: Hernández, 2000; Muller and Leeuven, 2004; Yaniv et al., 2014;. Ollson et al., 2022). We would like to point out that when characterizing this phenomenon, there is no strong consensus on how to estimate the Reynolds number, where some works used the above description whilst some use the peak gate of the buccal with peak speeds during suction. Given this slight discrepancy in the literature, we choose to use a conservative approach to the Reynolds number that does not capture the unsteady motion where we complement it with the Wormsley number, which scales unsteady forces with viscous (see Olsson et al., 2022); thus, this phenomenon is properly scaled using two nondimensional numbers. Since we already discuss the Reynolds number in the methods section, we have removed this context from the Results and discussion section.
Hernández, L.P. (2000). Intraspecific scaling of feeding mechanics in an ontogenetic series of zebrafish, Danio rerio. Journal of Experimental Biology, 203(19), 3033-3043.
Müller, U.K. and van Leeuwen, J.L. (2004). Swimming of larval zebrafish: ontogeny of body waves and implications for locomotory development. Journal of Experimental Biology, 207(5), 853-868.
Yaniv, S., Elad, D. and Holzman, R. (2014). Suction feeding across fish life stages: flow dynamics from larvae to adults and implications for prey capture. Journal of Experimental Biology, 217(20), 3748-3757.
Olsson, K. H., Gurka, R. and Holzman, R. (2022). Trophic guilds of suction-feeding fishes are distinguished by their characteristic hydrodynamics of swimming and feeding. Proceedings of the Royal Society B, 289(1966), 20211968.
Line 223, the authors consider that at Re of 1420, the viscous and inertia forces are comparable. This could be right if a steady flow is considered; however, this problem is closer to oscillating flow problems, in which the critical Re is different.
Reply: We agree with the reviewer that the Reynolds number does not consider oscillatory motion (unsteady flow). We agree that once the flow is not in steady state condition, then the critical Reynolds number indicating transition from laminar to turbulent flow will be different. In cases where oscillatory conditions are present, the Reynolds number can be re-defined to address the oscillatory motion (i.e.: Samson et al., 2019; Gurka et al., 2022) or an additional nondimensional number can be introduced (Ollson et al., 2022). Here, we choose to calculate two nondimensional numbers: Reynolds to provide the ratio between inertia and viscos forces, and Wormsley to provide the ratio between unsteady and viscous forces. It is noteworthy that the flow conditions in our facility were initially quiescent and the only motion generated was by the fish approaching the prey and opening its buccal, and thus, this scenario does not apply to a standard laminar to turbulent transition. Thus, the flow conditions are more aligned with a developed flow that dissipates fast once the prey was captured. Therefore, it is not expected to observe a critical Reynolds number that corresponds to transition from laminar to turbulence. Similar to the prior comment, we have removed this context from the manuscript.
Samson, J. E., Miller, L. A., Ray, D., Holzman, R., Shavit, U. and Khatri, S. (2019). A novel mechanism of mixing by pulsing corals. Journal of Experimental Biology, 222(15), jeb192518.
Gurka, R., Nafi, A.S. and Weihs, D. (2022). On an adaptation of the Reynolds number, applicable to body-caudal-fin aquatic locomotion. Frontiers in Marine Science, 9, 914214.
In Figure 5, the average and maximum pressure surrounding the mouth are plotted. Please define the zone considered in Figure 4. Why are there more than five circles at each phase?
Reply: Thanks for noticing this oversight. A description of the zone over which the average was taken has been added before introduction of figure 5.
There are five colors of circles – one for each fish. There are more than 5 circles because each point represents a PIV data acquisition trial in which that phase was captured well (well enough that the data is useable). Thus, the number of circles in each Phase is determined based-on the number of trials (out of the 36 total) at that phase.
“…we calculate the average pressure surrounding the mouth and the maximum pressure in the same area for each of the three phases, where the average is taken over 10.9 mm in the horizontal direction and 10.2 mm in the vertical direction directly in front of the buccal cavity. These results are shown in figure 5. Each point represents one of the 36 instantaneous pressure fields clustered based on phase, while each color represents a different fish.”
Some minor comments
Line 235/236, I think that you mean “averaged spatially in the x-direction within the rectangular region”
Reply: Yes, thanks. It has been corrected.
In the caption of Figure 3, the positions mentioned (e.g. 0.1ℎ) are not well defined. I think it should be ?=0.1ℎ. If this is correct, please define the origin of the x-axis.
Reply: This issue has been corrected, thank-you.
“Figure 3. Instantaneous velocity vertical profiles averaged over two areas: ‘close’ to the mouth (blue) and ‘far’ from the mouth (white) - see figure 2. A) Velocity profile for phase 1, blue: at x=0.1h; white: x=3.2h. B) Velocity profile of phase 2, blue: x=0.1h; white: x=1.5h. C) Velocity profile of phase 3, blue: x=0.06h; white: x=2.2h, where h is the peak gape and the fish mouth (buccal) is located at x=0. The orange line marks the location of the mouth.”
Line 256, Figure instead of “figure”
Reply: It has been corrected, thank-you.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have responded well for all the queries and manuscript has improved accordingly.
