Experimental and Numerical Analysis of the Hydrodynamics around a Vertical Cylinder in Waves
Round 1
Reviewer 1 Report
I am satisfied with the changes/amendments introduced in the present revised version of this paper and recommend publication in JMSE.
Author Response
Thank you
Reviewer 2 Report
Please see the attached file.
Comments for author File: 
Comments.pdf
Author Response
Title:
Experimentaland numerical analysis of the hydrodynamics around a vertical cylinder in waves
by
Corvaro Sara, Crivellini Andrea,Marini Francesco, Cimarelli Andrea, Capitanelli Loris and Mancinelli Alessandro
Reviewer’s comments:
The authors applied numerical and experimental methods to discuss the hydrodynamicanalysis of a three-dimensional nonlinear periodic wave interacting with a slender vertical cylinder, including details such as waveform, wave pressure, wave force and flow fields.After I read it, I think this is a goodarticle, which is quite rich in content. The experiments and numerical methods they usedare not easy works. I think that if some sentences are explained clearly, this can be considered for publication.
Questions:
The article mentioned the KC number. Its definition uses Um as the maximum bottom velocity. I don't know very well. Isn't the bottom velocity zero according to the non-slip condition?
The KC number is a non-dimensional parameter used to describe the relative importance of the drag forces over inertia forces in an oscillatory flow. In its general definition (Keulegan & Carpenter, 1958), Um represents the maximum velocity of the flow. The vertical velocity profile induced by waves is not constant. For the study of nearbed processes the Um value is usually computed on the bottom (Sumer et al., 1992). We agree with the reviewer that the non-slip condition at the bottom leads to a zero value of the horizontal velocity at the bottom.
Therefore, the proper definition of Um should be: Um is the maximum horizontal velocity just outside the bottom boundary layer. The proper definition of Um is added in the revised version of the manuscript.
Moreover, when the computation of the maximum velocity at the bottom (z=-h) is made by using the Stokes I order theory:
Um=Hσ/(2*sinh(kh)), hence Um≠0.
The author used the DNS numerical method, but did not explain clearly or cited the literatures on how to generate grids, discretize flow fields, etc.
The numerical results is obtained by means of standard numerical techniques for the solution of the incompressible Navier-Stokes equations.
We make use of a commercial code: ANSYS Fluent. We add this information in the revised manuscript. Being a commercial code all the details of the numerical solution, generation of grids, ecc. are reported in the manual of the software and its references.
Figure 7 compares the experimental and numerical wave elevations. The wave height of its incident wave is compared at S3. The numerical results are much higher, but the waveforms and peaks of S4 and S5 are similar. This seems to be inconsistent with common sense.
This effect is due to the wave generation and propagation along the flume. Indeed, in both the cases a first order Stokes wave is generated but in two different positions from the cylinder. In the experimental set-up the wave must be generated far enough from the area of study to exclude influence of exponential evanescent modes (Buldakov et al., 2017). In a numerical model the wave is usually generated closer to the studied area, otherwise the computational time will be increased dramatically. In the present case the wave is generated at about 3m from the pile. As highlighted in lines 277-281 of the original version of the manuscript, the wave generation and propagation processes in intermediate water depths lead to nonlinear effects such as change of the shape of the wave (not more sinusoidal). The nonlinear effects on the wave shape act differently during the wave propagation over the flume, being more significant at the beginning, closer to the wave generation. Therefore, such nonlinear effects are more evident in the numerical data because of the relative smaller distances between the water level gauges (S3, S4 and S5) and the wave generation boundary. In the experimental data the larger changes in the wave shape due to nonlinear effects was observed at the elevation gauge S1.
Some of the above comments are added in the revised version of the manuscript
The author discussed the distribution of pressure in Section 4.3. How is the numerical solutions of the wave pressure calculated, and can the authors list the mathematical formulas of total pressure and dynamic pressure? Theoretically, the numerical results can more easily show the pressure distribution at different angles of the cylinder. I don't know why the author only analyzed the results of the experiment without comparing it with the values in Figure 10.
Accordingly with the referee, in the revised version of the manuscript we report the definition of the dynamic pressure which is given by the difference between the pressure P and the hydrostatic pressure Ph=. The formula is also added in the revised version of the manuscript.
Pressure is directly solved by the model and, thus it is an output of the simulations such as the velocity field.
However, by considering the huge refinement level of the mesh it is not possible to export all the information of the flow field domain for each time step of the simulation. Therefore, in order to reduce the computational cost of the numerical simulation, the locations where the pressure were monitored have been chosen only at φ=0°, φ=90°, φ=180° and φ=270° and vertical depths z=0.00-0.08-0.16-0.24-0.32m (lines 123-124 of the manuscript).
Figure 10 is updated in the revised manuscript with the values (positive, null or negative) of the pressure gradients.
I don't quite understand the content of Figure 11. The data "force from pressure" in the figure is obtained from the DNS value or Eq. (2)? If it is Eq (2), how to use the CM and CD? I think that "force from load cell" is an experimental result, but the description in Figure 11 will make the reader think that is the result of calculation. Can this be rewritten so as not to mislead readers?
We agree with the Reviewer that the caption of Figure 11 can lead to misunderstandings as the description in the text. Both the forces are obtained from experimental data but none of them in this figure is computed from Eq. (2) or by the numerical model.
The force recorded by the load cell located at the top of the cylinder does not represent the total force on the pile due to the static scheme of the cylinder, which is equipped with a hinge at the bottom and fixed with the load cell at the upper side. Therefore, the force on the pile is not directly measured but it is “obtained” according to the method described in Section 4.4 (lines 390-396).
In order to make clearer the revised version of the manuscript, we modified the caption of Figure 11 and explain better in the text the data of Figure 11.
The meaning of this figure is to ensure the goodness of the experimental data.
The authors discussed the flow pattern in Section 4.5, and used the Q of equation (3) as a quantification. I suggest that this equation should be listed clearly, such as Eq. (11) of [15].
As suggested by the Reviewer, we list clearly equation (3) in the revised paper and add all the missing definitions.
The analysis of iso-surface in Figure 14, why is Q = 10, how is this value selected?
As shown in the text of the paper, the Q criterion for the detection of vortices simply requires that Q is positive, see the cited reference (Hunt, Wray, Moin, Eddies, “Stream and convergence zones in turbulent flows” Center for Turbulence Research Report, 1988). Once this criterion is satisfied, the choice of the exact value of Q is made simply on considerations about the visibility of the coherent structures detected. Hence, we report in the text the exact value of Q only for reproducibility reasons by other authors of the present results.
What is the physical quantization value of the scour patter in Figure 15? It was obtained from experiment. How to get this value experimentally? Does this have a formula expression?
The seabed morphology map (scour pattern) has been obtained by a previous experimental campaign. The evaluation of the scour in this pattern could be roughly obtained from the colorbar that gives the non-dimensional scour depth S/D (S is the scour depth and D is the pile diameter). The maximum scour is equal to 1.4cm (in Corvaro et al., 2018 all the details of the mobile bed experimental campaign are reported).
At the present, the most widely formula used for the scour prediction under regular waves is given by Sumer et al. (1992). Several adaptations have been proposed for random (Ong et al., 2013) and nonlinear waves (Carreiras et al., 2000). Further information on the experimental mobile bed campaign and on the main formulas for the scour evaluation can be found in Corvaro et al. (2018).
Accordingly with the suggestion of the Reviewer, in the revised version of the manuscript we add some information about the value of the scour and the reference for the scour prediction formula (Sumer et al., 1992).
What is the “wave test R1” mentioned in Figure 15? I don't see the description in the text.
In order to make clearer the paper we remove the mention of “wave test R1” from the caption of Figure 15 in the revised manuscript. The scour map of Figure 15 refers to a wave test with a KC similar to the wave analyzed in the present paper. The experiment with a mobile bed were conducted in a previous laboratory campaign.
Reference 15 should be published in issue 129, not 126. Please confirm and correct.
We thank the Reviewer for spotting this typo.
