An axisymmetric non-hydrostatic model for double-diffusive water systems

Hilgersom, Koen; Zijlema, Marcel; van de Giesen, Nick

doi:https://doi.org/10.5194/gmd-11-521-2018

Articles | Volume 11, issue 2

https://doi.org/10.5194/gmd-11-521-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/gmd-11-521-2018

© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 11, issue 2

Model description paper

|

06 Feb 2018

Model description paper |

| 06 Feb 2018

An axisymmetric non-hydrostatic model for double-diffusive water systems

Koen Hilgersom, Marcel Zijlema, and Nick van de Giesen

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Final revised paper (published on 06 Feb 2018)
Preprint (discussion started on 13 Sep 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

RC1: 'Comments on Hilgersom et al.', Anonymous Referee #1, 13 Oct 2016
- AC1: 'Author's response to Referee #1', Koen Hilgersom, 07 Dec 2016
RC2: 'Review', Anonymous Referee #2, 17 Oct 2016
- AC2: 'Author's response to Referee #2', Koen Hilgersom, 07 Dec 2016
RC3: 'Review comments', Anonymous Referee #3, 18 Oct 2016
- AC3: 'Author's response to Referee #3', Koen Hilgersom, 07 Dec 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Koen Hilgersom on behalf of the Authors (31 Mar 2017) Author's response Manuscript

ED: Referee Nomination & Report Request started (07 May 2017) by Ignacio Pisso

RR by Anonymous Referee #1 (12 May 2017)

RR by Anonymous Referee #2 (02 Jun 2017)

Suggestions for revision or reasons for rejection

I read the extensive response to reviewers that the authors prepared and the revised manuscript. Some improvements were made, but there are still some major flaws that need to be addressed.

MAJOR REMARKS

1) The authors claim that they solve the “Navier-Stokes equations” (abstract, line 4). Recalling one of my previous comments, I think that they should use a different terminology, “Reynolds-averaged Navier-Stokes (RANS) equation”, also in the abstract and not only in the introduction, in order to avoid misunderstanding with DNS models.

2) Eq. 6 is not correct yet: first of all, dQ/dt should read dQ/dr (the error is a copy&paste from Zijlema and Stelling, 2008)...
Second, the equation 6 is not integrated over the depth only, but also over a sector of amplitude y1-y0. I do not understand why this is necessary, and in any case the notation is confusing, the variable y is not defined and there is no reference to fig. 3 where a diagram is shown that is absolutely obscure, if not even wrong (e.g., y should be a tangential coordinate, not orthogonal to r).
Why not introducing the equation integrated only over the depth? By the way, the kinematic boundary condition at the free surface has to be specified.
In fact, the other equations are not presented as integrated over alpha, and only when discretized the “alpha terms” appear (section 2.3).

3) The sentence “In non-turbulent thermohaline systems, stability largely depends on density gradients and molecular heat and salt diffusion rates, which in turn are highly dependent on temperature and salinity” (l. 145-146) is not entirely correct. While I completely agree with the first part, the second part is an overstatement. Stability “highly” depends on the difference between heat and salt diffusion rates, but not on their dependence on temperature and salinity. Most of the models do not even consider this dependence and assume constant values for the two (different!) molecular diffusion coefficients.

4) I do not understand why the simulation of cases 1 and 2 (section 3.1) was stopped after 2 hours (l. 377).
Similar for cases 3 and 4 (section 3.2): “From the current results, we cannot tell whether the system converges after 2 h to a system where the salt flux exceeds the heat flux” (l. 430-431).
The fact that the simulations are short makes the authors hypothesize a subsequent behavior, which is not known. Why not running longer simulations?

5) The authors replied in the following way to my previous that the “standard” turbulence model cannot be taken as “perfect” in transitional (laminar/turbulent) double-diffusive systems: “Further, the referee points out his belief that a standard k-epsilon model is not suitable for these conditions. We would like to ask the referee to better explain why he has this belief for these applications” (p. 7 of their replies).
However, they seem to agree with my comment in the revised manuscript. For instance, “… might indicate that the standard k-epsilon model does not function for systems with high density gradients” (l. 385-386); “The poor performance of the standard k-epsilon model also appears” (l. 392); “confirming that the standard k-epsilon model suppresses the onset of double-diffusive convection” (l. 403-404); “… caused by a defective turbulence modelling for systems of large density gradients” (l. 498).
Frankly speaking, I do not understand such a different opinion in their reply to reviewers and in the manuscript.

6) In line with the comment above about the modelling of turbulence fluxes in systems with high density gradients, it is worth recalling that the actual requirements are quite simple: a model is needed that predict no turbulence in stable regions (hence molecular diffusion) and significantly higher convective fluxes in unstable regions. A few models that exploit this kind of simplified behavior have been proposed and, recently, Toffolon et al. (2015) showed how it is even possible to reproduce – by means of an minimal model of that kind – the formation of double-diffusive staircases. This considerations can be used in the discussion at l. 409-417.

7) When analyzing the case of salt fingers (section 3.2), the authors write: “The numerical results … confirm that salt-fingers are formed over the interface (Fig. 11)” (l. 419-420). I do not see what they refer to in figure 11.
Are they referring to the vertical stripes? In axisymmetric conditions, these are not fingers, they are circles (as I already noted in my previous review).

8) As a whole, it seems that the quantitative comparison (sections 3.1 and 3.2) is not so satisfactory.

9) I do not see why an axisymmetric 2-D model should be presented as “quasi 3-D”.

MINOR REMARKS

- At the free surface (l. 153), a kinematic boundary condition is required as well.

- (l. 419), “Case 4”: (Tu = 85.0°) not (Tu = 71.2°).

ADDITIONAL REFERENCES
Toffolon, M., A. Wüest, and T. Sommer (2015), Minimal model for double diffusion and its application to Kivu, Nyos and Powell Lake, J. Geophys. Res. Oceans, 120, 6202–6224, doi:10.1002/2015JC010970

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ED: Reconsider after major revisions (18 Jun 2017) by Ignacio Pisso

AR by Koen Hilgersom on behalf of the Authors (29 Aug 2017) Manuscript

ED: Referee Nomination & Report Request started (28 Sep 2017) by Ignacio Pisso

RR by Anonymous Referee #2 (08 Oct 2017)

ED: Publish subject to minor revisions (Editor review) (09 Oct 2017) by Ignacio Pisso

AR by Koen Hilgersom on behalf of the Authors (26 Oct 2017) Author's response Manuscript

ED: Publish as is (18 Dec 2017) by Ignacio Pisso

AR by Koen Hilgersom on behalf of the Authors (21 Dec 2017) Manuscript

Short summary

This study models the local inflow of groundwater at the bottom of a stream with large density gradients between the groundwater and surface water. Modelling salt and heat transport in a water body is very challenging, as it requires large computation times. Due to the circular local groundwater inflow and a negligible stream discharge, we assume axisymmetry around the inflow, which is easily implemented in an existing model, largely reduces the computation times, and still performs accurately.