> Review of manuscript tc-2023-100



> by Sönke Maus



> This is a review of the manuscript Experimental modelling of the growth of tubular ice



> brinicles from brine flows under sea ice by S. Teston-Martinez et al.



> Below I cite from the Cryosphere Discussions manuscript tc-2023-100 in italic font.



> I Summary



> The paper presents results from laboratory experiments on growth of tubular ice brini- cles that form when high-salinity brine is injected into solutions close to the salinity and freezing point of sea water. Such brinicles have been observed under natural sea ice and have been studied in a couple of previous studies. As the role that such brinicle may play in the earth system or regional ecosystems is not well known, laboratory studies of these features are of interest in sea ice research. The experiments by the authors indicate that brinicles do not form in very thin Hele Shaw Cells and therefore have not been observed in such experiments. For the 3D setups where brinicle growth was achieved the authors present some interesting results and imagery. However, the quantitative results could be presented better in terms of existing models, and the few equations given by the authors are not properly described or tested versus observations. While the manuscript is inter- esting and generally well written, I suggest to improve it along the following lines.



> I. Laboratory settings. From the short descriptions it is not clear under which condi- tions the different experiments have been performed. I recommend to add a table that gives an overview. Helpful would be a table that provides the essential information for the three experimental setups (e.g. temperature of water and injected brine, injection rates, temperature of cold room, etc...).







We have added a table as suggested.







> II. The work by Martin (1974) is mentioned in several sections. The paper could be improved by outlining some of Martins model equations in relation to the present work. The two equation (1) and (2) given by the authors are insufficiently explained and it is not clear how they are related to the presented results.







We anticipate that the revised version is improved.

> III. Many figures are missing scale bars and experimental time (for the time series) and could be improved.







We have added the missing scale bars and have added the experimental time elapsed to the caption of Figure 7.

> IV. Considerable parts from the ’Discussion’ section should better be presented in a ’Results’ section, and these too sections should thus be restructure. Focusing on the actual results rather than discussing hypothesis that cannot be tested by the data would also improve the paper.

Yes, we have restructured the manuscript.







> 1



> II Specific comments



> 1. Abstract



> L11–14 We present laboratory experiments on the growth of a tubular ice structure sur- rounding a plume of cold brine that descends under gravity into water with a higher freezing point. Brinicles are geological analogues of these structures found under sea ice in the po- lar regions on Earth. –> Not clear to me - it sounds as if brinicles are natural analogues of tubular ice structures produced in the lab. I would say that both are brinicles.







Yes, they are. Generally geologists like to call lab-grown structures analogues. It’s really not important.











> L14 They may be important for the energy budget of sea ice. –> Or they may not. The paper does not present an analysis of this question. I suggest to remove this sentence from the abstract and rather focus on some paper results.







True, we don’t enter into this.

> 1. Introduction



> L17 Ice brinicles –> When and by whom was this term used for the first time?

According to the OED, it was 2011 in a television programme  https://www.oed.com/dictionary/brinicle_n#eid1284695240

We are not sure whether that’s correct; what we can say is that some of us, when we wrote our first paper on them which appeared in 2013, used the term because we preferred it to ice stalactite. An ice stalactite is an icicle, and that has a rather different mechanism of formation and growth, so the alternative term brinicle seemed much preferable.

> L21–58 -20 °C –> -23 °C is sufficiently well known for seawater.







ok we have changed this











> L60–L91 –> The experimental description is not clear (e.g. chilling to -24 °C, then de- frosting at -4 °C, then brine was injected at -18 °C). Helpful would be a table that provides the essential information for the three experimental setups (e.g. temperature of water and injected brine, injection rates, temperature of cold room, etc...







As suggested we have added a table







> L70 –> brinicles have been described as an unusual example of an inverted chemical gar- den (Figure 2) –> Fig. 2 does not show or say anything about chemical gardens.







We meant to have a sketch and we have added one.







> Fig. 2 –> Could be inproved by giving typical brine and ice temperature + salinity during observations of brinicle formation.







ok







> 1. Methodology



> L57–58 as has been used in previous studies to create chemical gardens confined in two dimensions (Rocha et al. 2021; Ding et al. 2016; Haudin et al. 2014). –> The chemical garden is an interesting analogy, but not the first to mention here (and it was already mentioned in the introduction). More relevant references in comparison are the saline water freezing experiments in a Hele Shaw cell by Niedrauer and Martin (1979) and Mid- dleton et al. (2016).







Added

> L60–L91 –> The experimental description is not clear (e.g. chilling to -24 °C, then de- frosting at -4 °C, then brine was injected at -18 °C). Helpful would be a table that provides the essential information for the three experimental setups (e.g. temperature of water and injected brine, injection rates, temperature of cold room, etc...







As above

> L70 –> Schlieren optics setup, as in a previous study of salt fingers (Linden 1973) – > There are many applications of Schlieren optics in fluid dynamics, but here rather the



> 2



> sea ice applications, like Middleton et al. (2016) should be referenced to.







Added the reference.











> Fig. 4, 5 and 7 –> The times should be indicated for these series.







Added











> Fig. 8 –> Detail of the tip of the Brinicles formed in the beaker, showing its high porosity –> What shows the high porosity in this figure?







We have increased the contrast and added a zoom view as an inset.











> Fig. 8 and 9 –> Scale bars are missing.







added







> 3.Discussion



> L115-153 –> This part should rather be presented in a Results than in a Discussion section.







altered











> L129–132 Eventually, the brinicle reached the bottom of the cell (Figure 5d) and the brine flow began to accumulate at the bottom forming a bi-layer system with a high density brine phase and the water phase while continuing to freeze at the water/brine interface, forming a brine layer capped by an ice layer in the lower part of the cell making the deposited ice layer grow thicker (Figure 5e).–> The bottom evolution is not that clearly seen in the figure - a drawing could help to illustrate it better.







we have added a sketch











> L135 brane –> brine







changed











> L136–137 A series of upward flows are observed from the melting of this ice because of the



> rise in temperature –> I suspect this flow is rather due to dilution/freshening.







altered











> L137 and this time the ice and the contact with the brine solution –> Seems incom-



> plete - something lacking here?.







yes, it was rewritten.











> L150–151 These crystals 150 are probably oriented along the a axis, known to be the fastest growth direction in ice. –> a- or other axis have not been defined or mentioned so far. Give a reference. I also suggest ’normal to the c-axis’.







altered and added a reference.











> L157 These data fit the model from Martin (1974) that brinicle growth is proportional to the square root of time. –> The basic model features from Martin could be given here and discussed quantitatively in relation to the experiments. Which are the properties and mechanisms that govern the growth velocity?.







We have added a little more on the theoretical basis of Martin’s modelling here. His model is also mentioned around lines 40-45 in terms of his physical findings and we have moved one sentence from here to there.











> L167-168 As shown in Figure 9b, the brinicle walls grow thicker with time; –> How can this growth be observed in a single figure?







We had cited the wrong figure here, now fixed.











> L172-174 –>The oscillations visible in the curves imply an oscillatory growth instabil- ity that warrants further investigation. This may be related to the periodic popping regime observed in chemical gardens (Barge et al 2015; Thouvenal and Steinbock, 2003).–> As the oscillations are observed at the bottom of a growing brinicle they more likely present a spatial oscillation. The pattern that form in such a freezing system can be understood in terms of brine release, constitutional supercooling and morphological stability (Mullins and Sekerka, 1964; Hardy and Coriell, 1973; Sekerka, 1967).



> 3

Popping is a spatio-temporal oscillation. Popping involves the fluid dynamics of the flow in the brinicle. It’s not Mullins-Sekerka, which is a different sort of instability in a solid medium, only involving a stationary fluid. Since we haven’t any more data from this series of experiments on what is happening here we prefer to reserve further investigation for future work.

> Eq. (1) and Figure 11 –> The terms in the figure are not explained in the text or equation, e.g.: What is Rc? How is dP/dz determined in the experiment, and how is ∆ρi computed? Also helpful would be to discuss how Martin (1974) has incorporated Poiseuille flow in his model framework.







Add definition of Rc to the figure caption. Add how delta rho is computed. Explain that dP/dz must be estimated a posteriori.

Equation 1 is not from Martin but is from Cardoso and Cartwright 2017. We have rewritten the paragraph and replotted the figure to clarify and improve the presentation.











> Eq. (2) –> This is the second equation given, yet it is not tested at all in this work and remains rather hypothetic, and its relationship to the present observations or other previous work remains unclear. E.g., what heat flux Qh does the equation refer to? At least some plausible values from the field or laboratory should be used with Eq. (2) to estimate the length of a brinicle.







The heat flux is that in the plume, now clarified. We had omitted a figure, now added as fig 12, which shows brinicle length against flow velocity on Earth, and on Europa and Enceladus for a given heat flux.

> L277-283 –>...Therefore, we propose that brinicles may exist in some form even with currents in icy-world oceans.–> There are indeed a couple of observations, but there is no support in observations that brinicles would survive or form with currents. The recent paper by Katlein et al. (2000) only notes ’occasional’ observations of brinicles during the year-long MOSAiC expedition. Hence, without giving evidence in the present paper this hypothesis should be left out or rather formulated as a question and motivation for future work, for example: At which levels of under-ice flow and turbulence may brinicles form? How to design laboratory experiments to answer this question?







As we said, we had omitted a figure which is the basis of this discussion. That figure, now added, shows how under-ice flow affects brinicle length. This prediction from theory is presented as a motivation for future work, which might be both in the lab and in the field. 











> References



> Hardy, S.C., Coriell, S.R., 1973. Surface tension and interfacial kinetics of ice crystals freezing and melting in sodium chloride solutions. J. Cryst. Growth 20, 292–300.



> Martin, S., 1974. Ice stalactites: Comparison of laminar flow theory with experiments. J. Fluid Mech. 63, 51–79.



> Middleton, C.A., Thomas, C., Wit, A.D., Tison, J.L., 2016. Visualizing brine channel development and convective processes during artificial sea-ice growth using schlieren optical methods. J. Glaciol. 62, 1–17. doi:10.1017/jog.2015.1.



> Mullins, W.W., Sekerka, R.F., 1964. Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35, 444–451.



> Niedrauer, T.M., Martin, S., 1979. An experimental study of brine drainage and convec- tion in young sea ice. J. Geophys. Res. 84, 1176–1186.



> Sekerka, R.F., 1967. A time-dependent theory of satbility of a planar surface during dilute binary alloy solidification, in: Peiser, H.S. (Ed.), Crystal Growth, Pergamon Press, Boston, 20-24 June 1966. pp. 691–702.



> 4

RC2: 'Comment on tc-2023-100', Anonymous Referee #2, 14 Feb 2024

This is a curiosity-driven experimental study to examine the evolution of brinicles in laboratory conditions. Experiments have been conducted in a proper manner and they provide new insight how the brinicles form. The manuscript reads well and can be published with minor revisions. My two comments are

1. Authors state that brinicles "may be important for the energy budget of sea ice" and compare their biogeochemical effect on submarine hydrothermal vents on Earth. These statements are very vague and need to be quantified. Observations show that brinicles are rare, small and short-lived. What makes them important to the sea ice energy budget? As a first guess, I would argue their impact on the sea ice energy budget, ocean mixing, and primary production biodiversity is minimal.

Since we don’t go into that question further in this work, we have removed that statement.

2. In the concluding chapter authors claim that the brinicles could be relavant for origin of life. In this context, authors cite their own papers. That is speculative and entire chapter should removed

The prior work of ours that we cite has gone through peer review. In the revised version we have added a figure to the discussion that we had omitted to add before, and we have added citations to more recent papers of other groups that discuss the possibility of brinicles on icy worlds and how they might be of interest and relevance when searching for life.