the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Sep 2023
Transformation of internal solitary waves under ridged ice cover
Abstract. Internal wave-driven mixing is an important factor in the balance of heat and salt fluxes in the polar regions of the ocean. The breaking internal waves at the edge of the ice cover can essentially enhance the mixing and melting of ice in the Arctic Ocean and Antarctica. The internal solitary waves (ISWs) are generated by various sources, including tidal currents over the bottom topography, the interaction of ice keels with tides, varying in time wind, vortices, and lee waves. In the study, a numerical investigation of the transformation of ISW propagating from open water in the stratified sea under the edge of the ice cover is carried out to compare the depression ISW transformation and loss of energy on smooth ice surfaces, including those on the ice shelf and glacier outlets, with the processes beneath the ridged underside of the ice. They were carried out using a nonhydrostatic model which is based on the Reynolds averaged Navier-Stokes equations in the Boussinesq approximation for a continuously stratified fluid. The Smagorinsky turbulence model extended for stratified fluid was used to explicitly describe the small-scale turbulent mixing. Two series of numerical experiments were carried out in an idealized 2D setup. The first series aimed to study processes of the ISW-depression transformation under ice cover of constant submerged ice thickness. A loss of energy was estimated based on the budget of depth-integrated pseudoenergy before and after the wave transformation. The transformation of depression ISW is controlled by the blocking parameter β. For large positive and large negative values of parameter β which is the ratio of the height of the minimum depth of the upper layer under the ice cover to the incident wave amplitude. The energy loss was relatively small for large positive and large negative values of β. The maximal value of energy loss was about 38 % and it is reached at β ≈ 0 for ISW. In the second series of experiments, a number of keels were located underside of the ice layer of constant thickness. The ISW transformation under ridged ice also depends on the blocking parameter β. For large keels (β<0), more than 40 % is lost on the first keel, while for relatively small keels (β>0.3), the losses on the first keel are less than 6 %. Energy losses due to all keels depend on the distance between them which is characterized by the parameter μ which is the ratio keel depth to the distance between keels. If the tidal flow around the large keels is the source of internal waves, then under conditions of strongly ridged ice the waves excited by the tidal flow are dispersed in the vicinity of their formation.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-1992', Anonymous Referee #1, 02 Oct 2023
This manuscript considers two-dimensional simulations of internal solitary waves propagating into a region with modelled ice cover. The ice cover is modelled as not moving, and as represented by a piecewise constant value (or perhaps as smoothed) of a drag parameter (which is varied to some degree). The former is sensible, while the latter is perhaps a necessary choice for the model employed. The manuscript is interesting, and the figures provide useful information. The text needs a thorough reading for technical English (if necessary I can provide a list of suggestions when the scientific review is completed). I feel that a version of this manuscript can appear in NPG, but there are some necessary changes/improvements. I enumerate these below, but as an overall comment I would say the results need to discuss the new results in terms of existing literature and the second set of experiments needs a more complete analysis and discussion.
I note that for many of the Yes/No questions the journal asks, the manuscript falls between a strict Yes or NO.
1) Self-citation: Proof read to ensure that when a topic is introduced, e.g. shoaling of elevation, the references provided are more than just those of the authors (in particular for numerical studies). This is not just an issue of a longer bibliography. There are quite a few papers I would consider relevant listed, but they tend to appear as lists in the Introduction, and the opportunity to discuss the context of the numerical simulations in terms of these papers is missed.
2) Details of the numerical model. The basic idea of the top boundary condition is introduced, but right now an interested reader could not reproduce the results on their own. What needs to be done to implement the conditions? What complications result (e.g. in the pressure problem)? Can the drag coefficients really just be discontinuous?
3) The model resolution deserves comment. What can one expect to see/resolve (certainly I believe wave fissioning is accurately represented); what do we miss (I think the details of the high shear region near the ice cannot be accurately represented). The Carr et al corrugation paper gives details of the interaction with a no slip boundary layer, and hence provides an easy contrast.
4) I’d prefer “smoothed step” to “step”. It would also help to state for the reader how many points there are across the changing part of the tang-based step.
5) It would be good to indicate the integration region for the energetics calculations on the appropriate panel of Fig 4. Similarly the spacing of the equations in the system 6 could be improved (perhaps this is due to them lying at the bottom of the page, and they will likely move in a final version of the manuscript).
6) Presumably the g in equation (8) is a reduced gravity? Otherwise I cannot see how a supercritical regime is reached.
7) I found the second set of experiments, the ice keels, to be a bit tougher to digest, likely due to its brevity. I have questions about the way the boundary layer is parametrized (wouldn’t there be more drag over the downstream slope where Carr at all predicted “local hydraulic” phenomena?). The discussion of Fig 7 seems incomplete (what are the curves shown, what are the details of what is presumably a fitting process?).
8) I agree with the comments in line 220. At the same time, I think there have been simulations in the literature of related heat-salt phenomena. Tt least to point to these as a start of relevant studies.
Citation: https://doi.org/10.5194/egusphere-2023-1992-RC1 - AC2: 'Reply on RC1', Kateryna Terletska, 05 Dec 2023
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RC2: 'Comment on egusphere-2023-1992', Anonymous Referee #2, 26 Oct 2023
Transformation of internal solitary waves under ridged ice cover by Terletska et al.
This paper presents a numerical investigation of ISWs propagating under ice. A Reynolds averaged Navier-Stokes solver is utilised and both smooth and ridged ice is considered. The wave propagates from open water to under ice and two cases are focussed upon namely smooth ice and ridged ice. In the smooth ice case, a blocking parameter is shown to be the main control variable and flow dynamics in keeping with previous results by the first author and co-workers for an ISW of elevation over a step are seen. In the ridged case both the blocking parameter and a second parameter describing the ratio between keel depth and distance between keels are used to classify the flow.
The paper is original and interesting and I am supportive of publication subject to the minor remarks below.
The paper contains a lot of typographical and grammatical errors, these need to be fixed in advance of publication.
Citation is not thorough enough. Key papers are cited but the authors often fail to compare their work with published literature.
Abstract second sentence – you refer to ‘breaking IWs’ at the edge. How do they break? Do they always break? Is there evidence for this? May be the word ‘breaking’ should be deleted?
Abstract 3rd line – you talk about generation of ISWs, is this specific to polar oceans or in general?
Line 31. ISW shear, convective instabilities, and breaking on topographic inhomogeneities extract kinetic energy from ISWs for turbulence and subsequent mixing increases the melting of ice. Is the last part of this sentence true? If so can you give a suitable reference?
Line 50 – you say your wave goes from open water (with a free surface) to under-ice. Is this reflected in the numerical model or does the open water have a rigid lid in the numerical work? If so this should be made clear and potential differences with a free surface discussed.
Line 100 – you have compared free slip and no slip and found little difference however it is known that the upper boundary condition can effect wave properties such as amplitude and stability at least on the lab scale (see e.g. Carr et al 2008 PoF, Luzzatto-Fegiz & Helfrich 2014 JFM). Why does it not matter here? Is it because surface tension effects aren’t as important on your scale? Did you do any sensitivity test on the upper boundary condition?
Line 168 – you talk about reflected waves off the solid boundary step. Would you expect the same for real ice? Is there any way of assessing or inferring what will happen if the ice isn’t solid for e.g in the MIZ when the ice is mushy?
Line 200 how does this statement compare with published papers on the generation of IWs by ice keels see e.g. Zhang et al 2022 J. Ocean Limnol, Zhang et al 2022 JGR:Oceans, M. McPhee & L. Kantha. 1989 J. Geophys. Res.
Line 212 – the statement about ice roughness- is this in comparison to the blocking parameter?
Line 222 - could the authors say more about this ? How might this be represented within their numerical model for example ?
Citation: https://doi.org/10.5194/egusphere-2023-1992-RC2 - AC1: 'Reply on RC2', Kateryna Terletska, 05 Dec 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-1992', Anonymous Referee #1, 02 Oct 2023
This manuscript considers two-dimensional simulations of internal solitary waves propagating into a region with modelled ice cover. The ice cover is modelled as not moving, and as represented by a piecewise constant value (or perhaps as smoothed) of a drag parameter (which is varied to some degree). The former is sensible, while the latter is perhaps a necessary choice for the model employed. The manuscript is interesting, and the figures provide useful information. The text needs a thorough reading for technical English (if necessary I can provide a list of suggestions when the scientific review is completed). I feel that a version of this manuscript can appear in NPG, but there are some necessary changes/improvements. I enumerate these below, but as an overall comment I would say the results need to discuss the new results in terms of existing literature and the second set of experiments needs a more complete analysis and discussion.
I note that for many of the Yes/No questions the journal asks, the manuscript falls between a strict Yes or NO.
1) Self-citation: Proof read to ensure that when a topic is introduced, e.g. shoaling of elevation, the references provided are more than just those of the authors (in particular for numerical studies). This is not just an issue of a longer bibliography. There are quite a few papers I would consider relevant listed, but they tend to appear as lists in the Introduction, and the opportunity to discuss the context of the numerical simulations in terms of these papers is missed.
2) Details of the numerical model. The basic idea of the top boundary condition is introduced, but right now an interested reader could not reproduce the results on their own. What needs to be done to implement the conditions? What complications result (e.g. in the pressure problem)? Can the drag coefficients really just be discontinuous?
3) The model resolution deserves comment. What can one expect to see/resolve (certainly I believe wave fissioning is accurately represented); what do we miss (I think the details of the high shear region near the ice cannot be accurately represented). The Carr et al corrugation paper gives details of the interaction with a no slip boundary layer, and hence provides an easy contrast.
4) I’d prefer “smoothed step” to “step”. It would also help to state for the reader how many points there are across the changing part of the tang-based step.
5) It would be good to indicate the integration region for the energetics calculations on the appropriate panel of Fig 4. Similarly the spacing of the equations in the system 6 could be improved (perhaps this is due to them lying at the bottom of the page, and they will likely move in a final version of the manuscript).
6) Presumably the g in equation (8) is a reduced gravity? Otherwise I cannot see how a supercritical regime is reached.
7) I found the second set of experiments, the ice keels, to be a bit tougher to digest, likely due to its brevity. I have questions about the way the boundary layer is parametrized (wouldn’t there be more drag over the downstream slope where Carr at all predicted “local hydraulic” phenomena?). The discussion of Fig 7 seems incomplete (what are the curves shown, what are the details of what is presumably a fitting process?).
8) I agree with the comments in line 220. At the same time, I think there have been simulations in the literature of related heat-salt phenomena. Tt least to point to these as a start of relevant studies.
Citation: https://doi.org/10.5194/egusphere-2023-1992-RC1 - AC2: 'Reply on RC1', Kateryna Terletska, 05 Dec 2023
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RC2: 'Comment on egusphere-2023-1992', Anonymous Referee #2, 26 Oct 2023
Transformation of internal solitary waves under ridged ice cover by Terletska et al.
This paper presents a numerical investigation of ISWs propagating under ice. A Reynolds averaged Navier-Stokes solver is utilised and both smooth and ridged ice is considered. The wave propagates from open water to under ice and two cases are focussed upon namely smooth ice and ridged ice. In the smooth ice case, a blocking parameter is shown to be the main control variable and flow dynamics in keeping with previous results by the first author and co-workers for an ISW of elevation over a step are seen. In the ridged case both the blocking parameter and a second parameter describing the ratio between keel depth and distance between keels are used to classify the flow.
The paper is original and interesting and I am supportive of publication subject to the minor remarks below.
The paper contains a lot of typographical and grammatical errors, these need to be fixed in advance of publication.
Citation is not thorough enough. Key papers are cited but the authors often fail to compare their work with published literature.
Abstract second sentence – you refer to ‘breaking IWs’ at the edge. How do they break? Do they always break? Is there evidence for this? May be the word ‘breaking’ should be deleted?
Abstract 3rd line – you talk about generation of ISWs, is this specific to polar oceans or in general?
Line 31. ISW shear, convective instabilities, and breaking on topographic inhomogeneities extract kinetic energy from ISWs for turbulence and subsequent mixing increases the melting of ice. Is the last part of this sentence true? If so can you give a suitable reference?
Line 50 – you say your wave goes from open water (with a free surface) to under-ice. Is this reflected in the numerical model or does the open water have a rigid lid in the numerical work? If so this should be made clear and potential differences with a free surface discussed.
Line 100 – you have compared free slip and no slip and found little difference however it is known that the upper boundary condition can effect wave properties such as amplitude and stability at least on the lab scale (see e.g. Carr et al 2008 PoF, Luzzatto-Fegiz & Helfrich 2014 JFM). Why does it not matter here? Is it because surface tension effects aren’t as important on your scale? Did you do any sensitivity test on the upper boundary condition?
Line 168 – you talk about reflected waves off the solid boundary step. Would you expect the same for real ice? Is there any way of assessing or inferring what will happen if the ice isn’t solid for e.g in the MIZ when the ice is mushy?
Line 200 how does this statement compare with published papers on the generation of IWs by ice keels see e.g. Zhang et al 2022 J. Ocean Limnol, Zhang et al 2022 JGR:Oceans, M. McPhee & L. Kantha. 1989 J. Geophys. Res.
Line 212 – the statement about ice roughness- is this in comparison to the blocking parameter?
Line 222 - could the authors say more about this ? How might this be represented within their numerical model for example ?
Citation: https://doi.org/10.5194/egusphere-2023-1992-RC2 - AC1: 'Reply on RC2', Kateryna Terletska, 05 Dec 2023
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Kateryna Terletska
Elena Tobisch
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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