Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory

Regenauer-Lieb, Klaus; Hu, Manman; Schrank, Christoph; Chen, Xiao; Clavijo, Santiago Peña; Kelka, Ulrich; Karrech, Ali; Gaede, Oliver; Blach, Tomasz; Roshan, Hamid; Jacquey, Antoine B.

doi:https://doi.org/10.5194/se-12-869-2021

Articles | Volume 12, issue 4

https://doi.org/10.5194/se-12-869-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Special issue:

Thermo-hydro-mechanical–chemical (THMC) processes in natural...

https://doi.org/10.5194/se-12-869-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 12, issue 4

Research article

|

16 Apr 2021

Research article |

| 16 Apr 2021

Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory

Klaus Regenauer-Lieb, Manman Hu, Christoph Schrank, Xiao Chen, Santiago Peña Clavijo, Ulrich Kelka, Ali Karrech, Oliver Gaede, Tomasz Blach, Hamid Roshan, and Antoine B. Jacquey

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Final revised paper (published on 16 Apr 2021)
Preprint (discussion started on 11 Aug 2020)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Comments to “Cross-DiffusionWaves as a trigger for Multiscale, Multi-Physics Instabilities:Theory” by Regenauer-Lieb et al.', Angelo De Santis, 28 Sep 2020
- AC1: 'Response to Angelo de Santis comments', Klaus Regenauer-Lieb, 23 Oct 2020
RC2: 'review', Jean Paul Ampuero, 30 Sep 2020
- AC2: 'Jean-Paul Ampuero (Referee) review', Klaus Regenauer-Lieb, 23 Oct 2020

Peer-review completion

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

AR by Klaus Regenauer-Lieb on behalf of the Authors (24 Oct 2020) Manuscript

ED: Referee Nomination & Report Request started (30 Oct 2020) by Andre R. Niemeijer

RR by Angelo De Santis (25 Nov 2020)

RR by Anonymous Referee #3 (25 Jan 2021)

Suggestions for revision or reasons for rejection

This constitutes my review of the Regenauer-Lieb et al manuscript “Cross Diffusion Waves …: Theory. This is paper 1 of a two-paper series. I enjoyed reading this paper and feel that it should be accepted with minor revisions. I detail some minor corrections below (these are minor). The paper is a good companion to the Solid Earth Special Issue deriving from the recent GEOPROC conference in Ultrecht.

Two aspects present themselves which the authors should concern themselves in the revisions. First, much of the theory and discussion in this paper mirrors the treatment in the recent Hu et al. paper (J. Mechanics Phys Solids 135, 2020). The authors should discuss how the present paper differs in content from the Hu et al. paper.

Second, I feel that the “cross-diffusion” aspect of the wave propagation is confusing and potentially ill-suited to describe the onset of THMC instabilities. The authors accurately describe the “cross diffusion” matrix in analogy with the cross diffusion (non diagonal) terms arising in chemical diffusion as occurs in concentrated brines or melts e.g. These represent “linear” couplings between fluxes and forces in the Onsager sense. As such the terms in the matrix do not describe the (by necessity, as described by Prigogine) non-linear couplings that arise from 1. Non equilibrium conditions and 2. The existence of coupling feedbacks. I think its important to distinguish excitability (nonlinear growth of perturbations) which would be described by the reaction rate terms in their Table 1 or in their equations (21). I think this is well discussed in the Tsyganiov reference the authors include. Thus I question the linkage of “cross diffusion” with instability given in the title. The same would be true of the “acoustic tensor “ plasticity approach of Hill and Rudnicki and Rice – they discuss the “uniqueness” of plastic instabilities but a priori assume the “existence”. Or am I missing something? The phenomena discussed in this paper are related to the compaction/density waves discussed by Dan McKenzie in 1984 and in that case, the instabilities require a nonlinear coupling of porosity with permeability – surely the linear requirement of the cross diffusional matrix (which is explained better in the HU et al paper) preclude this type of instability? The authors may wish to elucidate these concerns, and hopefully these don’t muddy the waters but lead to a clarification. Certainly the non diagonal terms in the THMC matrix in the authors Table 1 are important considerations in the propagation of soliton-like waves, but by themselves they don’t describe the onset of instability leading to the development of such waves???

Line 42 – the authors may wish to consider a consistent way of referring to the second, companion paper (e.g., Paper 1, and Paper 2)

Line 79 – omit the second “s” in “systemss”

Line 89 – sentence is confusing (“processes travels”??)

Line 95 – omit “s” in details; omit comma after diffusion

Line 109 – omit semi colon and instead use parenthesis to be consistent with earlier terms in the sentence, i.e., “chemical driving forces (chemo-taxis)”

Line 110 – omit “Thermal, Hydrodynamic, Mechanical, and Chemical” as abbreviation has been defined previously

Line 123 – omit comma after “physics”

Line 134 – put references in parentheses.

Line 253 – It is confusing as to what is meant by “former” and “latter” with respect to the previous sentence; please rewrite

Line 276 – the creeping flow assumption ignores the acceleration terms in the Navier-Stokes equation, but there still can be effects of “gravitational acceleration”, i.e. creeping flow in a gravity field.

Line 285 – The phrasing “The compatibility condition relating jumps…” is not a complete sentence

Line 293 – I believe you want to make the phrase “It follows from Eq. 7” the start of a new sentence

Line 324 – “tabulated in Table 1. The reaction rates…”?
Line 326 – there is no operator H-hat-sub”THMC” in Table 1.

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ED: Publish subject to minor revisions (review by editor) (29 Jan 2021) by Andre R. Niemeijer

AR by Klaus Regenauer-Lieb on behalf of the Authors (04 Feb 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (09 Feb 2021) by Andre R. Niemeijer

ED: Publish as is (09 Feb 2021) by Susanne Buiter (Executive editor)

AR by Klaus Regenauer-Lieb on behalf of the Authors (15 Feb 2021)

Short summary

In this paper we expand on a recent discovery of slow cross-diffusion hydromechanical waves cast into a new concise reaction–diffusion equation for THMC coupling. If waves are excited through the THMC reaction terms unbounded reactions can be captured by inclusion of statistical information from the lower scale through nonlocal reaction–diffusion equations. These cross-diffusion coefficients regularize extreme earthquake-like events (rogue waves) through a new form of quasi-soliton wave.