Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory
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se-12-869-2021.pdf
Description
Published version
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3.89 MB
Format
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Author(s)
Regenauer-Lieb, Klaus
Hu, Manman
Schrank, Christoph
Chen, Xiao
Clavijo, Santiago Peña
Kelka, Ulrich
Karrech, Ali
Gaede, Oliver
Blach, Tomasz
Roshan, Hamid
Date Issued
April 16, 2021
Journal
Solid Earth
Publisher
Copernicus GmbH
Citation
Regenauer-Lieb, K., Hu, M., Schrank, C., Chen, X., Clavijo, S. P., Kelka, U., Karrech, A., Gaede, O., Blach, T., Roshan, H., and Jacquey, A. B.: Cross-diffusion waves resulting from multiscale, multi-physics instabilities: theory, Solid Earth, 12, 869–883.
Version
Final published version
Abstract
We propose a multiscale approach for coupling multi-physics processes across the scales. The physics is based on discrete phenomena, triggered by local thermo-hydro-mechano-chemical (THMC) instabilities, that cause cross-diffusion (quasi-soliton) acceleration waves. These waves nucleate when the overall stress field is incompatible with accelerations from local feedbacks of generalized THMC thermodynamic forces that trigger generalized thermodynamic fluxes of another kind. Cross-diffusion terms in the 4×4 THMC diffusion matrix are shown to lead to multiple diffusional P and S wave equations as coupled THMC solutions. Uncertainties in the location of meso-scale material instabilities are captured by a wave-scale correlation of probability amplitudes. Cross-diffusional waves have unusual dispersion patterns and, although they assume a solitary state, do not behave like solitons but show complex interactions when they collide. Their characteristic wavenumber and constant speed define mesoscopic internal material time–space relations entirely defined by the coefficients of the coupled THMC reaction–cross-diffusion equations. A companion paper proposes an application of the theory to earthquakes showing that excitation waves triggered by local reactions can, through an extreme effect of a cross-diffusional wave operator, lead to an energy cascade connecting large and small scales and cause solid-state turbulence.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.5194/se-12-869-2021
