×

zbMATH — the first resource for mathematics

Analysis of dynamics in multiphysics modelling of active faults. (English) Zbl 1372.37129
Summary: Instabilities in Geomechanics appear on multiple scales involving multiple physical processes. They appear often as planar features of localised deformation (faults), which can be relatively stable creep or display rich dynamics, sometimes culminating in earthquakes. To study those features, we propose a fundamental physics-based approach that overcomes the current limitations of statistical rule-based methods and allows a physical understanding of the nucleation and temporal evolution of such faults. In particular, we formulate the coupling between temperature and pressure evolution in the faults through their multiphysics energetic process(es). We analyse their multiple steady states using numerical continuation methods and characterise their transient dynamics by studying the time-dependent problem near the critical Hopf points. We find that the global system can be characterised by a homoclinic bifurcation that depends on the two main dimensionless groups of the underlying physical system. The Gruntfest number determines the onset of the localisation phenomenon, while the dynamics are mainly controlled by the Lewis number, which is the ratio of energy diffusion over mass diffusion. Here, we show that the Lewis number is the critical parameter for dynamics of the system as it controls the time evolution of the system for a given energy supply (Gruntfest number).
MSC:
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
74L05 Geophysical solid mechanics
Software:
REDBACK; Matlab
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/j.physa.2013.04.045
[2] DOI: 10.1038/srep05401
[3] DOI: 10.1016/j.amc.2014.07.063 · Zbl 1335.86008
[4] DOI: 10.1029/JB077i020p03690
[5] DOI: 10.1029/JB088iB12p10359
[6] DOI: 10.1016/0022-5096(84)90007-3 · Zbl 0542.73017
[7] DOI: 10.1103/PhysRevLett.87.148501
[8] DOI: 10.1002/2013JB010070
[9] DOI: 10.1002/2013JB010071
[10] DOI: 10.1002/2014JB011004
[11] DOI: 10.1016/j.jmps.2010.06.010 · Zbl 1429.74049
[12] DOI: 10.1029/2008JB006004
[13] DOI: 10.1016/j.compgeo.2015.12.015
[14] DOI: 10.1007/s00603-016-0927-y
[15] Law, Combustion Physics (2006)
[16] Fowler, Mathematical Models in the Applied Sciences (1997) · Zbl 0997.00535
[17] DOI: 10.1038/nature05717
[18] DOI: 10.1007/s00603-016-0996-y
[19] Gottlieb, Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics (1987)
[20] Trefethen, Spectral Methods in MatLab (2000)
[21] DOI: 10.1137/0903012 · Zbl 0497.65028
[22] DOI: 10.1122/1.548954 · Zbl 0139.43804
[23] DOI: 10.1002/2014GL061715
[24] DOI: 10.1103/RevModPhys.65.1331
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.