Summary Patterns in nature are often interpreted as a product of reaction-diffusion processes which result in dissipative structures. Thermodynamic constraints allow prediction of the final state but the dynamic evolution of the micro-processes is hidden. We introduce a new microphysics-based approach that couples the microscale cross-constituent interactions to the large-scale dynamic behaviour, which leads to the discovery of a family of soliton-like excitation waves. These waves can appear in hydromechanically coupled porous media as a reaction to external stimuli. They arise, for instance, when mechanical forcing of the porous skeleton releases internal energy through a phase change, leading to tight coupling of the pressure in the solid matrix with the dissipation of the pore fluid pressure. In order to describe these complex multiscale interactions in a thermodynamic consistent framework, we consider a dual-continuum system, where the large-scale continuum properties of the matrix-fluid interaction are described by a reaction-self diffusion formulation, and the small-scale dissipation of internal energy by a reaction-cross diffusion formulation that spells out the macroscale reaction and relaxes the adiabatic constraint on the local reaction term in the conventional reaction-diffusion formalism. Using this approach, we recover the familiar Turing bifurcations (e.g., rhythmic metamorphic banding), Hopf bifurcations (e.g., Episodic Tremor and Slip), and present the new excitation wave phenomenon. The parametric space is investigated numerically and compared to serpentinite deformation in subduction zones.
Abstract. Theoretical approaches to earthquake instabilities propose shear-dominated source mechanisms. Here we take a fresh look at the role of possible volumetric instabilities preceding a shear instability. We investigate the phenomena that may prepare earthquake instabilities using the coupling of thermo-hydro-mechano-chemical reaction–diffusion equations in a THMC diffusion matrix. We show that the off-diagonal cross-diffusivities can give rise to a new class of waves known as cross-diffusion or quasi-soliton waves. Their unique property is that for critical conditions cross-diffusion waves can funnel wave energy into a stationary wave focus from large to small scale. We show that the rich solution space of the reaction–cross-diffusion approach to earthquake instabilities can recover classical Turing instabilities (periodic in space instabilities), Hopf bifurcations (spring-slider-like earthquake models), and a new class of quasi-soliton waves. Only the quasi-soliton waves can lead to extreme focussing of the wave energy into short-wavelength instabilities of short duration. The equivalent extreme event in ocean waves and optical fibres leads to the appearance of “rogue waves” and high energy pulses of light in photonics. In the context of hydromechanical coupling, a rogue wave would appear as a sudden fluid pressure spike. This spike is likely to cause unstable slip on a pre-existing (near-critically stressed) fault acting as a trigger for the ultimate (shear) seismic moment release.
<p>Coupled Thermo-Hydro-Mechano-Chemical (THMC) patterns are ubiquitous in nature yet their origin is not yet fully understood. We propose a generic framework for pattern formation in terms of quasi-solitary wave instabilities that are triggered by cross-scale THMC-feedbacks considering a general topology of saturated porous media [1]. We identify the important aspect of cross-diffusion terms and present a linear stability analysis of the governing partial differential equations (pde&#8217;s). Multiple transient wave instabilities are found as solutions of the coupled THMC pde&#8217;s and in the standing wave limit (infinite time scale) these waves form the solitary wave patterns frozen into the geosystems at various scales.</p><p>Cross diffusion in a complex system is defined by the phenomenon that a gradient of one generalised thermodynamic force drives a generalised thermodynamic flux of another kind. Thermodynamic forces and fluxes in a THMC-system are defined as follows. Thermodynamic forces are the gradients of the THMC-system. The flux (T) represents Fourier&#8217;s law where thermal conductivity represents its characteristic diffusivity. The flux (H) describes Darcy&#8217;s law, where the diffusivity depends on the intrinsic permeability of the porous structure and the viscosity of saturating fluid. The flux (M) represents the incremental change in the solid-phase overstress adopting a Representative Elementary Volume (REV) formalism. The fluid phase within the REV, as an immediate environment surrounding the solid matrix, synchronously feels the pressure change, and vice versa. The flux (C) is Fick&#8217;s law, where chemical reaction and transport processes occur predominantly at/around the solid-fluid interfacial areas.</p><p>In order to express the THMC feedback we write the governing reaction diffusion equations as coupled HM equations with generalized source terms depending on temperature, concentration, fluid pressure and solid overstress and further consider the cross-diffusion terms as a generic framework:</p><p><img src="data:image/png;base64, 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