[1] A laboratory analogue of a three-layer linear viscous slab-upper mantle-lower mantle system is established in a silicone putty, honey and crystallized honey tank experiment. The same setup as in the numerical investigation (part 1) is used. We focus on the interaction of the slab with the induced passive mantle flow by widely varying the mantle volume flux boundary conditions. In our numerical experiments the lateral volume flux was set to zero. In interpreting the results relative to the real Earth, the base of the box is taken as the bottom of the mantle convection system, while the lateral boundaries may be associated with the presence of other nearby slabs. Dynamic force equilibrium, assessed on the basis of an analytical review of forces, is described for four different phases: (1) the subduction initiation instability, (2) the accelerating dynamic free fall phase of the slab, (3) the dynamic interaction with the 660-km discontinuity, and (4) a final phase of steady state trench retreat. Phase 3 is an important feature not observed in the numerical experiments. This highly dynamic phase of interrupted trench retreat can therefore be attributed to boundary conditions on mantle volume flux. On the basis of integration constants of force equilibrium in phases 2 and 4 we identify two different classes of volume flux: one in which the lateral boundary can be considered open and the other class where it is ''closed.'' Closed boundary condition cases are obtained if any of the lateral box boundaries are 600 km away from the slab. Assuming a one-to-one relation between trench retreat and back arc spreading, enigmatic observations of episodic opening of back arc basins can be explained by our experimental observations.

[1] We use two-dimensional numerical experiments to investigate the long-term dynamics of an oceanic slab. Two problems are addressed: one concerning the influence of rheology on slab dynamics, notably the role of elasticity, and the second dealing with the feedback of slab-mantle interaction to be resolved in part 2. The strategy of our approach is to formulate the simplest setup that allows us to separate the effects of slab rheology (part 1) from the effects of mantle flux (part 2). Therefore, in this paper, we apply forces to the slab using simple analytical functions related to buoyancy and viscous forces in order to isolate the role of rheology on slab dynamics. We analyze parameters for simplified elastic, viscous, and nonlinear viscoelastoplastic single-layer models of slabs and compare them with a stratified thermomechanical viscoelastoplastic slab embedded in a thermal solution. The near-surface behavior of slabs is summarized by assessing the amplitude and wavelength of forebulge uplift for each rheology. In the complete thermomechanical solutions, vastly contrasting styles of slab dynamics and force balance are observed at top and bottom bends. However, we find that slab subduction can be modeled using simplified rheologies characterized by a narrow range of selected benchmark parameters. The best fit linear viscosity ranges between 5 Â 10 22 Pa s and 5 Â 10 23 Pa s. The closeness of the numerical solution to nature can be characterized by a Deborah number >0.5, indicating that elasticity is an important ingredient in subduction.

Abstract. An important and novel mechanism for ductile failure of the lithosphere is identified here, which is intrinsic to the thermal-mechanical feedback in a temperature dependent plastic body with coupled elastic fields. Both a temperaturedependent power-law visco-elasto-plastic theology and a temperature-dependent elasto-plastic theology are employed to study in a self-consistent fashion the deformation of the lithosphere subject to extension by means of a two-dimensional, finite-element code. A structural perturbation initially localizes elasto-plastic deformation only in its immediate vicinity. However, after 800,000 years have elapsed the localized zone of deformation takes off in a 'crack-like' fashion and travels to the bottom of the lithosphere in about 50,000 years time. When the plate is severed, thermal runaway is caused by mechanical heating triggered by the rapid energy transfer of the globally stored elastic energy into localized plastic dissipation in the ductile fault.

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtosecond to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth's core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth's surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults.

Measuring Earth material behaviour on time scales of millions of years transcends our current capability in the laboratory. We review an alternative path considering multiscale and multiphysics approaches with quantitative structure-property relationships. This approach allows a sound basis to incorporate physical principles such as chemistry, thermodynamics, diffusion and geometry-energy relations into simulations and data assimilation on the vast range of length and time scales encountered in the Earth. We identify key length scales for Earth systems processes and find a substantial scale separation between chemical, hydrous and thermal diffusion. We propose that this allows a simplified two-scale analysis where the outputs from the micro-scale model can be used as inputs for meso-scale simulations, which then in turn becomes the micro-model for the next scale up. We present two fundamental theoretical approaches to link the scales through asymptotic homogenisation from a macroscopic thermodynamic view and percolation renormalisation from a microscopic, statistical mechanics view.