Effective Viscosity (effective + viscosity)

Distribution by Scientific Domains

Selected Abstracts

A unified continuum representation of post-seismic relaxation mechanisms: semi-analytic models of afterslip, poroelastic rebound and viscoelastic flow

Sylvain Barbot
SUMMARY We present a unified continuum mechanics representation of the mechanisms believed to be commonly involved in post-seismic transients such as viscoelasticity, fault creep and poroelasticity. The time-dependent relaxation that follows an earthquake, or any other static stress perturbation, is considered in a framework of a generalized viscoelastoplastic rheology whereby some inelastic strain relaxes a physical quantity in the material. The relaxed quantity is the deviatoric stress in case of viscoelastic relaxation, the shear stress in case of creep on a fault plane and the trace of the stress tensor in case of poroelastic rebound. In this framework, the instantaneous velocity field satisfies the linear inhomogeneous Navier's equation with sources parametrized as equivalent body forces and surface tractions. We evaluate the velocity field using the Fourier-domain Green's function for an elastic half-space with surface buoyancy boundary condition. The accuracy of the proposed method is demonstrated by comparisons with finite-element simulations of viscoelastic relaxation following strike-slip and dip-slip ruptures for linear and power-law rheologies. We also present comparisons with analytic solutions for afterslip driven by coseismic stress changes. Finally, we demonstrate that the proposed method can be used to model time-dependent poroelastic rebound by adopting a viscoelastic rheology with bulk viscosity and work hardening. The proposed method allows one to model post-seismic transients that involve multiple mechanisms (afterslip, poroelastic rebound, ductile flow) with an account for the effects of gravity, non-linear rheologies and arbitrary spatial variations in inelastic properties of rocks (e.g. the effective viscosity, rate-and-state frictional parameters and poroelastic properties). [source]

Magnetic and viscous coupling at the core,mantle boundary: inferences from observations of the Earth's nutations

B. A. Buffett
SUMMARY Dissipative core,mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short-wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen & Aubert (2006) to assess whether the required short-wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short-wavelength field, we obtain a total ohmic dissipation of 0.7,1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m2 s,1 or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10,4 m2 s,1, which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle. [source]

Microfabric of folded quartz veins in metagreywackes: dislocation creep and subgrain rotation at high stress

Abstract The microfabrics of folded quartz veins in fine-grained high pressure,low temperature metamorphic greywackes of the Franciscan Subduction Complex at Pacheco Pass, California, were investigated by optical microscopy, scanning electron microscopy including electron backscatter diffraction, and transmission electron microscopy. The foliated host metagreywacke is deformed by dissolution,precipitation creep, as indicated by the shape preferred orientation of mica and clastic quartz without any signs of crystal-plastic deformation. The absence of crystal-plastic deformation of clastic quartz suggests that the flow stress in the host metagreywacke remained below a few tens of MPa at temperatures of 250,300 °C. In contrast, the microfabric of the folded quartz veins indicates deformation by dislocation creep accompanied by subgrain rotation recrystallization. For the small recrystallized grain size of ,8 ± 6 ,m, paleopiezometers indicate differential stresses of a few hundred MPa. The stress concentration in the single phase quartz vein is interpreted to be due to its higher effective viscosity compared to the fine-grained host metagreywacke deforming by dissolution,precipitation creep. The fold shape suggests a viscosity contrast of one to two orders of magnitude. Deformation by dissolution,precipitation creep is expected to be a continuous process. The same must hold for folding of the vein and deformation of the vein quartz by dislocation creep. The microfabric suggests dynamic recrystallization predominantly by subgrain rotation and only minor strain-induced grain boundary migration, which requires low contrasts in dislocation density across high-angle grain boundaries to be maintained during climb-controlled creep at high differential stress. The record of quartz in these continuously deformed veins is characteristic and different from the record in metamorphic rocks exhumed in seismically active regions, where high-stress deformation at similar temperatures is episodic and related to the seismic cycle. [source]

The effects of porphyroblast growth on the effective viscosity of metapelitic rocks: implications for the strength of the middle crust

Abstract Numerical models are used to examine the effects of porphyroblast growth on the rheology of compositionally layered rocks (metapelites and metapsammites) and by extension the middle crust during prograde metamorphism. As porphyroblast abundance increases during prograde metamorphism, metapelitic layers will strengthen relative to porphyroblast-free metapelitic units, and potentially relative to quartzofeldspathic metapsammitic units. As metapelitic layers become stronger, the integrated strength of compositionally layered successions increases, potentially causing large volumes of mid-crustal rock to strengthen, altering the strain-rate distribution in the middle crust and affecting the geodynamic evolution of an orogenic belt. The growth of effectively rigid porphyroblasts creates strength heterogeneities in the layer undergoing porphyroblast growth, which leads to complex strain-rate distributions within the layer. At the orogen scale, the strengthening of large crustal volumes (on the order of thousands of cubic kilometres) changes the strain-rate distribution, which may change exhumation rates of high-grade metamorphic rocks, the geothermal structure and the topography of the orogen. The presence of a strong zone in the middle crust causes strain-rate partitioning around the zone, suppressed uplift rates within and above the zone and leads to the development of a basin on the surface. [source]

Non-linear bending waves in Keplerian accretion discs

G. I. Ogilvie
ABSTRACT The non-linear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary non-linear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative non-linear Schrödinger (DNLS) equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The non-linear and dispersive effects both depend on the compressibility of the gas through its adiabatic index ,. In the physically realistic case , < 3, non-linearity does not lead to the steepening of bending waves but instead enhances their linear dispersion. In the opposite case , > 3, non-linearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs. [source]

The effect of particle shape on pipeline friction for newtonian slurries of fine particles

Jason Schaan
Abstract Experiments have been conducted to assess the effect of particle shape on pipeline friction in turbulent flow, using laboratory pipelines of nominal diameter 50 mm and 150 mm. The experiments were intended to examine the extent to which a fluid model is appropriate for slurries of this type, especially at high solids concentrations. The experiments confirm that fluid friction at low and moderate solids concentrations is proportional to slurry density, with particle shape being of minor importance. At high solids concentrations, additional increases in friction are observed and these depend upon the ratio of the solids concentration to the maximum settled concentration. Although this friction increase is qualitatively similar to that which would result from increased slurry viscosity, the evidence suggests that particle-wall contact is the mechanism. However, the transition from turbulent to laminar flow indicates that an effective viscosity should be used in calculating critical Reynolds numbers. Afin d'évaluer l'effet de la forme des particules sur le frottement dans les pipelines en régime turbulent, des expériences ont été menées avec des pipelines de laboratoire d'un diamétre nominal de 50 mm et de 150 mm. Le but de ces expériences était de voir jusqu'à quel point un fluide modèle est approprié pour ce type de suspensions, en particulier à de fortes concentrations de solides. Les expériences confirment que le frottement du fluide à des concentrations de solides faibles ou moyennes est proportionnel à la masse volumique des suspensions, la forme des particules étant de peu d'importance. À de fortes concentrations de solides, on observe un accroissement supplémentaire du frottement qui est lié au rapport entre la concentration de solides et la concentration sédimentée maximum. Bien que cette augmentation du frottement soit d'un point de vue qualitatif semblable à ce qu'il réulterait d'une viscosité accrue des suspensions, selon toutes les apparences le mécanisme réside dans le contact particules-paroi. Cependant, la transition de l'écoulement turbulent à l'écoulement laminaire indique qu'une viscosité effective devrait ##etre utilisée dans le calcul des nombres de Reynolds critiques. [source]