Strain Rate Fluctuations Research Articles

Spatial migration of temporal earthquake clusters driven by the transfer of differential stress between neighbouring fault/shear-zone structures

Uncertainty concerning the processes responsible for slip-rate fluctuations associated with temporal clustering of surface faulting earthquakes is a fundamental, unresolved issue in tectonics, because strain-rates accommodated by fault/shear-zone structures are the key to understanding the viscosity structure of the crust and seismic hazard. We constrain the timing and amplitude of slip-rate fluctuations that occurred on three active normal faults in central Italy over a time period of 20–30 kyrs, using in situ36Cl cosmogenic dating of fault planes. We identify five periods of rapid slip on individual faults lasting a few millennia, separated time periods of up to 10 millennia with low or zero slip-rate. The rapid slip pulses migrated across the strike between the faults in two waves from SW to NE. We replicate this migration with a model where rapid slip induces changes in differential stress that drive changes in strain-rate on viscous shear zones that drive slip-rate variability on overlying brittle faults. Earthquakes increase the differential stress and strain-rate on underlying shear zones, which in turn accumulate strain, re-loading stress onto the overlying brittle fault. This positive feedback produces high strain-rate episodes containing several large magnitude surface faulting earthquakes (earthquake clusters), but also reduce the differential stress on the viscous portions of neighbouring fault/shear-zones slowing the occurrence of large-magnitude surface faulting earthquakes (earthquake anticlusters). Shear-zones on faults experiencing anticlusters continue to accumulate viscous strain at a lowered rate, and eventually this loads the overlying brittle fault to failure, initiating a period of rapid slip through the positive feedback process described above, and inducing lowered strain-rates onto neighbouring fault/shear-zones. We show that these patterns of differential stress change can replicate the measured earthquake clustering implied by the 36Cl data. The stress changes are related to the fault geometry in terms of distance and azimuth from the slipping structure, implying that (a) strain-rate and viscosity fluctuations for studies of continental rheology, and (b) slip-rates for seismic hazard purposes are to an extent predictable given knowledge of the fault system geometry.

Fully optimized second-order estimates for the macroscopic behavior and field statistics of particle-reinforced viscoplastic composites

This paper is concerned with the characterization of the macroscopic behavior and statistics for the distribution of the stress and strain-rate fields in composites consisting of random and isotropic suspensions of rigid spherical particles in power-law viscoplastic materials. For this purpose, use is made of the Fully Optimized Second-Order (FOSO) homogenization method (Ponte Castañeda, 2016) in combination with recently developed estimates (Kammer and Ponte Castañeda, 2022) for the macroscopic properties of the associated ‘linear comparison composite’ (LCC). Special attention is devoted to the method’s ability to account for the dependence of the homogenized properties of the nonlinear composite on the Lode angle (third invariant) of the applied loading. It is found that, while, for large particle volume fractions c, the effective flow stress is only weakly dependent on the Lode angle, for dilute volume fractions, the dependence on the Lode angle becomes more pronounced. In the ideally plastic limit, as c tends to zero, the effective yield stress is shown to depend linearly on c for axisymmetric shear, while this dependence becomes weaker with a non-analytic leading-order correction of O(c/lnc) for pure shear loading. This strong dependence on the Lode angle at dilute concentrations is shown to be due to significant differences in the local deformation patterns, which become strongly anisotropic and localize for pure shear conditions, but do not for axisymmetric shear. In turn, the FOSO homogenization method is able to capture the statistical features of these different deformation patterns by providing consistent estimates for the covariance tensor of the strain-rate field fluctuations in the matrix phase, which tend to become more strongly anisotropic for the pure shear case. As c increases, the shear bands are deflected by the randomly dispersed spheres leading to a more isotropic distribution of the stress and strain-rate fields, which is consistent with a weaker Lode angle effect. The estimates can also capture the effect of strong particle interactions, including the existence of a rigidity threshold where the macroscopic flow stress and field fluctuations blow up.

Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

Polymers in turbulence: stretching statistics and the role of extreme strain rate fluctuations

Spatiotemporal characterization of wave-augmented varicose explosions

The onset of three-dimensional instabilities during “Wave-Augmented Varicose Explosions” (WAVE) liquid disintegration is characterized for an annular flow of a shear-thinning slurry that is fed into a central transonic steam flow. Droplet production inside the nozzle is enhanced by ligaments radially flicking up from the slurry wave into the steam flow with radial:axial velocity ratios exceeding 0.5. The wave also leaves residual ligaments in its wake, which facilitate further disintegration. After birth, a wave spends 80% of the wave cycle period building up to peak height at the nozzle exit. Two effervescent mechanisms are provided as 1) steam penetrates the rising wave and surface deformation allows steam fingers to force through, and 2) the wave collapses on itself, trapping steam. Baroclinic torque drives the development of Rayleigh-Taylor (RT) instabilities and reaches values on the order of 1×1013 1/s2. Both RT and Kelvin-Helmholtz instabilities are self-amplified in a viscosity-shear-temperature instability cycle because the slurry is non-Newtonian. Velocities inside the nozzle (wave formation region) are generally azimuthally similar (two-dimensional), but those outside the nozzle (radial bursting region) are azimuthally uncorrelated (three-dimensional). Inter-variable correlations show significant decoupling of quantities beyond the nozzle exit, and local strain rate fluctuations were found to correlate particularly well with bulk system pulsation. Although adaptive mesh refinement (AMR) can provide computationally efficient resolution of gas–liquid interfaces, this technique produced different results than an equivalent non-dynamic mesh when modeling WAVE. Gradients were particularly affected by AMR, and turbulent kinetic energy showed differences greater than 150% outside the nozzle.

Power fluctuations in sheared amorphous materials: A minimal model.

The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical microrheological experiments.

Giant fluctuations in strain rate as part of normal leaf growth

We report the effects of abrupt transitions of light intensity on the growth patterns and mechanical properties of young tobacco leaves. Changes in light intensity induce large variations in the leaf strain rate, which can be an order of magnitude larger than the average growth rates, and include both tissue expansion and shrinkage. These are accompanied by large changes in the tissue’s mechanical properties. Similar effects are observed in response to wind. We show evidence supporting the hypothesis that these effects originate from hydraulic mechanisms, i.e., variations in turgor pressure. In the context of growth patterns and growth regulation, we show giant fluctuations in strain rate to be a normal part of the growth process of leaves, which should be taken into account as a means for redistributing the stresses accumulated during the process of growth.

Energy analysis of unsteady negative edge flames in a periodic flow

Non-premixed laminar or turbulent flames can undergo extinction when scalar dissipation rates exceed a critical value. When local extinction occurs, negative edge flames that act to expand the region of extinction are initially present. Steady negative edge flames have been previously studied in a combustor designed to support the negative propagation velocity of the flame edge, but unsteady negative edge flames have not received significant attention. The current study uses numerical simulations in a simple flowfield to produce unsteady negative edge flames which oscillate in response to imposed strain rate fluctuations in order to understand the dynamic response of extinction edge propagation. An energy balance through the edge shows that the unsteady behavior can be well described by a simple extension of the energy balance from steady flames. Furthermore, the edge velocity was calculated, and a physical interpretation of the extinction velocity was derived using the energy budget. The time scale of the imposed strain rate fluctuations was varied to show a limited response time for the extinction edge flame dynamics.

Assessment of gas-particle flow models for pseudo-2D fluidized bed applications

ABSTRACTThe aim of this work is to provide more insight into the general modeling criteria for simulating pseudo-2D bubbling fluidized beds. For this purpose, two experimental-based problems are studied. First, a fluidized bed with a high-speed central jet problem is analyzed. A qualitative study of the first bubble indicates that the bubble shape prediction is highly sensitive to the frictional model adopted. The most accurate results in terms of bubble shape and detachment time are given by a frictional model that relates the strain-rate fluctuations with the granular temperature. Second, a uniformly fluidized bed problem in bubbling regime is considered. For this case, the drag models and boundary conditions for the particulate phase are investigated. Time-averaged solid phase velocity profiles are compared with the results of the literature where it is found that no-slip conditions (or partial slip with a high specularity coefficient) are more appropriate than slip conditions at the walls for these regimes. Regarding the drag force, although none of the models presented could match the experimental velocity predictions for low gas velocities at the lower region of the bed, the Di Felice model produces the most accurate results for the whole range of regimes considered.

Compressibility and heat release effects in high-speed reactive mixing layers I.: Growth rates and turbulence characteristics

A new set of three-dimensional direct numerical simulations (DNS) of spatially-developing high-speed H2/air mixing layers is presented and analysed. It corresponds to three distinct values of the convective Mach number Mc for both inert and reactive conditions. The results obtained from this new set of DNS data confirms that the mixing layer growth rate decreases according to pressure-dilatation Π11. However, an interesting point is that, in contrast to previous analyses, the decay of pressure fluctuations may not be the sole reason for this reduced growth rate, since strain-rate fluctuations decrease in a similar amount. For reactive mixing layers, depending on the value of Mc, the thermal runaway occurs in either the mixing layer development zone (small value of Mc) or the fully developed turbulence region (larger value of Mc). The examination of the mixture fraction probability density functions shows that the influence of engulfment processes, which play an important role at small Mc, tends to disappear in the presence of heat release as well as for increasing values of Mc. The present database of spatially-developing mixing layers featuring both detailed chemistry and detailed transport (i.e., Soret, Dufour and bulk viscosity effects) thus confirms some of the conclusions that were previously drawn from results issued from temporal mixing layer DNS studies conducted with single-step chemistry.

Unsteady dynamics of PAH and soot particles in laminar counterflow diffusion flames

Due to their low chemical time scales, the production of soot particles in turbulent diffusion flames is highly impacted by large range of local strain rate fluctuations.In order to understand the response of soot production to strain rate fluctuations, unsteady laminar counterflow diffusion flames with an imposed oscillating strain rate are investigated both analytically and numerically. First an analytical linearized model is developed to predict the unsteady response of a flame quantity of interest from information on laminar steady flames. Three critical parameters governing flame response are identified: the Stokes number which compares the characteristic time associated to the mean imposed strain rate to the oscillation frequency, the Damköhler number associated to the quantity of interest, and a third one characterizing the response of this quantity to an imposed steady strain rate. This model is then applied to soot predictions. Parallely, the response of soot production in propane-air counterflow diffusion flames to unsteady strain harmonic oscillations is studied numerically using a detailed sectional soot model. A wide range of frequencies and amplitudes are considered. A specific trend is highlighted for soot precursors and particles production according to their respective chemical time scales: the bigger the PAH or soot particle, the higher its chemical time scale, resulting in a more damped and phase-lagged response. The particle size distribution evolves accordingly during the considered oscillations, so that the quasi-steady state behavior is not verified for high frequencies. The numerical results are compared to those obtained by the analytical approach and a very good agreement is obtained at low amplitudes. Non-linear response of soot precursors and soot particles production to strain oscillations are finally discussed in case of high oscillation amplitudes and the limits of the proposed analytical model are identified.

On the pressure-strain correlation in fibrous drag-reduced turbulent channel flow

The pressure-strain correlation is studied in detail using the direct numerical simulation data obtained by a direct Monte-Carlo simulation of turbulent drag reduction in a channel flow caused by rigid fiber additives. This is used to analyze the energy redistribution process and to explain the pronounced anisotropy of the drag-reduced flow as compared to its Newtonian counterpart. Moreover, the change in pressure fluctuations and strain-rate fluctuations are studied to explain the modifications in the pressure-strain term. It is found that the reduction in strain-rate fluctuations is mainly responsible for the change in the pressure-strain term and the effect of pressure fluctuations is modest.

Probing the transition between seismically coupled and decoupled segments along an ancient subduction interface

AbstractThe transition zone at the downdip end of seismic coupling along subduction interfaces is often the site of megathrust earthquake nucleation and concentrated postseismic afterslip, as well as the focus site of episodic tremor and slip features. Exhumed remnants of the former Alpine subduction zone found in the Swiss Alps allow analyzing fluid and deformation processes near the transition zone region (30–40 km paleodepth). The Dent Blanche Thrust (DBT) is a lower blueschist‐facies shear zone interpreted as a fossilized subduction interface where granitic mylonites overlie a metamorphosed accretionary wedge. We report field observations from the DBT region where multiple, several tens of meters thick foliated cataclastic networks are interlayered within the basal DBT mylonites. Petrological results and microstructural observations indicate that the various cataclasis events took place at near‐peak metamorphic conditions (400–500°C, 1.1–1.3 GPa) during subduction of the Tethyan seafloor in Eocene times (42–48 Ma). Some of these networks exhibit mutual crosscutting relationships between mylonites, foliated cataclasites, and vein systems indicating mutual overprinting between brittle deformation and ductile creep. Whole‐rock chemical compositions, in situ 40Ar‐39Ar age data of recrystallized phengite, and Sr isotopic signatures reveal that DBT rocks also underwent multiple hydrofracturing and metasomatic events via the infiltration of fluids mainly derived from the oceanic metasediments underneath the DBT. From the rock fabrics, we infer strain rate fluctuations of several orders of magnitude beyond subduction strain rates (∼10−12 s−1) accompanied by fluctuation of supralithostatic and quasi‐lithostatic fluid pressures (1 ≥ λ > 0.95). DBT brittle‐plastic deformation switches highlight the diversity of deformation processes and fluid‐rock interactions in the transition zone region of the subduction interface.

Intermittent dislocation density fluctuations in crystal plasticity from a phase-field crystal model.

Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density 1/f2 at high frequencies f. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternates at irregular times with high populations of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.

Densification of polar snow: Measurements, modeling, and implications for altimetry

Density profiles in the upper 10–14 m of snow have been measured along a 500 km traverse across the Greenland ice sheet, using a neutron scattering technique. Repeat measurements, over periods ranging from a few days to 5 years, allow strain rates to be determined as a function of depth. Very large strain rates are observed in the surface layer of snow over summer periods. In the underlying multiyear snow, strain rate decreases with decreasing porosity. However, once this effect has been removed, the effect of increasing overburden pressure is counteracted by increasing strength of the material. There are fluctuations in strain rate associated with the annual layering, which indicate that winter and summer snow have different strengths. Based on these observations, we derive a new densification equation which includes the effect of snow density and snow type, and the effect of temperature, described by an Arrhenius expression with activation energy of the order of 110 kJ mol−1 and an exponential prefactor determined simply by the temperature history of the snow. For multiyear snow and meteorological conditions that do not vary from year to year, our equation reduces to a form similar to the Herron and Langway equation for first‐stage densification. Using the new equation, we calculate the sensitivity of compaction rate to short‐term fluctuations in temperature and accumulation as 0.11–0.20 m a−1 K−1 and 0.33–0.95 m a−1(meters water equivalent)−1, respectively, and discuss the consequent uncertainty in satellite measurements of the long‐term elevation trend in this area of the Greenland ice sheet.

Pulsating instability of externally forced premixed counterflow flame

The diffusive-thermal pulsating instability of Le>1 flames can considerably alter global quantities such as the flammability limit and mass burning rate, making its study practically relevant. In the present study we investigate the behavior of pulsating flames in unsteady flow fields using one-dimensional and two-dimensional flame simulations of laminar premixed rich hydrogen/air flame in a counterflow configuration, focusing on the response of the flame to imposed fluctuations in strain rate and equivalence ratio. These effects become important when the flame propagates in an unsteady flow field, for example, in turbulent flows. In the case of strain rate forcing, the flame is found to undergo oscillatory extinction if the forcing frequency is less than the pulsation frequency. For strain rate forcing frequencies higher than the pulsation frequency, the flame is found to be largely unresponsive to the upstream flow velocity fluctuations. The parametric study for equivalence ratio forcing shows that the pulsating instability is promoted with increasing inlet velocity, increasing amplitude and mean value of the imposed composition fluctuation. At the same time, it is observed that increasing the frequency of the imposed oscillations may attenuate the pulsating instability. Moreover, it is found that a flame subjected to pulsating extinction may be able to sustain pulsating combustion if forced with high-frequency inlet composition variation. Based on the insights gained from one-dimensional simulations, two-dimensional simulations of these pulsating flames are performed to provide additional insights on the shape and location of cells and cusp formation in these flames.

Strain-rate fluctuations during macroscopically uniform deformation of a solution-strengthened alloy

Using a work-hardened aluminum alloy that exhibits dynamic strain aging, oscillations in strain rate transitioning into intermittent local plastic activity are observed through an extended elastoplastic transition, before onset of the Portevin–Le Chatelier effect. Fourier analysis confirms this intermittency spans multiple scales. Wavelet analysis provides a method of quantifying transitions in the deformation behavior in both the time and frequency domains, and reveals a period doubling transition in both the local strain rate and global load signals.

Fluid dynamic simulation in a chemical looping combustion with two interconnected fluidized beds

Flow behavior of gas and particles is simulated in a 2-D chemical-looping combustion (CLC) process with two interconnected fluidized beds. A Eulerian continuum two-fluid model is applied for both the gas phase and the solid phase. Gas turbulence is modeled by using a k–ε turbulent model. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. Instantaneous and local velocity, concentration of particles and granular temperature are obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in the air reactor. Flow behavior of bubbles is predicted in the fuel reactor and pot-seal. Computed leakage qualitatively agrees with experimental data in the fuel reactor and pot-seal.

Hydrodynamic simulation of fuel-reactor in chemical looping combustion process

A multiphase CFD-based model with gas–solid hydrodynamics and chemical reactions is used to model flow behavior of gas and particles in the fuel reactor of chemical looping combustion process. The granular kinetic theory model is used to model the interaction of particle collisions. The friction stress of particles is considered to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. The reaction kinetics model of the fuel reactor is presented. The instantaneous mass fractions of both reactant and products are predicted, and the time averaged distributions are calculated in the fuel reactor. Simulated fuel reactor flows reveal a high weight fraction of unburned methane fuel in the flue gas along with CO 2 and H 2O. This behavior implies high fuel loss at the exit of the reactor and indicates the necessity to increase the residence time and improve mixing in the fuel reactor using circulating fluidized bed technology.

Fluctuations and Scaling in Creep Deformation

The spatial fluctuations of deformation are studied in the creep in Andrade's power law and the logarithmic phases, using paper samples. Measurements by the digital image correlation technique show that the relative strength of the strain rate fluctuations increases with time, in both creep regimes. In the Andrade creep phase characterized by a power-law decay of the strain rate ϵt∼t(-θ), with θ≈0.7, the fluctuations obey Δϵt∼t(-γ), with γ≈0.5. The local deformation follows a data collapse appropriate for a phase transition. Similar behavior is found in a crystal plasticity model, with a jamming or yielding transition.

Numerical simulations of flow behavior of gas and particles in spouted beds using frictional-kinetic stresses model

Flow behavior of gas and particles is simulated in the spouted beds using a Eulerian–Eulerian two-fluid model on the basis of kinetic theory of granular flow. The kinetic–frictional constitutive model for dense assemblies of solids is incorporated. The kinetic stress is modeled using the kinetic theory of granular flow, while the friction stress is from the combination of the normal frictional stress model proposed by Johnson and Jackson (1987) and the frictional shear viscosity model proposed by Schaeffer (1987) to account for strain rate fluctuations and slow relaxation of the assembly to the yield surface. An inverse tangent function is used to provide a smooth transitioning from the plastic and viscous regimes. The distributions of concentration, velocity and granular temperature of particles are obtained in the spouted bed. Calculated particle velocities and concentrations in spouted beds are in agreement with the experimental data obtained by He et al. (1994a, b). Simulated results indicate that flow behavior of particles is affected by the concentration of the transition point in spouted beds.