Averaged Slip Research Articles

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

Fluctuation-driven instability of nanoscale liquid films on chemically heterogeneous substrates

The instability and dewetting of bounded liquid films at the nanoscale are shown to strongly depend on thermal fluctuations. In this work, this fluctuation-driven instability of films on a chemically heterogeneous substrate is investigated both by a stochastic lubrication equation (SLE), which models thermal fluctuations with white noise, and by molecular dynamics (MD). Linear instability analysis for the SLE, considering slip and intermolecular forces of the heterogeneous substrates, is employed to derive a spectrum of the thermal capillary waves and their corresponding interface roughness, which are then quantitatively confirmed by numerical solutions for the SLE and MD. The fluctuation-driven instability is found to be enhanced by the slip and intermolecular forces, with the latter becoming dominant toward the final rupture. Moreover, the results suggest that a heterogeneous substrate can be approximated as a homogeneous one with effective (averaged) slip lengths and Hamaker constants for the intermolecular forces. The gradients of the slip and intermolecular forces due to the heterogeneities are shown not to affect the instability significantly.

Revealing the hidden signature of fault slip history in the morphology of degrading scarps

Active faults accommodate tectonic plate motion through different slip modes, some stable and aseismic, others characterized by the occurrence of large earthquakes after long periods of inactivity. Although the slip mode estimation is of primary importance to improve seismic hazard assessment, this parameter inferred today from geodetic observations needs to be better constrained over many seismic cycles. From an analytical formulation developed for analyzing fault scarp formation and degradation in loosely consolidated material, we show that the final topographic shape generated by one earthquake rupture or by creep (i.e., continuous slip) deviates by as much as 10–20%, despite a similar cumulated slip and a constant diffusion coefficient. This result opens up the theoretical possibility of inverting, not only the cumulated slip or averaged slip rate, but also the number of earthquakes and their sizes from scarp morphologies. This approach is all the more relevant as the number of rupture events is limited. Estimating the fault slip history beyond a dozen earthquakes becomes very difficult as the effect of erosion on scarp morphology prevails. Our modeling also highlights the importance of trade-offs between fault slip history and diffusive processes. An identical topographic profile can be obtained either with a stable fault creep associated with rapid erosion, or a single earthquake rupture followed by slow erosion. These inferences, derived from the simplest possible diffusion model, are likely to be even more pronounced in nature.

Response of shear critical reinforced concrete frames and walls under monotonic loading

This paper focuses on a novel finite element formulation which can predict the bending moment-shear force-axial force interaction of reinforced concrete frames and walls, and validate it against 170 experiments available in literature. This distributed plasticity element is established on force-based finite element method, where the relationship between element nodal forces and section forces are exactly known. Hence, element discretization is nonessential when modelling frames using this formulation, reducing the number of degrees of freedom in the numerical model compared to displacement-based formulations. The computations are carried out at four hierarchical levels, namely structure, element, section and fibre. There are two nested iterative procedures at the structure level and the section level. In the existing formulation, these iterative procedures are computationally demanding due to use of initial stiffness matrices. Furthermore, it uses Modified Compression Field Theory at the fibre level, which has inherent drawbacks compared to its more evolved version, the Disturbed stress Field Model. The current study refines the iterative procedures at structure and section levels to fully operate with tangent stiffness matrices to improve the speed of convergence. In addition, the Modified Compression Field Theory is replaced with the Disturbed stress Field Model at the fibre level to compute fibre resisting force for a given fibre deformation, accounting for both averaged behaviour and local crack slip. The novel element is validated by comparing the predicted results with experimental results of 170 tests found in the literature. It is shown that the novel element predicts the load carrying capacity well with an average experimental-to-predicted load carrying capacity ratio of 0.99 and a coefficient of variation of 12.8%. Furthermore, the element can be used to discuss the different failure mechanisms of reinforced concrete frame elements.

Coseismic and Early Postseismic Deformation Due to the 2021 M7.4 Maduo (China) Earthquake

AbstractThe 2021 Maduo earthquake ruptured a 150 km‐long left‐lateral fault in the northeast Tibet. We used Synthetic Aperture Radar data collected by the Sentinel‐1A/B satellites within days of the earthquake to derive a finite fault model and investigate the details of slip distribution with depth. We generated coseismic interferograms and pixel offsets from different look directions corresponding to the ascending and descending satellite orbits. At the eastern end the rupture bifurcated into two sub‐parallel strands, with larger slip on the northern strand. Inversions of coseismic displacements show maximum slip to the east of the epicenter. The averaged coseismic slip has a peak at depth of 3–4 km, similar to slip distributions of a number of shallow strike‐slip earthquakes. Postseismic observations over several weeks following the Maduo earthquake reveal surface slip with amplitude up to 0.1 m that at least partially eliminated the coseismic slip deficit in the uppermost crust.

Slow viscous flow near a superhydrophobic surface with trapped gas bubbles

AbstractThe Boundary Element Method (BEM) is used to solve the problem of Stokes flow of a viscous fluid over a periodic striped texture of a superhydrophobic surface (SHS), partially filled with frictionless gas bubbles. The shape of the bubble surfaces and the position of the meniscus pinning points relative to the cavity walls are taken into account in the study. Two kinds of flows important for practical applications are considered: a pressure‐driven flow in a thin channel with a bottom superhydrophobic wall and a shear‐driven flow over a periodic texture. We study the flow pattern in the fluid over a single cavity containing a bubble with a curved phase interface shifted into the cavity. A parametric numerical study of the averaged slip length of the SHS is performed as a function of the geometric parameters of the texture. It is shown that the curvature of the phase interface and/or its shift into the cavity both result in the decrease in the average slip length. It is demonstrated that the BEM can be an efficient tool for studying Stokes flows over textured superhydrophobic surfaces with different geometries of microcavities and phase interfaces. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling slow‐slip segmentation in Cascadia subduction zone constrained by tremor locations and gravity anomalies

AbstractAlong‐strike segmentation of slow‐slip events (SSEs) and nonvolcanic tremors in Cascadia may reflect heterogeneities of the subducting slab or overlying continental lithosphere. However, the nature behind this segmentation is not fully understood. We develop a 3‐D model for episodic SSEs in northern and central Cascadia, incorporating both seismological and gravitational observations to constrain the heterogeneities in the megathrust fault properties. The 6 year automatically detected tremors are used to constrain the rate‐state friction parameters. The effective normal stress at SSE depths is constrained by along‐margin free‐air and Bouguer gravity anomalies. The along‐strike variation in the long‐term plate convergence rate is also taken into consideration. Simulation results show five segments of ∼Mw6.0 SSEs spontaneously appear along the strike, correlated to the distribution of tremor epicenters. Modeled SSE recurrence intervals are equally comparable to GPS observations using both types of gravity anomaly constraints. However, the model constrained by free‐air anomaly does a better job in reproducing the cumulative slip as well as more consistent surface displacements with GPS observations. The modeled along‐strike segmentation represents the averaged slip release over many SSE cycles, rather than permanent barriers. Individual slow‐slip events can still propagate across the boundaries, which may cause interactions between adjacent SSEs, as observed in time‐dependent GPS inversions. In addition, the moment‐duration scaling is sensitive to the selection of velocity criteria for determining when SSEs occur. Hence, the detection ability of the current GPS network should be considered in the interpretation of slow earthquake source parameter scaling relations.

Numerical investigation and comparison of coarse grain CFD – DEM and TFM in the case of a 1 MWth fluidized bed carbonator simulation

This work focuses on a comparison between the Euler-Euler Two Fluid Model (TFM) approach and the coupled coarse grain discrete element CFD-DEM numerical model for the simulation of a 1MWth CFB carbonator reactor located at TU Darmstadt (TUD). The effect of the drag force formulation and its associated application in the numerical model for both approaches in terms of their numerical accuracy, compared to experimental data is investigated, by implementing either the conventional Gidaspow model or the advanced EMMS one. Moreover, for the coarse grain CFD – DEM model, the range of values for important numerical parameters as the particle per parcel and cell to parcel size ratios are investigated to shed light on the necessary resolution such a model should have in order to reproduce valid and not parameter dependent numerical results. An adequate cell length to parcel diameter ratio is found to be around 2.6 while as concerns the parcel to particle diameter ratio a value around 58.5 proved to be sufficient, at least for the range of parameters investigated in this paper (size of riser, flow rates and particles average diameter). The EMMS model improved the accuracy of results derived by the coarse grain CFD – DEM model, while further research on the appropriate drag models for the coarse grain CFD – DEM is a sine qua non for its successful implementation in similar studies. For instance it is of interest to answer whether the individual particles slip velocity instead of the particles cell averaged slip, should be used for the calculation of the momentum interexchange coefficient (β) as well as the treatment of different particle diameters in the EMMS equation scheme.

Computation of the effective slip of rough hydrophobic surfaces via homogenization

We present a quantitative analysis of the effect of rough hydrophobic surfaces on viscous Newtonian flows. We use a model introduced by Ybert and coauthors in [Achieving large with superhydrophobic surfaces: Scaling laws for generic geometries, Phys. Fluids 19 (2007) 123601], in which the rough surface is replaced by a flat plane with alternating small areas of slip and no-slip. We investigate the averaged slip generated at the boundary, depending on the ratio between these areas. This problem reduces to the homogenization of a nonlocal system, involving the Dirichlet to Neumann map of the Stokes operator, in a domain with small holes. Pondering on the works of Allaire [Homogenization of the Navier–Stokes equations in open sets perforated with tiny holes. I. Abstract framework, a volume distribution of holes, Arch. Rational Mech. Anal. 113 (1990) 209–259; Homogenization of the Navier–Stokes equations in open sets perforated with tiny holes. II. Noncritical sizes of the holes for a volume distribution and a surface distribution of holes, Arch. Rational Mech. Anal. 113 (1990) 261–298]. We compute accurate scaling laws of the averaged slip for various types of roughness (riblets, patches). Numerical computations complete and confirm the analysis.

The geochemical and temporal evolution of the continental lithosphere and its relationship to continental‐scale faulting: The Karakoram Fault, eastern Karakoram, NW Himalayas

New laser ablation multicollector–inductively coupled plasma–mass spectrometry and isotope dilution‐thermal ionization mass spectrometry U‐Pb ages, coupled with Sm‐Nd isotope and geochemical analysis, define the temporal and geochemical evolution of the continental lithosphere in the eastern Karakoram, India, NW Himalaya. Our analysis demonstrates that magmatism occurred between ~108 and 69 Ma and ~22 and 13 Ma. The new age data, coupled with geochemical examination of the granitoids, confirm a parallel evolution with the western Karakoram in Pakistan and supports a model of regional continental crustal thickening and related metamorphism. Middle to Late Cretaceous magmatism immediately adjacent to the Karakoram fault suggests that crustal melting and associated metamorphism are unrelated to shearing along the fault. Miocene leucogranite magmatism occurred almost exactly concomitant with the emplacement of the Baltoro batholith in Pakistan. These trans‐Karakoram leucogranites also display similar geochemical evolution trends. Our new data clearly link the leucogranites along the fault to the regional Baltoro batholith and related metamorphic complexes to the west. This supports previous work suggesting that magmatism and metamorphism were not syn‐kinematic with continental‐scale faulting. The data demonstrate that the Karakoram fault could not have accommodated lateral offset in this region prior to ~16 Ma, limiting the long‐term averaged slip rate to a maximum of ~10 mm/yr.

Slip-Flow Pressure Drop in Microchannels of General Cross Section

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

Stateline fault system: A new component of the Miocene-Quaternary Eastern California shear zone

The Eastern California shear zone is an active, north-northwest–trending zone of intraplate right-lateral shear that absorbs ∼25% of Pacific-North America relative plate motion. The Stateline fault system (SFS), which includes several previously recognized, discontinuously exposed Quaternary structures along the California-Nevada border, is in this paper defined as a continuous, 200-km–long zone of active dextral shear that includes (from south to north) the Mesquite, Pahrump, and Amargosa Valley segments. Recognition of this system expands the known extent of the Eastern California shear zone ∼50 km to the east-northeast from its traditionally recognized boundary along the Death Valley fault system. Proximal volcanic and rock avalanche deposits offset across the Mesquite segment of the SFS indicate 30 ± 4 km of slip on this structure since 13.1 ± 0.2 Ma. This offset is an order of magnitude larger than previous estimates across this section of the SFS, but it is consistent with larger offsets previously proposed for the central and northern sections. The total offset and averaged slip rate since mid-Miocene time (2.3 ± 0.35 mm/yr) are similar to those of other major faults across this portion of the Basin and Range, which, from east to west, include the Death Valley, Panamint Valley-Hunter Mountain, and Owens Valley fault systems. However, in contrast to these faults, the average post–mid-Miocene slip rate on the SFS is approximately twice that estimated from present-day geodetic observations and an order of magnitude greater than estimates of average post–mid-Pleistocene slip rates. This discrepancy between long-term, short-term, and geodetically derived slip rates differs from other geologic-geodetic, slip-rate discrepancies in the Eastern California shear zone, where geodetic slip rates are significantly faster than both long-term and short-term geologic slip rates. This suggests that either the slip rate on the SFS has diminished over time, such that the system is an abandoned strand of the relatively young Eastern California shear zone, or that the present-day slip rate represents a transient period of slow slip, such that strands of the shear zone must accommodate a complex spatial and temporal distribution of slip.

Rock deformation processes in the Karakoram fault zone, Eastern Karakoram, Ladakh, NW India

The Karakoram fault shows a full range of fault rocks from ductile (deformation by intracrystalline plasticity) mylonites to low temperature brittle fault rocks along the trace of the fault in the Eastern Karakoram, Ladakh, NW India. The Karakoram fault is a prominent feature on satellite images and has estimated long-term average slip rates between 3 and 11 mm/year, based on U-Pb geochronology of mapped offset markers, notably mid-Miocene leucogranites. Mylonitic marbles, superimposed by cataclastic deformation and clay-bearing fault gouges and late fracturing were found on a presently active strand of the fault, and testify to progressive deformation from plastic through brittle deformation during unroofing and cooling. From microstructural analysis we confirmed the right-lateral strike slip character of the fault, estimated peak differential stresses of ca. 200 MPa at the transition from plastic to brittle deformation, and found microstructural features to be consistent with inferences from the extrapolation of deformation behaviour from experimental rock deformation studies. Implied long-term averaged slip rates from microstructural constraints were found to be broadly consistent with estimates from geochronologic and geodetic studies.

Tarapacá intermediate‐depth earthquake (Mw 7.7, 2005, northern Chile): A slab‐pull event with horizontal fault plane constrained from seismologic and geodetic observations

A large (Mw 7.7) intermediate‐depth earthquake occurred on 13 June 2005 in the Tarapacá region of the northern Chile seismic gap. Source parameters are inferred from teleseismic broadbands, strong motions, GPS and InSAR data. Relocated hypocenter is found at ∼98 km depth within the subducting slab. The 21‐days aftershock distribution, constrained by a postseismic temporary array, indicates a sub‐horizontal fault plane lying between the planes of the double seismic zone and an upper bound of the rupture area of 60 km × 30 km. Teleseismic inversion shows a slab‐pull down dip extension mechanism on a nearly horizontal plane. Total seismic and geodetic moments are ∼5.5 × 1020 N.m, with an averaged slip of 6.5 m from geodesy. The earthquake rupture is peculiar in that the effective velocity is slow, 3.5 Km.s−1 for a high stress‐drop, 21–30 MPa. We propose that rupture was due to the reactivation by hydraulic embrittlement of a inherited major lithospheric fault within the subducting plate. The stress‐drop suggests that the region of the slab between planes of the double seismic zone can sustain high stresses.

Evidence of Quaternary activity along the Deshir Fault: implication for the Tertiary tectonics of Central Iran

Geological and geomorphologic offsets are used to constrain the total displacement and estimate the slip rate of the right-lateral Deshir Fault. Cumulative morphologic offsets have been found along the southern portion of the fault, on the Iranian Plateau. High-resolution SPOT5 images (pixel size 2.5 m) combined with SRTM DEM document right-lateral offsets of rills, terrace risers and successive alluvial fan systems. Cumulative offsets range from 25 to 900 m and increase with relative elevation, hence relative age, of offset markers. The smallest cumulative offsets are most probably of Holocene age (12 ± 2 ka) and suggest that the fault slips at an average slip rate close to 2 mm yr−1. Coeval normal faulting is associated to strike-slip motion at several places along the southern portion of the fault. Normal and probably active faults are encountered within the High Zagros 70 km ahead the tip of the Deshir Fault and may suggest the fault is propagating southwards. The total displacement of the Deshir fault, estimated from right-lateral offset of the Nain-Baft suture, is 65 ± 15 km. The total displacement would have accumulated over the last 25–40 Ma at an averaged Holocene slip rate of 2 mm yr−1. Placing these observations within the framework of the tectonics of Iran allows a discussion of the timing of the transition between collision and subduction in Eastern Iran.

水平性視運動性後眼振の検討 Ｒｅｔｉｎａｌ Ｓｌｉｐ速度との関係

We studied horizontal optokinetic nystagmus (OKN) and horizontal optokinetic afternystagmus (OKAN) in five normal human subjects. The cylinder was rotated with an equal velocity of 40°/sec, 60°/sec, 70°/sec, 80°/sec, 90°/sec, 100°/sec. In a dark room, illumination was switched on for 30 sec and then turned off. Eye movements were analyzed by computer. We examined the relationship among averaged retinal slip velocity (RSV, drum velocity minus averaged slow-phase velocity of OKN), slow phase velocity of the first OKAN, duration of OKAN and time constant of the decay of slow phase velocity of OKAN.We supposed that the most effective RSV for OKAN ranged from 20°/sec to 40°/sec.We also found that fixation of a small target during optokinetic stimulation almost completely prevented the development of OKAN. We speculated that the target image across the fovea (retinal slip on the fovea) was very important for generation of OKAN.

Calculation of the characteristics of particles in inhomogeneous turbulent streams

The influence of inertia, averaged phase slip, and inhomogeneity of the turbulent carrier stream on the parameters of the disperse phase in the flow of a gas suspension in a round pipe is investigated on the basis of a closed system of equations for the first and second moments of particle velocity pulsations.

Correlation of the pulsation velocities of a disperse phase in jet flows

The correlation moment of the field of the pulsation velocities of the disperse phase is obtained by averaging the product of the pulsation velocities of the disperse particles for the law of interphase interaction determined by the standard resistance curve with allowance for the averaged slip of the constituent phases in both the longitudinal and transverse directions. The Eulerian space-time correlation of the velocities of the medium along the trajectory of a particle is approximated by the exponential dependence proposed by Shraiber, Milyutin, and Yatsenko [5].