Shear Velocity Research Articles

Turbulent blood flow in a cerebral artery with an aneurysm

Unruptured intracranial aneurysms are common in the general population, and many uncertainties remain when predicting rupture risks and treatment outcomes. One of the cutting-edge tools used to investigate this condition is computational fluid dynamics (CFD). However, CFD is not yet mature enough to guide the clinical management of this disease. In addition, recent studies have reported significant flow instabilities when refined numerical methods are used. Questions remain as to how to properly simulate and evaluate this flow, and whether these instabilities are really turbulence. The purpose of the present study is to evaluate the impact of the simulation setup on the results and investigate the occurrence of turbulence in a cerebral artery with an aneurysm. For this purpose, direct numerical simulations were performed with up to 200 cardiac cycles and with data sampling rates of up to 100,000 times per cardiac cycle. Through phase-averaging or triple decomposition, the contributions of turbulence and of laminar pulsatile waves to the velocity, pressure and wall shear stress fluctuations were distinguished. For example, the commonly used oscillatory shear index was found to be closely related to the laminar waves introduced at the inlet, rather than turbulence. The turbulence energy cascade was evaluated through energy spectrum estimates, revealing that, despite the low flow rates and Reynolds number, the flow is turbulent near the aneurysm. Phase-averaging was shown to be an approach that can help researchers better understand this flow, although the results are highly dependent on simulation setup and post-processing choices.

Ultra‐Low Velocity Zone Beneath the Atlantic Near St. Helena

AbstractThere are various hotspots in the Atlantic Ocean, which are underlain by mantle plumes that likely cross the mantle and originate at the core‐mantle boundary. We use teleseismic core‐diffracted shear waves to look for an Ultra‐Low Velocity Zone (ULVZ) at the potential base of central Atlantic mantle plumes. Our data set shows delayed postcursory phases after the core‐diffracted shear waves. The observed patterns are consistent in frequency dependence, delay time, and scatter pattern with those caused by mega‐ULVZs previously modeled elsewhere. Synthetic modeling of a cylindrical structure on the core‐mantle boundary below St. Helena provides a good fit to the data. The preferred model is 600 km across and 20 km high, centered at approximately 15° South, 15° West, and with a 30% S‐wave velocity reduction. Significant uncertainties and trade‐offs do remain to these parameters, but a large ULVZ is needed to explain the data. The location is west of St. Helena and south of Ascension. Helium and neon isotopic systematics observed in samples from this region could point to a less‐outgassed mantle component mixed in with the dominant signature of recycled material. These observations could be explained by a contribution from the Large Low Shear Velocity Province (LLSVP). Tungsten isotopic measurements would be needed to understand whether a contribution from the mega‐ULVZ is also required at St. Helena or Ascension.

Intensified Currents Associated With Benthic Storms Underneath an Eddying Jet

AbstractBenthic storms are episodes of intensified near‐bottom currents capable of sediment resuspension in the deep ocean. They typically occur under regions of high surface eddy kinetic energy (EKE), such as the Gulf Stream. Although they have long been observed, the mechanism(s) responsible for their formation and their relationships with salient features of the deep ocean, such as bottom mixed layers (BMLs) and benthic nepheloid layers (BNLs), remain poorly understood. Here we conduct idealized experiments with a primitive‐equation model to explore the impacts of the unforced instability of a surface‐intensified jet on near‐bottom flows of a deep zonal channel. Vertical resolution is increased near the bottom to represent the bottom boundary layer. We find that the unstable near‐surface jet develops meanders and evolves into alternating, deep‐reaching cyclones and anticyclones. Simultaneously, EKE increases near the bottom due to the convergence of vertical eddy pressure fluxes, leading to near‐bottom currents comparable to those observed during benthic storms. These currents in turn form BMLs with thickness of O(100 m) from enhanced velocity shears and turbulence production near the bottom. The deep cyclonic eddies transport fluid particles both laterally and vertically, from near the bottom through the entire BML and may contribute to the formation of the lower part of BNLs. A sloping bottom reduces both the intensity of the near‐bottom currents and the extent of vertical transport. Overall, our study highlights a significant response of the abyssal environment to near‐surface current instability, with potential implications for sediment transport in the deep ocean.

Mesoscale Eddies and Near-Inertial Internal Waves Modulate Seasonal Variations of Vertical Shear Variance in the Northern South China Sea

Abstract Diapycnal mixing in the South China Sea (SCS) is commonly attributed to the vertical shear variance S2 of horizontal ocean current velocity, but the seasonal modulation of S2 is still poorly understood due to the scarcity of long-term velocity observations. Here, this issue is explored in detail based on nearly 10-yr-long acoustic Doppler current profiler (ADCP) velocity data from a mooring in the northern SCS. We find that S2 in the northern SCS exhibits significant seasonal variations at both the near-surface (90–180 m) and subsurface (180–400 m) layers, but their seasonal cycles and modulation mechanisms are quite different. For the near-surface layer, S2 is stronger in late summer, autumn, and winter but weaker in spring and early summer, while in the subsurface layer, it is much stronger in winter than in other seasons. Further analysis suggests that in the near-surface layer, the stronger S2 in autumn and winter is primarily caused by typhoon-induced near-inertial internal waves (NIWs) and the large subinertial (SI) velocity shear of the baroclinic mesoscale eddies, respectively. With respect to the subsurface layer, the enhanced wintertime S2 is primarily associated with the “inertial chimney” effect of anticyclonic eddies, trapping wind-forced downward-propagating NIWs and significantly increasing the near-inertial shear at the critical layer. The findings in this study highlight the potentially important roles of mesoscale eddies and NIWs in modulating the seasonality of upper-ocean mixing in the northern SCS. This modulation is attributed not only to the strong shear of these features but also to their interactions. Significance Statement Vertical shear variance of velocity S2 significantly modulates turbulent mixing in the thermocline, but its climatologically seasonal variations and the associated mechanisms are still obscure due to the scarcity of long-term in situ velocity data. By analyzing nearly a decade of velocity data, we reveal significant seasonal variations in S2 at different ocean layers in the northern SCS and uncover different seasonal cycles and modulation mechanisms. The study sheds light on the pivotal roles of mesoscale eddies and near-inertial internal waves in modulating seasonality of S2 in the upper ocean. These findings have important implications for improving mixing parameterizations in numerical models.

Present day mantle structure from global mantle convection models since the Cretaceous

SUMMARY Using forward mantle convection models starting at 140 Ma, and assimilating plate reconstructions as surface velocity boundary condition, we predict present-day mantle structure and compare them with tomography models, using geoid as an additional constraint. We explore a wide model parameter space, such as different values of Clapeyron slope and density change across 660 km, density and viscosity of the thermochemical piles at the core–mantle boundary (CMB), internal heat generation rate, and model initiation age. We also investigate the effects of different strengths of a weak layer below 660 km and weaker asthenosphere and slabs. Our results suggest that slab structures at different subduction zones are sensitive to the viscosity of the asthenosphere, strength of slabs, values of Clapeyron slope and the density and viscosity of the thermochemical piles, while different internal heat generation rates do not affect the slab structures. We find that with a moderately weak asthenosphere ($10^{20}$ Pa·s) and strong slabs, the predicted slab structures are consistent with the tomography models, and the observed geoid is also matched well. Moreover, our models successfully reproduce the degree-2 structure of the lower mantle beneath Africa and the Pacific, also known as Large Low Shear Velocity provinces (LLSVPs). A moderate Clapeyron slope of −2.5 MPa K−1 at 660 km aids in slab stagnation while higher values result in massive slab accumulation at that depth, ultimately leading to slab avalanches. We also find that the convective patterns in the thermal and thermochemical cases with slightly denser LLSVPs are similar, although the geoid amplitudes are lower for the latter. However, with more dense LLSVPs, the slabs cannot perturb them and no plumes are generated. Plumes arise as thermal instabilities from the edges of the LLSVPs, when cold and viscous slabs perturb them. While our predicted plume locations are consistent with the observed hotspot locations, matching the plume structures in tomography models is difficult. These plumes are essential in fitting the finer features of the observed geoid. In longer-duration models, more voluminous subducted material reaches the CMB, which tends to erode the LLSVPs significantly, and yields a poor fit to the observed geoid. Our results suggest that with the presence of a thin, moderately weak layer below 660 km, a slightly dense LLSVP, and Clapeyron slope of −2.5 MPa K−1, the velocity anomalies in seismic tomography and the long-wavelength geoid can be matched well. One of the limitations of our models is that the assimilated plate motion history may be too short to overcome arbitrary initial conditions effects. Also, assimilated true plate velocities in our models may not represent the true convective vigour of the Earth.

How Switchbacks Can Maintain a Longer Time in the Interplanetary Space

Parker Solar Probe, the closest spacecraft to the Sun, has renewed our understanding of the solar corona and the interplanetary space. One of its important findings is the prevalence of switchbacks, which display localized magnetic reversals along the otherwise Parker spirals. While some switchbacks might disappear quickly, others can maintain for a long period of time, and there are indications that many switchbacks strengthen from the solar corona to the interplanetary space despite their magnetic tension force, which tends to straighten the magnetic field lines. Therefore, how these switchbacks could be maintained for a long period of time remains a mystery. In this paper, we employed a 3D data-driven global full magnetohydrodynamics numerical model to explore the evolution of switchbacks formed in the dynamic corona. Our simulations indicate that two factors can affect the lifetime of a switchback. One factor is the combination of angle and leg length ensures that the switchback with greater curvature after reconnection can last longer, and the greater the angle, the more magnetic field lines that can be reconnected, and thus the longer the duration. We call this influencing factor flux tube shape factor. The other factor is the velocity shear, i.e., when the solar wind at the convex-outward turning of a switchback is faster than that at the concave-outward turning, the switchback becomes enhanced during propagation, and it weakens when the velocity difference is opposite.

Dynamic mechanical response and constitutive model of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass

In this work, the mechanical response and fracture characteristics of (Ti37.31Zr22.75Be26.39Al4.55Cu9)94Co6 high-entropy bulk metallic glass (HE-BMG) were investigated in detail over a wide range of strain rates (10−4–105 s−1). The HE-BMG exhibited a negative strain rate sensitivity under uniaxial compression, with the strength showing more significant rate dependence under dynamic conditions. The shear band behavior translated from the dominance of multiple shear bands propagations under quasi-static compression to the rapid propagation of a single shear band to form cracks under dynamic compression. Under dynamic loading, the shearing velocity increased along an arc-shaped displacement path, and the local stress state on the shear fracture surface shifted from compressive-shear to tensile-shear, accompanied by changes in fracture morphologies. The spall strength of HE-BMG decreased as flyer impact speed increased, while the long-term dependence of spall strength on strain rate may be positive. With the increase of impact speed, the main microstructural features of the spalling surface translated from flat regions accompanied by dimples to cup-cone structures. Furthermore, the complete parameters of the Johnson–Holmquist II (JH-2) model for HE-BMG were obtained based on experimental data. Numerical simulations of planar impact, penetration, and hypervelocity impact are in good agreement with experimental results, demonstrating the validity of the JH-2 model parameters. The current work has important guiding value for the application of HE-BMG in space debris protection.

Computational Hemodynamic Analysis of a Patient Specific Abdominal Aortic Aneurysm

Abdominal aortic aneurysm (AAA) is a cardiovascular disease caused by the enlargement of the aorta in the abdomen over time. Unless treated, the growth of AAA continues, resulting in 80% death in the case of rupture. Today, the width of the aneurysm diameter is taken into account in clinical practice to examine the status of AAA. Although there are aneurysms that do not rupture despite reaching a diameter of 9 cm, it is reported that aneurysms with a diameter of 3 cm are ruptured in several cases. Therefore, analyzing only the AAA diameter is not a reliable method, and a deeper investigation is necessary for the rupture risk assessment. In this study, a patient's situation is analyzed using computational fluid dynamics (CFD) simulations, which allows to elucidate the flow dependent parameters such as velocity, vorticity, pressure, and wall shear stress (WSS). First, the patient-specific geometry was obtained and boundary conditions were defined at the inlet and the outlet of the flow domain. The effects of intraluminal thrombus (ILT) formation and patient’s effort conditions were also included in the analysis. According to the results, WSS and vorticity increase with the increasing blood flow velocity. In terms of the rupture risk, it has been found that the effect of patient’s effort level is more critical than the amount of ILT in the AAA.

Non-contact discharge estimation at a river site by using only the maximum surface flow velocity

The study proposes a novel method of computing river discharge based on the maximum surface velocity recorded using a non-contact-based measurement at a singular water surface point. This location, generally, coincides with the maximum flow depth of the cross-section and accounts for the dip phenomena, where the maximum instream velocity occurs below the water surface. The method is based on information entropy theory developed by Shannon (1948) and applied to river hydraulics. In this study an alternate form of entropy is used to compute discharge as a function of the cross-sectional mean velocity, maximum velocity and shear velocity (Keulegan,1938) by minimizing the error of the state equilibrium constant, ΦM, which is the ratio between the mean and maximum flow velocity, and that estimated using the Keulegan-based relationship. To test the accuracy of the proposed method, the maximum surface flow velocities measured at two gauging stations, each located on two different Italian rivers were studied. The estimated discharges by the proposed method were found to be comparable with the existing non-contact discharge method advocated by Moramarco et al. (2017) and, the traditional velocity-area method, using, e.g., the mean-section approach, based on the following metrics: the Nash-sutcliffe Efficiency (NSE), the coefficient of correlation and the percent bias (PBIAS). The mean velocity error emulates a Gaussian distribution for both the gauging stations and was within 95% and 5% confidance levels. Further, the entropy-based velocity profiles generated by the proposed method at the y-axis are consistent with those of the depth-based velocity profiles observed by the mechanical-current meter, thus, proving the appropriateness of the proposed discharge estimation method.

Comparative analysis of compressible inviscid flow over symmetric and supercritical airfoil

Studying compressible inviscid flow over symmetric and supercritical airfoils is important because it is useful to understand and maximize aerodynamic performance in a range of industrial contexts. This study addresses the analysis of symmetric and supercritical airfoils for compressible inviscid flow for both time-dependent and stationary scenarios. The primary goal of these simulations’ is to look at how different velocity variations affected certain airfoil parameters. Air is utilized as the material above airfoils. The best fit for these simulations is the Spalart-Allmaras Turbulence model, which shows good agreement over a wider velocity range with published experimental data from other studies. The COMSOL Multiphysics software is used for all the analysis, for angle of attack 0°, temperature 288K, pressure 1bar and the airfoils that are constructed by importing airfoil data file in COMSOL in the form of excel file. On the comparison of compressible inviscid flow, the supercritical airfoil has better results on the basis of velocity magnitude, pressure, vorticity magnitude, shear rate and rotation rate. The results are converging faster in supercritical airfoil than symmetric airfoil. At a zero-degree angle of attack, velocity increases more on the suction side while decreases on the pressure side (bottom). The final solution error for supercritical airfoil is 1.6E-05, while final residual error for “velocity u pressure p” is 1.2E-05. For symmetric airfoil, final solution error is 0.15, although final residual error is 2.6. Based on the error plot, it decreases rapidly in case of supercritical with a range from 100 to 10-4. Additionally, the wall resolution is constructed for both cases i.e., symmetric airfoil and supercritical airfoil. The main result is that ,with the passage of time, the flow is becoming to stationary state. In the end, model validation via comparison with experimental data highlights the validity and applicability of the results.

Assessing Zebra Mussels’ Impact on Fishway Efficiency: McNary Lock and Dam Case Study

The Columbia River Basin faces a threat from the potential invasion of zebra mussels (Dreissena polymorpha), notorious for their ability to attach to various substrates, including concrete, which is common in fishway construction. Extensive mussel colonization within fishways may affect fish passage by altering flow patterns or creating physical barriers, leading to increased travel times, or potentially preventing passage altogether. Many factors affect mussel habitat suitability including vectors of dispersal, water parameters, and various hydrodynamic quantities, such as water depth, velocity, and turbulence. The objective of this study is to assess the potential for zebra mussels to attach to fishway surfaces and form colonies in the McNary Lock and Dam Oregon-shore fishway and evaluate the potential impact of this infestation on the fishway’s efficiency. A computational fluid dynamics (CFD) model of the McNary Oregon-shore fishway was developed using the open-source code OpenFOAM, with the two-phase solver interFoam. Mesh quality is critical to obtain a reliable solution, so the numerical mesh was refined near the free surface and all solid surfaces to properly capture the complex flow patterns and free surface location. The simulation results for the 6-year average flow rate showed good agreement with the measured water column depth over each weir. Regions susceptible to mussel infestation were identified, and an analysis was performed to determine the mussel’s preference to colonize as a function of the depth-averaged velocity, water depth, and wall shear stress. Habitat suitability criteria were applied to the output of the hydraulic variables from the CFD solution and provided insight into the potential impact on the fishway efficiency. Details on the mesh construction, model setup, and numerical results are presented and discussed.

Computational fluid dynamics study of respiratory mask for neonatal resuscitation

Face cups form a vital component of breathing, assisting with devices that aid in artificial breathing for neonates. This study aims to evaluate the flow parameters in the nasal cavity for two different types of face cups. The neonatal nasal cavity model was developed from CT scans using MIMICS 21.0. Two face cups, one hemispherical and the other anatomical shaped cups are developed around the nasal cavity and the airflow is simulated using ANSYS 2021 R2. Results are compared with a nasal-only model. At the nasal valve region, the highest velocity is seen for the nasal-only model which is 16.3% higher than that of the hemispherical face cup and 15.2% superior to the anatomical-shaped face cup. In addition, the decrease in pressure across the nasal-only model is 7.4 and 6.6% below that of the hemispherical cup and anatomical cup masks. The nasal resistance values across the nasal cavity are the lowest for the nasal-only model, 7.7 and 6.7% lower respectively than the hemispherical and anatomical-shaped cups. There were very minor changes in the flow parameters such as velocity, pressure and wall shear stress when comparing the hemispherical and anatomic-shaped masks for the airflow inside the nasal cavity.

Polarization and coriolis forces impact on the Kelvin- Helmholtz instability of viscous dusty plasma

The Kelvin-Helmholtz instability in a dusty plasma with sheared velocity variations is analyzed, considering the effects of viscosity, rotation, and polarization parameters in dust. A theoretical framework is proposed to describe the behavior of three distinct fluid components: electron and ion fluids governed by the Boltzmann equation, as well as magnetized dust fluids influenced by nearby particles' polarization force. The dispersion relation for the KH instability is derived using normal mode analysis on linearized perturbed equation. It is found that rotation, viscosity, and polarization force based on the dusty acoustic mode optimize the basic dispersion relation of Kelvin-Helmholtz instability accurately. The critical shear is important for exciting the Kelvin-Helmholtz instability and is influenced by factors such as rotation, polarization, and dusty cyclotron frequency. The growth rate of the Kelvin-Helmholtz instability appears to be suppressed due to the presence of rotation, viscosity, and polarization force.

Transport Barriers in magnetized plasmas- general theory with dynamical constraints

A fundamental dynamical constraint—that fluctuation induced charge-weighted particle flux must vanish- can prevent instabilities from accessing the free energy in the strong gradients characteristic of Transport Barriers (TBs). Density gradients, when large enough, lead to a violation of the constraint and hence preclude unstable modes and turbulent transport. This mechanism, then, broadens the class of configurations (in magnetized plasmas) where these high confinement states can be formed and sustained. The need for velocity shear, the conventional agent for TB formation, is obviated. The most important ramifications of the constraint is to permit a charting out of the domains conducive to TB formation and hence to optimally confined fusion worthy states; the detailed investigation is conducted through new analytic methods and extensive gyrokinetic simulations.

Towards LES-RANS/LES coupling for simulation of a wind turbine rotor in a nocturnal atmospheric condition

A segregated approach with either synthetically generated velocity fluctuations or a precursor Large-Eddy Simulation (LES) of the atmospheric boundary layer (ABL) and a subsequent hybrid RANS/LES (HRLS) of the resolved rotor is presented in this paper. At first the approach is validated with synthetically generated velocity fluctuations that resemble neutrally stratified conditions. Subsequently the same turbine is artificially exposed to a stably stratified atmospheric inflow (nocturnal boundary layer) with a comparable mean velocity but different shear and veer characteristics. The HRLS simulations with the neutrally stratified and stably stratified inflow are compared to LESs with an implemented actuator disc (AD) model. The presented work is a first important step towards a digital twin for research wind parks.

Lithospheric Evolution of the South‐Central United States Constrained by Joint Inversion of Receiver Functions and Surface Wave Dispersion

AbstractIn the present study, we use broadband seismic data recorded by 190 stations of the EarthScope program's Transportable Array to construct a 3‐D shear wave velocity model for the upper 180 km using a non‐linear Bayesian Monte‐Carlo joint inversion of receiver functions (RFs) and Rayleigh wave dispersion curves. Ambient noise and teleseismic data are used for obtaining Rayleigh wave phase velocity dispersion curves. A resonance removal filtering technique is applied to the RFs contaminated by reverberations from the thick sedimentary layers that cover most of the region. Our observations of the higher crustal shear velocities (∼3.40 km/s) beneath the Sabine Block (SB), along with the estimated relatively thicker crust (∼34.0 km) and lower crustal Vp/Vs estimates (∼1.80) in comparison with the rest of the Gulf Coastal Plain (GCP) (∼3.10 km/s for crustal shear velocities, ∼29.0 km for crustal thickness, and ∼1.90 for crustal Vp/Vs estimates), indicating that this crustal block has different crustal properties from the surrounding coastal plain regions. The southern Ouachita Mountains have a thin crust (∼30.0 km) and low mean crustal Vp/Vs value (∼1.73), suggesting that lower crustal delamination has occurred in this region. Low velocities in the upper mantle beneath most of the GCP are interpreted as a combined result of thin lithosphere, higher‐than‐normal temperatures, and possibly compositional variations.

Elasticity of Hydrous SiO2 Across the Post‐Stishovite Transition in the Lower Mantle

AbstractElastic properties of Si0.95H0.21O2 with hydrogarnet substitution (4H+ = Si4+) across the post‐stishovite transition (28–42 GPa) are determined up to 70 GPa using ab initio calculations and a pseudo‐proper type Landau model. At 28 GPa, elastic coefficients C11 and C12 converge, and the average shear and compressional velocity (VS and VP) decrease by a maximum of 25.5% and 5.2%, respectively. Hydrogarnet substitution reduces ambient elastic moduli and sound velocities, and shifts shear softening to lower pressure. 2%–13% Si0.95H0.21O2 may cause a VS anomaly of −0.5% to −2.6% at 700–820 km depth, explaining low VS layers beneath North America and the European Alps. Additionally, 20 vol % SiO2 in subducted basalt, with decreasing water content from 3.2 wt% to zero, could cause a VS anomaly of up to −7(4) % from 700 to 1,900 km depth, aligning with seismic scatterers identified in some subduction regions.

Understanding the flow behavior around marine biofilms

In vitro platforms capable of mimicking the hydrodynamic conditions prevailing in natural aquatic environments have been previously validated and used to predict the fouling behavior on different surfaces. Computational Fluid Dynamics (CFD) has been used to predict the shear forces occurring in these platforms. In general, these predictions are made for the initial stages of biofilm formation, where the amount of biofilm does not affect the flow behavior, enabling the estimation of the shear forces that initial adhering organisms have to withstand. In this work, we go a step further in understanding the flow behavior when a mature biofilm is present in such platforms to better understand the shear rate distribution affecting marine biofilms. Using 3D images obtained by Optical Coherence Tomography, a mesh was produced and used in CFD simulations. Biofilms of two different marine cyanobacteria were developed in agitated microtiter plates incubated at two different shaking frequencies for 7 weeks. The biofilm-flow interactions were characterized in terms of the velocity field and shear rate distribution. Results show that global hydrodynamics imposed by the different shaking frequencies affect biofilm architecture and also that this architecture affects local hydrodynamics, causing a large heterogeneity in the shear rate field. Biofilm cells located in the streamers of the biofilm are subjected to much higher shear values than those located on the bottom of the streamers and this dispersion in shear rate values increases at lower bulk fluid velocities. This heterogeneity in the shear force field may be a contributing factor for the heterogeneous behavior in metabolic activity, growth status, gene expression pattern, and antibiotic resistance often associated with nutrient availability within the biofilm.

Variational solution to the lattice Boltzmann method for Couette flow.

Literature studies of the lattice Boltzmann method (LBM) demonstrate hydrodynamics beyond the continuum limit. This includes exact analytical solutions to the LBM, for the bulk velocity and shear stress of Couette flow under diffuse reflection at the walls through the solution of equivalent moment equations. We prove that the bulk velocity and shear stress of Couette flow with Maxwell-type boundary conditions at the walls, as specified by two-dimensional isothermal lattice Boltzmann models, are inherently linear in Mach number. Our finding enables a systematic variational approach to be formulated that exhibits superior computational efficiency than the previously reported moment method. Specifically, the number of partial differential equations(PDEs) in the variational method grows linearly with quadrature order while the number of moment method PDEs grows quadratically. The variational method directly yields a system of linear PDEs that provide exact analytical solutions to the LBM bulk velocity field and shear stress for Couette flow with Maxwell-type boundary conditions. It is anticipated that this variational approach will find utility in calculating analytical solutions for novel lattice Boltzmann quadrature schemes and other flows.

Mechanical effects of nanomaterials on the residual shear strength of dry sandy mixtures: Implication for the high mobility of rock avalanches

Nanoparticles found in rock avalanches and natural faults were inferred to be the reason for the ultra-low shear resistance of the materials along the shear surface. Nevertheless, this inference has not been physically verified yet. To investigate the role of nanoparticles in the shear behavior of granular materials, we conducted a series of ring shear tests on silicon dioxide nanoparticles (SN), silica sand (S8), and mixtures of the S8 with different contents of SN, under varying normal stresses (σ) and shear velocities (V). Our results showed that the shear strength (μ) of SN is high when σ is small (≤ 215 kPa at our test range), even though the maximum shear velocity is about 210 cm/s, but shows a great decrease under higher σ (≥ 619 kPa). The shear strength of mixtures varied with SN content. For S8 (M0) and the mixture of 10% SN (M10), when sheared under small σ, μ first decreased slightly with increasing V when V is smaller than 1 cm/s, after that it increased slightly with further increase of V. Nevertheless, this kind of shear-rate dependent behavior was not observed in the tests under higher σ. When the content of SN in the mixture was <20%, μ increased with the increase of SN content. However, with further increase of SN content, μ decreased. Under high normal stress conditions, distinctive powder rolls were observed on the shear surface formed on the tests. When the mixtures with lower SN content (≤50%), the powder rolls were not observed. We inferred that powder rolls can be produced under high SN content and high normal stress conditions, and this structure altered the particle movement mode from sliding friction to rolling resistance, resulting in a significant decrease in the shear strength. These findings provide valuable insights into the shear behavior of granular materials with nanoparticles and then provide evidence for a better understanding of the high mobility of rock avalanches.