Anisotropic Viscosity Research Articles

Experimental measurements of anisotropic viscosity in naturally sourced dunite with a preexisting CPO

Naturally deformed dunite cores with a preexisting crystallographic preferred orientation (CPO), collected from a shear zone in the Josephine peridotite (southwest Oregon, USA), were deformed experimentally in triaxial compression. The compression axis was varied relative to the CPO geometry to measure the anisotropy in viscosity of these rocks. Deformation experiments were performed in a gas-medium apparatus at three constant displacement-rate steps, at a temperature of 1250 °C and a confining pressure of 300 MPa. Cores were dehydrated at 1200 °C in a controlled CO/CO2 atmosphere prior to deformation to achieve nominally dry conditions. Data from individual experiments were fit by a power-law, yielding a stress exponent of n ≈ 3.6, indicative of deformation by dislocation creep. The maximum difference in viscosity was a factor of 2.6 at constant stress. The CPO of the olivine grains was measured after deformation by electron backscatter diffraction (EBSD). The flow stress correlated with the mean Schmid factor (or resolved shear stress) on the easiest dislocation slip systems, calculated from grain orientations determined from EBSD analyses. Analysis of our data with a simplified effective-medium model, which incorporated constraints from published single-crystal flow laws, demonstrated the link between CPO and anisotropy in viscosity. Predictions from viscoplastic self-consistent (VPSC) models support our simplified analysis of the measured anisotropy.

Multiparticle collision dynamics simulations of a squirmer in a nematic fluid

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer’s speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.Graphic abstract

Data assimilation for turbulent mean flow and scalar fields with anisotropic formulation

This work presents an anisotropic formulation for data assimilation (DA) of turbulent flows using the continuous adjoint system. This DA scheme serves as a tool to complement flow measurement data (the observations), which are usually limited in spatial range and measurable quantities, with the help of a predictive model in the framework of the Reynolds-averaged Navier–Stokes approach (the estimator). Herein, the measured data profiles at several locations are used as observations. In the estimator, a forcing term $${\varvec{F}}$$ is added to the momentum equation to compensate for the contribution of the anisotropic eddy viscosity, whilst the isotropic part of the eddy viscosity is determined by conventional turbulence models. $${\varvec{F}}$$ is optimised using the continuous adjoint equations, driving the predicted flow quantities towards the observations. Similar treatments are conducted for the scalar prediction. Three test cases are used for assessment and validation of the present DA scheme. The results of a circular jet demonstrate that the mean flow and scalar fields can be perfectly reproduced from the observations due to the $${\varvec{F}}$$ optimisation. The flow over a blunt plate demonstrates the ability of the present DA scheme to reconstruct global flow fields from several measured velocity profiles. The flow and heat transfer on a ribbed wall reveal that once the global flow field is well recovered, the wall heat transfer characteristics can be correctly determined with a limited number of observations. The present anisotropic DA approach is quite practical for complex flow applications, serving as a complement to our previous isotropic adjoint-based data assimilation for further DA work.

Evolution and demise of passive margins through grain mixing and damage

How subduction-the sinking of cold lithospheric plates into the mantle-is initiated is one of the key mysteries in understanding why Earth has plate tectonics. One of the favored locations for subduction triggering is at passive margins, where sea floor abuts continental margins. Such passive margin collapse is problematic because the strength of the old, cold ocean lithosphere should prohibit it from bending under its own weight and sinking into the mantle. Some means of mechanical weakening of the passive margin are therefore necessary. Spontaneous and accumulated grain damage can allow for considerable lithospheric weakening and facilitate passive margin collapse. Grain damage is enhanced where mixing between mineral phases in lithospheric rocks occurs. Such mixing is driven both by compositional gradients associated with petrological heterogeneity and by the state of stress in the lithosphere. With lateral compressive stress imposed by ridge push in an opening ocean basin, bands of mixing and weakening can develop, become vertically oriented, and occupy a large portion of lithosphere after about 100 million y. These bands lead to anisotropic viscosity in the lithosphere that is strong to lateral forcing but weak to bending and sinking, thereby greatly facilitating passive margin collapse.

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

Evolving Viscous Anisotropy in the Upper Mantle and Its Geodynamic Implications

AbstractAsthenospheric shear causes some minerals, particularly olivine, to develop anisotropic textures that can be detected seismically. In laboratory experiments, these textures are also associated with anisotropic viscous behavior, which should be important for geodynamic processes. To examine the role of anisotropic viscosity for asthenospheric deformation, we developed a numerical model of coupled anisotropic texture development and anisotropic viscosity, both calibrated with laboratory measurements of olivine aggregates. This model characterizes the time‐dependent coupling between large‐scale formation of lattice‐preferred orientation (i.e., texture) and changes in asthenospheric viscosity for a series of simple deformation paths that represent upper mantle geodynamic processes. We find that texture development beneath a moving surface plate tends to align the a axes of olivine into the plate motion direction, which weakens the effective viscosity in this direction and increases plate velocity for a given driving force. Our models indicate that the effective viscosity increases for shear in the horizontal direction perpendicular to the a axes. This increase should slow plate motions and new texture development in this perpendicular direction and could impede changes to the plate motion direction for tens of millions of years. However, the same well‐developed asthenospheric texture may foster subduction initiation perpendicular to the plate motion and deformations related to transform faults, as shearing on vertical planes seems to be favored across a sublithospheric olivine texture. These end‐member cases examining shear deformation in the presence of a well‐formed asthenospheric texture illustrate the importance of the mean olivine orientation, and its associated viscous anisotropy, for a variety of geodynamic processes.

Olivine-induced viscous anisotropy in fossil strike-slip mantle shear zones and associated strain localization in the crust

SUMMARYWe propose that strain localization in plate interiors, such as linear belts of intraplate seismicity, may arise from spatial variations in viscous anisotropy produced by preferred orientation of olivine crystals (CPO or texture) inherited from previous deformation episodes in the lithospheric mantle. To quantify this effect, we model the deformation of a plate containing a fossil strike-slip mantle shear zone at different orientations relative to an imposed horizontal shortening, but no initial heterogeneity in the crust. The fossil shear zone is characterized by different orientation and intensity of the olivine CPO relatively to the surrounding mantle, which is isotropic in most simulations. The anisotropy in viscosity produced by the CPO, which remains fixed throughout the simulations, is described by an anisotropic (Hill) yield function parametrized based on second-order viscoplastic self-consistent (SO-VPSC) models. The results indicate that lateral variations in viscous anisotropy in the mantle affect the strain distribution in the entire lithosphere. Reactivation of the strike-slip mantle shear zone and strain localization in the crust above it occur for horizontal compression at 35–55° to the fossil shear plane, with a maximum at 45°. The magnitude of strain localization depends on (i) the contrast in viscous anisotropy and, hence, on the variations in CPO orientation and intensity in the mantle, (ii) the boundary conditions and (iii) the feedbacks between mantle and crustal deformation. For a strong olivine CPO, when the boundary conditions do not hinder shear parallel to the fossil mantle shear zone, strain rates within it are up to a factor 30 higher than in an isotropic surrounding mantle or up to a factor 200 when the surrounding mantle is anisotropic, which results in strain rates up to a factor 10 or up to a factor 100 higher in the crust right above the fossil shear zone. Frictional weakening in the crust faults increases strain localization in the entire lithospheric column. High strength contrasts between the mantle and the ductile crust result in less efficient mechanical coupling, with strong localization in the mantle and lower crust, but weak in the brittle upper crust. Decrease in the crust–mantle strength contrast enhances the coupling and produces more homogenous strain distribution with depth, as well as a time-dependent evolution of strain localization, which reaches a peak and decreases before attaining steady-state. Comparison of seismic anisotropy, regional stress and focal mechanism data in linear arrays of intraplate seismicity, like the New Madrid and South Armorican seismic zones, to our models' predictions corroborates that olivine CPO preserved in fossil lithospheric-scale shear zones may be key for the development of such structures.

Two-dimensional MHD model of gas flow dynamics near a young star with a jet and a protoplanetary disk

AbstractA numerical nonstationary two-dimensional MHD model of a protoplanetary disk near T Tauri star with a jet is developed. The model assumes consideration of pure gas ionization, optically thin cooling, anisotropic thermal conductivity and viscosity. The relaxation of gas-dynamic flows is analyzed. Based on the evolution of plasma flows, profiles of hydrogen spectral lines have been obtained.

Near-Field Simulations of Film Cooling with a Modified DES Model

Modeling the heat transfer characteristics of highly turbulent flow in gas turbine film cooling is important for providing better insights and engineering solutions to the film cooling problem. This study proposes a modified detached eddy simulation (DES) model for better film cooling simulations. First, spatially varying anisotropic eddy viscosity is found from the results of the large eddy simulation (LES) of film cooling. Then the correlation for eddy viscosity anisotropy ratio has been established based on the LES results and is proposed as the modification approach for the DES model. The modified DES model has been tested for the near-field film cooling simulations under different blowing ratios. Detailed comparisons of the centerline and 2D film cooling effectiveness indicate that the modified DES model enhances the spanwise spreading of the temperature field. The DES model leads to deviations of 62.4%, 39.8%, and 33.5% from the experimental centerline effectiveness under blowing ratios of 0.5, 1.0, and 1.5, respectively, while the modified DES reduces the deviations to 51.5%, 26.7%, and 28.9%. The modified DES model provides a promising approach for film cooling numerical simulations. It embraces the advantage of LES in resolving detailed vortical structure dynamics with a moderate computational cost. It also significantly improves the original DES model on the spanwise counter rotating vortex pair (CRVP) spreading, mixing, and effectiveness prediction.

Numerical simulation of separation flows induced by shockwave using an anisotropic turbulence model

This paper studies the performance of a nonlinear anisotropic turbulence model developed in the basis of a statistical partial average scheme. The first order velocity of turbulent fluctuations, retained by a novel average scheme, and turbulent length scale can be determined from the momentum equations and mechanical energy equation of the fluctuation flow, respectively. The two physical quantities are readily to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve computational results. Two typical shock-wave-boundary-layer-interaction (SWBLI) separation flows are deeply studied using CFD method. One is an incident oblique shock wave impinging on a flat plate with a turbulent boundary layer, and the other one is a transonic turbulent separation flow in a converging-diverging transonic diffuser. Comparisons between the computational results and experimental data are carried out for velocity profiles, density contours, pressure distribution, skin friction coefficient, Reynolds stress as well as streamline vectors distribution. Without using any empirical coefficients and wall functions, the numerical results are in good agreement with the available experimental data, which further confirms that the nonlinear anisotropic eddy viscosity tensor is of the decisive factor for the success of the computational results.

Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples

ABSTRACT Weakly collisional, magnetized plasmas characterized by anisotropic viscosity and conduction are ubiquitous in galaxies, haloes, and the intracluster medium (ICM). Cosmic rays (CRs) play an important role in these environments as well, by providing additional pressure and heating to the thermal plasma. We carry out a linear stability analysis of weakly collisional plasmas with CRs using Braginskii MHD for the thermal gas. We assume that the CRs stream at the Alfvén speed, which in a weakly collisional plasma depends on the pressure anisotropy (Δp) of the thermal plasma. We find that this Δp dependence introduces a phase shift between the CR-pressure and gas-density fluctuations. This drives a fast-growing acoustic instability: CRs offset the damping of acoustic waves by anisotropic viscosity and give rise to wave growth when the ratio of CR pressure to gas pressure is ≳αβ−1/2, where β is the ratio of thermal to magnetic pressure, and α, typically ≲1, depends on other dimensionless parameters. In high-β environments like the ICM, this condition is satisfied for small CR pressures. We speculate that the instability studied here may contribute to the scattering of high-energy CRs and to the excitation of sound waves in galaxy-halo, group and cluster plasmas, including the long-wavelength X-ray fluctuations in Chandra observations of the Perseus cluster. It may also be important in the vicinity of shocks in dilute plasmas (e.g. cluster virial shocks or galactic wind termination shocks), where the CR pressure is locally enhanced.

Spontaneous helical flows in active nematics lying on a cylindrical surface.

Within the framework of the two-dimensional Ericksen-Leslie model, we explore the effect of geometric confinement on the spontaneous flow of active nematic gels. The nematic particles are assumed to flow on a cylindrical surface, while a degenerate tangential anchoring is enforced. Using the linear approximation of the motion equations, we show that there is a close interplay among extrinsic curvature, flow, director alignment, and activity. We find that the extrinsic curvature promotes the director alignment parallel to the cylindrical axis and is responsible for raising the critical threshold with respect to the flat case. Our analysis reveals a very rich scenario where the key quantities are the activity coefficient, the tumbling parameter, and the anisotropic viscosity ratio. Thus, solutions can exhibit a double periodicity in both the azimuthal and axial variables. As a consequence, the velocity field can make a finite angle with the cylinder axis and the active flow winds on the surface with a helical pattern, while the director oscillates around the cylinder generators. Our results can be validated on thin layers of nematic gels placed between two concentric cylinders and suggest which material properties are most suited for the design of active microfluidic devices.

Anisotropic viscoelastic phase separation in polydisperse hard rods leads to nonsticky gelation

Spinodal demixing into two phases having very different viscosities leads to viscoelastic networks-i.e., gels-usually as a result of attractive particle interactions. Here, however, we demonstrate demixing in a colloidal system of polydisperse, rod-like clay particles that is driven by particle repulsions instead. One of the phases is a nematic liquid crystal with a highly anisotropic viscosity, allowing flow along the director, but suppressing it in other directions. This phase coexists with a dilute isotropic phase. Real-space analysis and molecular-dynamics simulations both reveal a long-lived network structure that is locally anisotropic, yet macroscopically isotropic. We show that our system exhibits the characteristics of colloidal gelation, leading to nonsticky gels.

Variational analysis of the influence of grain shape anisotropy on shear viscosity in Nabarro-Herring-Coble creep

The effect of strain-induced grain shape anisotropy on diffusional creep viscosity is analysed in two dimensions via a model representing grains by cylinders with elliptical cross section. Both cases of dominance of grain boundary diffusion and lattice diffusion are considered. Anisotropic creep viscosity is described by two coefficients calculated by considering different loading configurations with respect to the ellipse axes. Upper and lower bounds on these coefficients are obtained using kinematic and statical variational principles and assuming affine velocity, or uniform stress trial boundary fields, respectively. The analysis emphasises the dependence of the viscosity coefficients on aspect ratio and grain boundary viscosity. The difference between the bounds increases with grain elongation. A method is proposed for deriving estimates for the effective viscosity coefficients by coupling the two bounds. The strain hardening effect is analysed. Lattice diffusion contributes less to viscosity anisotropy than diffusion and sliding at grain boundaries.

On the Striated Regularity for the 2D Anisotropic Boussinesq System

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with anisotropic thermal diffusion or anisotropic viscosity and with striated initial data. Using the key idea of Chemin to solve 2-D vortex patch of ideal fluid, namely the striated regularity can help to bound the gradient of the velocity, we can prove the global well-posedness of the Boussinesq system with anisotropic thermal diffusion with initial vorticity being discontinuous across some smooth interface. In the case of an anisotropic horizontal viscosity we can study the propagation of the striated regularity for the smooth temperature patches problem.

On the survival of cool clouds in the circumgalactic medium

ABSTRACT We explore the survival of cool clouds in multiphase circumgalactic media. We revisit the ‘cloud-crushing problem’ in a large survey of simulations including radiative cooling, self-shielding, self-gravity, magnetic fields, and anisotropic Braginskii conduction and viscosity (with saturation). We explore a wide range of parameters including cloud size, velocity, ambient temperature and density, and a variety of magnetic field configurations and cloud turbulence. We find that realistic magnetic fields and turbulence have weaker effects on cloud survival; the most important physics is radiative cooling and conduction. Self-gravity and self-shielding are important for clouds that are initially Jeans-unstable, but largely irrelevant otherwise. Non-self-gravitating, realistically magnetized clouds separate into four regimes: (1) at low column densities, clouds evaporate rapidly via conduction; (2) a ‘failed pressure confinement’ regime, where the ambient hot gas cools too rapidly to provide pressure confinement for the cloud; (3) an ‘infinitely long-lived’ regime, in which the cloud lifetime becomes longer than the cooling time of gas swept up in the leading bow shock, so the cloud begins to accrete and grow; and (4) a ‘classical cloud destruction’ regime, where clouds are eventually destroyed by instabilities. In the final regime, the cloud lifetime can exceed the naive cloud-crushing time owing to conduction-induced compression. However, small and/or slow-moving clouds can also evaporate more rapidly than the cloud-crushing time. We develop simple analytic models that explain the simulated cloud destruction times in this regime.

The effect of anisotropic viscosity on the nonlinear MHD kink instability

The kink instability of magnetohydrodynamics is believed to be fundamental to many aspects of the dynamic activity of the solar atmosphere, such as the initiation of flares and the heating of the solar corona. In this work, we investigate the importance of viscosity on the kink instability. In particular, we focus on two forms of viscosity; isotropic viscosity (independent of the magnetic field) and anisotropic viscosity (with a preferred direction following the magnetic field). Through the detailed analysis of magnetohydrodynamic simulations of the kink instability with both types of viscosity, we show that the form of viscosity has a significant effect on the nonlinear dynamics of the instability. The different viscosities allow for different flow and current structures to develop, thus affecting the behaviour of magnetic relaxation, the formation of secondary instabilities and the Ohmic and viscous heating produced. Our results have important consequences for the interpretation of solar observations of the kink instability.

Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

The purpose of this work is to study the generalized Navier–Stokes equations with nonlinear viscosity that, in addition, can be fully anisotropic. Existence of very weak solutions is proved for the associated initial and boundary-value problem, supplemented with no-slip boundary conditions. We show that our existence result is optimal in some directions provided there is some compensation in the remaining directions. A particular simplification of the problem studied here, reduces to the Navier–Stokes equations with (linear) anisotropic viscosity used to model either the turbulence or the Ekman layer in atmospheric and oceanic fluid flows.

Effects of Anisotropic Viscosity on the Evolution of Active Galactic Nuclei Bubbles in Galaxy Clusters

Abstract The interaction between jets from active galactic nuclei (AGNs) and the intracluster medium (ICM) provides key constraints on the feeding and feedback of supermassive black holes. Much understanding about AGN feedback is gained from purely hydrodynamic models; however, whether such an approximation is adequate for the magnetized, weakly collisional ICM needs to be critically examined. For example, AGN-blown bubbles in hydrodynamic simulations are easily disrupted by fluid instabilities, making it difficult to explain the coherence of observed bubbles such as the northwest ghost bubble in Perseus. In order to investigate whether magnetic tension and viscosity in realistic conditions could preserve the bubble integrity, we performed the first Braginskii-magnetohydrodynamic simulations of jet-inflated bubbles in a medium with tangled magnetic field. We find that magnetic tension alone is insufficient to prevent bubble deformation due to large velocity shear at early stage of the evolution. Although unsuppressed anisotropic viscosity in tangled magnetic field can have similar effects as isotropic viscosity, when the pressure anisotropy is bounded by microscopic plasma instabilities, the level of viscosity is substantially limited, thereby failing to prevent bubble deformation as in the inviscid case. Our results suggest that Braginskii viscosity is unlikely to be the primary mechanism for suppressing the fluid instabilities for AGN bubbles, and it remains a challenging task to reproduce smooth and coherent bubbles as observed. Because the dynamical influence and heating of the ICM critically depend on the bubble morphology, our study highlights the fundamental role of “microphysics” on the macroscopic properties of AGN feedback processes.

Hot Accretion Flow in Two-Dimensional Spherical Coordinates: Considering Pressure Anisotropy and Magnetic Field

For systems with extremely low accretion rate, such as Galactic Center Sgr A* and M87 galaxy, the ion collisional mean free path can be considerably larger than its Larmor radius. In this case, the gas pressure is anisotropic to magnetic field lines. In this paper, we pay attention to how the properties of outflow change with the strength of anisotropic pressure and the magnetic field. We use an anisotropic viscosity to model the anisotropic pressure. We solve the two-dimensional magnetohydrodynamic (MHD) equations in spherical coordinates and assume that the accretion flow is radially self-similar. We find that the work done by anisotropic pressure can heat the accretion flow. The gas temperature is heightened when anisotropic stress is included. The outflow velocity increases with the enhancement of strength of the anisotropic force. The Bernoulli parameter does not change much when anisotropic pressure is involved. However, we find that the energy flux of outflow can be increased by a factor of 20 in the presence of anisotropic stress. We find strong wind (the mass outflow is about 70% of the mass inflow rate) is formed when a relatively strong magnetic field is present. Outflows from an active galactic nucleus can interact with gas in its host galaxies. Our result predicts that outflow feedback effects can be enhanced significantly when anisotropic pressure and a relatively powerful magnetic field is considered.