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arXiv2014

Transport coefficients of a granular gas of inelastic rough hard spheres

The Boltzmann equation for inelastic and rough hard spheres is considered as a model of a dilute granular gas. In this model, the collisions are characterized by constant coefficients of normal and tangential restitution and hence the translational and rotational degrees of freedom are coupled. A normal solution to the Boltzmann equation is obtained by means of the Chapman-Enskog method for states near the homogeneous cooling state. The analysis is carried out to first order in the spatial gradients of the number density, the flow velocity, and the granular temperature. The constitutive equations for the momentum and heat fluxes and for the cooling rate are derived and the associated transport coefficients are expressed in terms of the solutions of linear integral equations. For practical purposes, a first Sonine approximation is used to obtain explicit expressions of the transport coefficients as nonlinear functions of both coefficients of restitution and the moment of inertia. Known results for purely smooth inelastic spheres and perfectly elastic and rough spheres are recovered in the appropriate limits.

cond-mat.stat-mech↗

arXiv2014

Rayleigh-Bénard convection with uniform vertical magnetic field

We present the results of direct numerical simulations of Rayleigh-Bénard convection in the presence of a uniform vertical magnetic field near instability onset. We have done simulations in boxes with square as well as rectangular cross-sections in the horizontal plane. We have considered horizontal aspect ratio $η= L_y/L_x =1$ and $2$. The onset of the primary and secondary instabilities are strongly suppressed in the presence of the vertical magnetic field for $η=1$. The Nusselt number $\mathrm{Nu}$ scales with Rayleigh number $\mathrm{Ra}$ close to the primary instability as $[\mathrm{\{Ra - Ra_c (Q)\}/Ra_c (Q)} ]^{0.91}$, where $\mathrm{Ra_c (Q)}$ is the threshold for onset of stationary convection at a given value of the Chandrasekhar number $\mathrm{Q}$. $\mathrm{Nu}$ also scales with $\mathrm{Ra/Q}$ as $(\mathrm{Ra/Q})^μ$. The exponent $μ$ varies in the range $0.39 \le μ\le 0.57$ for $\mathrm{Ra/Q} \ge 25$. The primary instability is stationary as predicted by Chandrasekhar. The secondary instability is temporally periodic for $\mathrm{Pr}=0.1$ but quasiperiodic for $\mathrm{Pr} = 0.025$ for moderate values of $\mathrm{Q}$. Convective patterns for higher values of $\mathrm{Ra}$ consist of periodic, quasiperiodic and chaotic wavy rolls above onset of the secondary instability for $η=1$. In addition, stationary as well as time dependent cross-rolls are observed, as $\mathrm{Ra}$ is further raised. The ratio $r_{\circ}/\mathrm{Pr}$ is independent of $\mathrm{Q}$ for smaller values of $\mathrm{Q}$. The delay in onset of the oscillatory instability is significantly reduced in a simulation box with $η=2$. We also observe inclined stationary rolls for smaller values of $\mathrm{Q}$ for $η=2$.

physics.flu-dyn↗

arXiv2014

Optimum reduction of the dynamo threshold by a ferromagnetic layer located in the flow

We consider a fluid dynamo model generated by the flow on both sides of a moving layer. The magnetic permeability of the layer is larger than that of the flow. We show that there exists an optimum value of magnetic permeability for which the critical magnetic Reynolds number for dynamo onset is smaller than for a nonmagnetic material and also smaller than for a layer of infinite magnetic permeability. We present a mechanism that provides an explanation for recent experimental results. A similar effect occurs when the electrical conductivity of the layer is large.

physics.flu-dyn↗

arXiv2014

Magnetic helicity and the evolution of decaying magnetohydrodynamic turbulence

Ensemble averaged high resolution direct numerical simulations of reverse spectral transfer are presented, extending on the many single realization numerical studies done up to now. This identifies this type of spectral transfer as a statistical property of magnetohydrodynamic turbulence and thus permits reliable numerical exploration of its dynamics. The magnetic energy decay exponent from these ensemble runs has been determined to be $n_E = (0.47 \pm 0.03) + (13.9 \pm 0.8)/R_λ$ for initially helical magnetic fields. We show for the first time that even after removing the Lorentz force term in the momentum equation, thus decoupling it from the induction equation, reverse spectral transfer still persists. The induction equation is now linear with an externally imposed velocity field, thus amenable to numerous analysis techniques. A new door has opened for analyzing reverse spectral transfer, with various ideas discussed.

physics.flu-dyn↗

arXiv2014

Kinetics of Gravity-Driven Water Channels Under Steady Rainfall

We investigate the formation of fingered flow in dry granular media under simulated rainfall using a quasi-2D experimental set-up composed of a random close packing of mono-disperse glass beads. Using controlled experiments, we analyze the finger instabilities that develop from the wetting front as a function of fundamental granular (particle size) and fluid properties (rainfall, viscosity).These finger instabilities act as precursors for water channels, which serve as outlets for water drainage. We look into the characteristics of the homogeneous wetting front and channel size as well as estimate relevant time scales involved in the instability formation and the velocity of the channel finger tip. We compare our experimental results with that of the well-known prediction developed by Parlange and Hill [1976]. This model is based on linear stability analysis of the growth of perturbations arising at the interface between two immiscible fluids. Results show that in terms of morphology, experiments agree with the proposed model. However, in terms of kinetics we nevertheless account for another term that describes the homogenization of the wetting front. This result shows that the manner we introduce the fluid to a porous medium can also influence the formation of finger instabilities.

cond-mat.soft↗

arXiv2014

Magnetic induction and diffusion mechanisms in a liquid sodium spherical Couette experiment

We present a reconstruction of the mean axisymmetric azimuthal and meridional flows in the DTS liquid sodium experiment. The experimental device sets a spherical Couette flow enclosed between two concentric spherical shells where the inner sphere holds a strong dipolar magnet, which acts as a magnetic propeller when rotated. Measurements of the mean velocity, mean induced magnetic field and mean electric potentials have been acquired inside and outside the fluid for an inner sphere rotation rate of 9 Hz (Rm 28). Using the induction equation to relate all measured quantities to the mean flow, we develop a nonlinear least square inversion procedure to reconstruct a fully coherent solution of the mean velocity field. We also include in our inversion the response of the fluid layer to the non-axisymmetric time-dependent magnetic field that results from deviations of the imposed magnetic field from an axial dipole. The mean azimuthal velocity field we obtain shows super-rotation in an inner region close to the inner sphere where the Lorentz force dominates, which contrasts with an outer geostrophic region governed by the Coriolis force, but where the magnetic torque remains the driver. The meridional circulation is strongly hindered by the presence of both the Lorentz and the Coriolis forces. Nevertheless, it contributes to a significant part of the induced magnetic energy. Our approach sets the scene for evaluating the contribution of velocity and magnetic fluctuations to the mean magnetic field, a key question for dynamo mechanisms.

physics.flu-dyn↗

arXiv2014

Generic transport coefficients of a confined electrolyte solution

Physical parameters characterising electrokinetic transport in a confined electrolyte solution are reconstructed from the generic transport coefficients obtained within the classical non-equilibrium statistical thermodynamic framework. The electro-osmotic flow, the diffusio-osmotic flow, the osmotic current, as well as the pressure-driven Poiseuille-type flow, the electric conduction, and the ion diffusion, are described by this set of transport coefficients. The reconstruction is demonstrated for an aqueous NaCl solution between two parallel charged surfaces with a nanoscale gap, by using the molecular dynamic (MD) simulations. A Green-Kubo approach is employed to evaluate the transport coefficients in the linear-response regime, and the fluxes induced by the pressure, electric, and chemical potential fields are compared with the results of non-equilibrium MD simulations. Using this numerical scheme, the influence of the salt concentration on the transport coefficients is investigated. Anomalous reversal of diffusio-osmotic current, as well as that of electro-osmotic flow, is observed at high surface charge densities and high added-salt concentrations.

cond-mat.soft↗

arXiv2014

Turbulent diffusion of chemically reacting gaseous admixtures

We study turbulent diffusion of chemically reacting gaseous admixtures in a developed turbulence. In our previous study [Phys. Rev. Lett. {\bf 80}, 69 (1998)] using a path-integral approach for a delta-correlated in time random velocity field, we demonstrated a strong modification of turbulent transport in fluid flows with chemical reactions or phase transitions. In the present study we use the spectral tau approximation, that is valid for large Reynolds and Peclet numbers, and show that turbulent diffusion of the reacting species can be strongly depleted by a large factor that is the ratio of turbulent and chemical times (turbulent Damköhler number). We have demonstrated that the derived theoretical dependence of turbulent diffusion coefficient versus the turbulent Damköhler number is in a good agreement with that obtained previously in the numerical modelling of a reactive front propagating in a turbulent flow and described by the Kolmogorov-Petrovskii-Piskunov-Fisher equation. We have found that turbulent cross-effects, e.g., turbulent mutual diffusion of gaseous admixtures and turbulent Dufour-effect of the chemically reacting gaseous admixtures, are less sensitive to the values of stoichiometric coefficients. The mechanisms of the turbulent cross-effects are different from the molecular cross effects known in irreversible thermodynamics. In a fully developed turbulence and at large Peclet numbers the turbulent cross-effects are much larger than the molecular ones. The obtained results are applicable also to heterogeneous phase transitions.

physics.flu-dyn↗

arXiv2014

Effective surface dilatational viscosity of highly concentrated particle-laden interfaces

The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with half-immersed monodisperse rigid spherical non-Brownian particles in the limit of high particle concentration. The derivation is based upon the facts that (i) highly-concentrated particle arrays in a plane form hexagonal structure, and (ii) the dominant contribution to the viscous dissipation rate arises in the thin gaps between neighboring particles.

cond-mat.soft↗

arXiv2014

Contact angles in the pseudopotential lattice Boltzmann modeling of wetting

In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction formulated in the present paper, are numerically investigated and compared in terms of the achievable contact angles, the maximum and the minimum densities, and the spurious currents. It is found that the pseudopotential-based interaction works well for simulating small static (liquid) contact angles, however, is unable to reproduce static contact angles close to 180 degrees. Meanwhile, it is found that the proposed modified pseudopotential-based interaction performs better in light of the maximum and the minimum densities and is overall more suitable for simulating large contact angles as compared with the other two types of fluid-solid interactions. Furthermore, the spurious currents are found to be enlarged when the fluid-solid interaction force is introduced. Increasing the kinematic viscosity ratio between the vapor and liquid phases is shown to be capable of reducing the spurious currents caused by the fluid-solid interactions.

physics.flu-dyn↗

arXiv2014

Active nematic materials with substrate friction

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.

cond-mat.soft↗

arXiv2014

Single-wavenumber Representation of Nonlinear Energy Spectrum in Elastic-Wave Turbulence of {F}öppl-von {K}ármán Equation: Energy Decomposition Analysis and Energy Budget

A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wavenumber space, and analytical expressions of detailed energy budget in the nonlinear interactions are obtained for the first time in wave turbulence systems. We numerically solved the FvK equation and observed the following facts. Kinetic and bending energies are comparable with each other at large wavenumbers as the weak turbulence theory suggests. On the other hand, the stretching energy is larger than the bending energy at small wavenumbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode $a_{\bm{k}}$ and its companion mode $a_{-\bm{k}}$ is observed at the small wavenumbers. Energy transfer shows that the energy is input into the wave field through stretching-energy transfer at the small wavenumbers, and dissipated through the quartic part of kinetic-energy transfer at the large wavenumbers. A total-energy flux consistent with the energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

nlin.CD↗

arXiv2017

Is the kinetic equation for turbulent gas-particle flows ill-posed?

This paper is about well-posedness and realizability of the kinetic equation for gas-particle flows and its relationship to the Generalized Langevin Model (GLM) PDF equation. Previous analyses claim that this kinetic equation is ill-posed, that in particular it has the properties of a backward heat equation and as a consequence, its solutions will in the course of time exhibit finite-time singularities. We show that the analysis leading to this conclusion is fundamentally incorrect because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra $+ve$ diffusion that always outweighs the contribution from the$-ve$ diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these $+ve$ and $-ve$ contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing we have drawn attention to the limitations of the GLM approach which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

physics.flu-dyn↗

arXiv2018

Galilean Invariant Preconditioned Central Moment Lattice Boltzmann Method without Cubic Velocity Errors for Efficient Steady Flow Simulations

Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third order diagonal moments on the first order moments for standard lattices, and strategies have recently been introduced to restore GI without such errors using a modified collision operator involving either corrections to the relaxation times or to the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that alleviates the numerical stiffness. In the present study, we present a GI formulation of the preconditioned cascaded central moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. Improvements in accuracy and convergence acceleration are demonstrated.

physics.flu-dyn↗

arXiv2018

Network community-based model reduction for vortical flows

A network community-based reduced-order model is developed to capture key interactions amongst coherent structures in high-dimensional unsteady vortical flows. The present approach is data-inspired and founded on network-theoretic techniques to identify important vortical communities that are comprised of vortical elements that share similar dynamical behavior. The overall interaction-based physics of the high-dimensional flow field is distilled into the vortical community centroids, considerably reducing the system dimension. Taking advantage of these vortical interactions, the proposed methodology is applied to formulate reduced-order models for the inter-community dynamics of vortical flows, and predict lift and drag forces on bodies in wake flows. We demonstrate the capabilities of these models by accurately capturing the macroscopic dynamics of a collection of discrete point vortices, and the complex unsteady aerodynamic forces on a circular cylinder and an airfoil with a Gurney flap. The present formulation is found to be robust against simulated experimental noise and turbulence due to its integrating nature of the system reduction.

physics.flu-dyn↗

arXiv2018

Symmetrized Operator Split Schemes for Force and Source Modeling in Cascaded Lattice Boltzmann Methods for Flow and Scalar Transport

Operator split forcing schemes exploiting a symmetrization principle, i.e. Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and three-dimensions for fluid flows with impressed local forces are presented. Analogous scheme for the passive scalar transport represented by a convection-diffusion equation with a source term in a novel cascaded LB formulation is also derived. They are based on symmetric applications of the split solutions of the changes on the scalar field/fluid momentum due to the sources/forces over half time steps before and after the collision step. The latter step is effectively represented in terms of the post-collision change of moments at zeroth and first orders, respectively, to represent the effect of the sources on the scalar transport and forces on the fluid flow. Such symmetrized operator split cascaded LB schemes are consistent with the second-order Strang splitting and naturally avoid any discrete effects due to forces/sources by appropriately projecting their effects for higher order moments. All the force/source implementation steps are performed only in the moment space and they do not require formulations as extra terms and their additional transformations to the velocity space. These result in particularly simpler and efficient schemes to incorporate forces/sources in the cascaded LB methods unlike those considered previously. Numerical study for various benchmark problems in 2D and 3D for fluid flow problems with body forces and scalar transport with sources demonstrate the validity and accuracy, as well as the second-order convergence rate of the symmetrized operator split forcing/source schemes for the cascaded LB methods.

physics.flu-dyn↗

arXiv2018

Twist-induced crossover from 2D to 3D turbulence in active nematics

While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-2D to 3D chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines spanning the height of the channel and exhibiting effectively 2D active turbulence. Upon increasing channel height, we find a crossover to 3D chaotic flows due to the contortion of disclinations above a critical activity. We further show that these contortions are engendered by twist perturbations producing a sharp change in the curvature of disclinations.

cond-mat.soft↗

arXiv2018

Flow Characteristics of Chlamydomonas result in Purely Hydrodynamic Scattering

It has long been believed that swimming eukaryotes feel solid boundaries through direct ciliary contact. Specifically, based on observations of behavior of green alga Chlamydomonas reinhardtii it has been reported that it is their "flagella [that] prevent the cell body from touching the surface" [Kantsler et al. PNAS, 2013]. Here, via investigation of a model swimmer whose flow field closely resembles that of C. reinhardtii, we show that the scattering from a wall can be purely hydrodynamic and that no mechanical/flagellar force is needed for sensing and escaping the boundary.

physics.flu-dyn↗