scholarly journals Rheology of dense granular flows in two dimensions: Comparison of fully two-dimensional flows to unidirectional shear flow

2018 ◽  
Vol 3 (6) ◽  
Author(s):  
Ashish Bhateja ◽  
Devang V. Khakhar
Keyword(s):  
Shear Flow ◽  
Granular Flows ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Dense Granular Flows ◽  
Two Dimensional Flows

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

scholarly journals SLOW DENSE GRANULAR FLOWS AS A SELF-INDUCED PROCESS

2001 ◽  
Vol 04 (04) ◽  
pp. 441-450 ◽  
Author(s):  
OLIVIER POULIQUEN ◽  
YOËL FORTERRE ◽  
STÉPHANE LE DIZES
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Granular Material ◽  
Granular Flows ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Stress Fluctuation ◽  
The Media ◽  
Granular Shear ◽  
Dense Granular Flows

A simple model is presented for the description of steady uniform shear flow of granular material. The model is based on a stress fluctuation activated process. The basic idea is that shear between two particle layers induces fluctuations in the media that may trigger a shear at some other position. Based on this idea, a minimum model is derived and applied to different configurations of granular shear flow.

scholarly journals Integrals of the Vorticity Equation. Part II: Special Two-Dimensional Flows

2006 ◽  
Vol 63 (2) ◽  
pp. 611-616 ◽  
Author(s):  
Robert Davies-Jones
Keyword(s):  
Shear Flow ◽  
Formal Solution ◽  
Inviscid Flow ◽  
Vorticity Equation ◽  
Two Dimensional ◽  
General Integral ◽  
2D Flow ◽  
Stratified Shear Flow ◽  
Two Dimensional Flows

Abstract In Part I, a general integral of the 2D vorticity equation was obtained. This is a formal solution for the vorticity of a moving tube of air in a 2D unsteady stratified shear flow with friction. This formula is specialized here to various types of 2D flow. For steady inviscid flow, the integral reduces to an integral found by Moncrieff and Green if the flow is Boussinesq and to one obtained by Lilly if the flow is isentropic. For steady isentropic frictionless motion of clear air, several quantities that are invariant along streamlines are found. These invariants provide another way to obtain Lilly’s integral from the general integral.

Granular hydrodynamics and pattern formation in vertically oscillated granular disk layers

2008 ◽  
Vol 597 ◽  
pp. 119-144 ◽  
Author(s):  
JOSÉ A. CARRILLO ◽  
THORSTEN PÖSCHEL ◽  
CLARA SALUEÑA
Keyword(s):  
Numerical Scheme ◽  
Granular Flows ◽  
Quantitative Agreement ◽  
Vertical Vibration ◽  
Two Dimensions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Faraday Waves ◽  
Periodic Patterns ◽  
Hydrodynamic Description

The goal of this study is to demonstrate numerically that certain hydrodynamic systems, derived from inelastic kinetic theory, give fairly good descriptions of rapid granular flows even if they are way beyond their supposed validity limits. A numerical hydrodynamic solver is presented for a vibrated granular bed in two dimensions. It is based on a highly accurate shock capturing state-of-the-art numerical scheme applied to a compressible Navier–Stokes system for granular flow. The hydrodynamic simulation of granular flows is challenging, particularly in systems where dilute and dense regions occur at the same time and interact with each other. As a benchmark experiment, we investigate the formation of Faraday waves in a two-dimensional thin layer exposed to vertical vibration in the presence of gravity. The results of the hydrodynamic simulations are compared with those of event-driven molecular dynamics and the overall quantitative agreement is good at the level of the formation and structure of periodic patterns. The accurate numerical scheme for the hydrodynamic description improves the reproduction of the primary onset of patterns compared to previous literature. To our knowledge, these are the first hydrodynamic results for Faraday waves in two-dimensional granular beds that accurately predict the wavelengths of the two-dimensional standing waves as a function of the perturbation's amplitude. Movies are available with the online version of the paper.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Self-diffusion scalings in dense granular flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Riccardo Artoni ◽  
Michele Larcher ◽  
James T. Jenkins ◽  
Patrick Richard
Keyword(s):  
Shear Rate ◽  
Solid Fraction ◽  
Granular Flows ◽  
The Self ◽  
Granular Temperature ◽  
Restitution Coefficient ◽  
Self Diffusion ◽  
Diffusivity Tensor ◽  
Dense Granular Flows

The self-diffusivity tensor in homogeneously sheared dense granular flows is anisotropic. We show how its components depend on solid fraction, restitution coefficient, shear rate, and granular temperature.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals The strain rate in evolutions of (elliptical) vortices in inviscid two-dimensional flows

2001 ◽  
Vol 13 (12) ◽  
pp. 3699-3708 ◽  
Author(s):  
P. W. C. Vosbeek ◽  
G. J. F. van Heijst ◽  
V. P. Mogendorff
Keyword(s):  
Strain Rate ◽  
Two Dimensional ◽  
Two Dimensional Flows
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