Inverse cascades of angular momentum

1996 ◽  
Vol 56 (3) ◽  
pp. 615-639 ◽  
Author(s):  
Shuojun Li ◽  
David Montgomery ◽  
Wesley B. Jones
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Galerkin Approximation ◽  
Periodic Boundary Conditions ◽  
Navier Stokes ◽  
Box Dimension ◽  
Physical Situation ◽  
Two Dimensional ◽  
Decaying Turbulence

Most theoretical and computational studies of turbulence in Navier—Stokes fluids and/or guiding-centre plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently reproduced result that two-dimensional and/or MHD decaying turbulence leads to structures comparable in length scale to a box dimension, it is natural to ask if periodic boundary conditions are an adequate representation of any physical situation. Here, we study, computationally, the decay of two-dimensional turbulence in a Navier—Stokes fluid or guiding-centre plasma in the presence of circular no-slip rigid walls. The method is wholly spectral, and relies on a Galerkin approximation by a set of functions that obey two boundary conditions at the wall radius (analogues of the Chandrasekhar— Reid functions). It is possible to explore Reynolds numbers up to the order of 1250, based on an RMS velocity and a box radius. It is found that decaying turbulence is altered significantly by the no-slip boundaries. First, strong boundary layers serve as sources of vorticity and enstrophy and enhance the early-time energy decay rate, for a given Reynolds number, well above the periodic boundary condition values. More importantly, angular momentum turns out to be an even more slowly decaying ideal invariant than energy, and to a considerable extent governs the dynamics of the decay. Angular momentum must be taken into account, for example, in order to achieve quantitative agreeement with the predicition of maximum entropy, or ‘most probable’, states. These are predicitions of conditions that are established after several eddy turnover times but before the energy has decayed away. Angular momentum will cascade to lower azimuthal mode numbers, even if absent there initially, and the angular momentum modal spectrum is eventually dominated by the lowest mode available. When no initial angular momentum is present, no behaviour that suggests the likelihood of inverse cascades is observed.

scholarly journals Probabilistic Methods for the Incompressible Navier–Stokes Equations With Space Periodic Conditions

2013 ◽  
Vol 45 (3) ◽  
pp. 742-772
Author(s):  
G. N. Milstein ◽  
M. V. Tretyakov
Keyword(s):  
Boundary Conditions ◽  
Numerical Integration ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Weak Sense ◽  
Periodic Boundary Conditions ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Probabilistic Nature

We propose and study a number of layer methods for Navier‒Stokes equations (NSEs) with spatial periodic boundary conditions. The methods are constructed using probabilistic representations of solutions to NSEs and exploiting ideas of the weak sense numerical integration of stochastic differential equations. Despite their probabilistic nature, the layer methods are nevertheless deterministic.

scholarly journals Mixing and demixing of binary mixtures of polar chiral active particles

Soft Matter ◽  
2018 ◽  
Vol 14 (21) ◽  
pp. 4388-4395 ◽  
Author(s):  
Bao-quan Ai ◽  
Zhi-gang Shao ◽  
Wei-rong Zhong
Keyword(s):  
Binary Mixture ◽  
Boundary Conditions ◽  
Binary Mixtures ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Active Particles

We study a binary mixture of polar chiral (counterclockwise or clockwise) active particles in a two-dimensional box with periodic boundary conditions.

scholarly journals Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces

2015 ◽  
Vol 28 (1) ◽  
pp. 49-67 ◽  
Author(s):  
M. D. Korzec ◽  
P. Nayar ◽  
P. Rybka
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Initial Conditions ◽  
Periodic Boundary Conditions ◽  
Global Attractors ◽  
Sixth Order ◽  
Two Dimensional ◽  
One Dimensional ◽  
Crystalline Surface ◽  
Dimensional Version

Abstract A spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x, y, t) that undergoes faceting is considered with periodic boundary conditions, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes $$u_1=h_{x}$$ u 1 = h x and $$u_2=h_y$$ u 2 = h y to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in $$\dot{H}^2_{per}$$ H ˙ p e r 2 , we consider the solution operator $$S(t): \dot{H}^2_{per} \rightarrow \dot{H}^2_{per}$$ S ( t ) : H ˙ p e r 2 → H ˙ p e r 2 , to gain our results. We prove the necessary continuity, dissipation and compactness properties.

SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA

1996 ◽  
Vol 07 (06) ◽  
pp. 873-881 ◽  
Author(s):  
NIELS GRØNBECH-JENSEN
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Two Dimensional ◽  
Trigonometric Functions ◽  
Periodic Media ◽  
Two Dimensional System

We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.

scholarly journals Must be the wave function single-valued? Ring vs. periodic boundary conditions, spinors and double rotations

2022 ◽  
Author(s):  
Josep Planelles
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Boundary Conditions ◽  
Undergraduate Students ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Unitary Groups ◽  
Lecture Notes

This is a lecture notes for undergraduate students. We try to tackle the single valuedness of spatial and double valuedness of spin functions. Also, we adress the need of spinors to accommodate spin functions with some parallelism to the need of axial vectors (or antisymmetric traceless tensors) to accommodate angular momentum. Finally, we revisit the Dirac and Weyl tricks on the non-equivalence of a 2 pi and a 4 pi rotation related the topology of rotation and unitary groups.

Two-dimensional periodic boundary conditions for demagnetization interactions in micromagnetics

2010 ◽  
Vol 49 (1) ◽  
pp. 84-87 ◽  
Author(s):  
Weiwei Wang ◽  
Congpu Mu ◽  
Bin Zhang ◽  
Qingfang Liu ◽  
Jianbo Wang ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Two Dimensional

scholarly journals Limits of the Stokes and Navier–Stokes equations in a punctured periodic domain

2019 ◽  
Vol 18 (02) ◽  
pp. 211-235
Author(s):  
Michel Chipot ◽  
Jérôme Droniou ◽  
Gabriela Planas ◽  
James C. Robinson ◽  
Wei Xue
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Stokes Equations ◽  
Periodic Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Periodic Domain ◽  
Navier Stokes Equations ◽  
Forcing Function ◽  
Connected Set

We treat three problems on a two-dimensional “punctured periodic domain”: we take [Formula: see text], where [Formula: see text] and [Formula: see text] is the closure of an open connected set that is star-shaped with respect to [Formula: see text] and has a [Formula: see text] boundary. We impose periodic boundary conditions on the boundary of [Formula: see text], and Dirichlet boundary conditions on [Formula: see text]. In this setting we consider the Poisson equation, the Stokes equations, and the time-dependent Navier–Stokes equations, all with a fixed forcing function [Formula: see text], and examine the behavior of solutions as [Formula: see text]. In all three cases we show convergence of the solutions to those of the limiting problem, i.e. the problem posed on all of [Formula: see text] with periodic boundary conditions.

Unphysical Frozen States in Monte Carlo Simulation of 2D Ising Model

1998 ◽  
Vol 09 (06) ◽  
pp. 881-886 ◽  
Author(s):  
Andres R. R. Papa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Random Access ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Ising Systems

We show that for two-dimensional square Ising systems unphysical frozen states are obtained by just changing the instant of application of periodic boundary conditions during Monte Carlo simulations. The strange behavior is observed up to sample sizes currently used in literature. The anomalous results appear to be associated to the simultaneous use of type writer updating algorithms; they disappear when random access routines are implemented.

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