273 research outputs found
Hydromagnetic Stability of a Streaming Cylindrical Incompressible Plasma
A dispersion relation is derived and analyzed for the case where the equilibrium velocity of an incompressible, nonresistive, cylindrical plasma has a spiral motion along magnetic field lines. The symmetric hydromagnetic equations are used to derive the plasma hydromagnetic pressure. The dispersion relation is found by matching plasma and outer-region hydromagnetic pressures across a sharp-moving interface. The zeros of the dispersion relation are obtained by a sequence of mappings between three complex planes. The presence of flow introduces overstable modes. For m = 0 the time-divergences are removed by flow. For m = 1 the divergences are enhanced by flow such that the growth rates and oscillation frequencies increase linearly with the flow velocity. The smaller is the wavelength of the disturbance in the z direction, the larger are the overstable eigenvalues
Recommended from our members
Two-Layer Geostrophic Vortex Dynamics. Part 1. Upper-Layer V-States and Merger
We generalize the methods of two-dimensional contour dynamics to study a two-layer rotating fluid that obeys the quasi-geostrophic equations. We consider here only the case of a constant-potential-vorticity lower layer. We derive equilibrium solutions for monopolar (rotating) and dipolar (translating) geostrophic vortices in the upper layer, and compare them with the Euler case. We show that the equivalent barotropic (infinite lower layer) case is a singular limit of the two-layer system. We also investigate the effect of a finite lower layer on the merger of two regions of equal-sign potential vorticity in the upper layer. We discuss our results in the light of the recent laboratory experiments of Griffiths and Hopfinger (1986). The process of filamentation is found to be greatly suppressed for equivalent barotropic dynamics on scales larger than the radius of deformation. We show that the variation of the critical initial distance for merger as a function of the radius of deformation and the ratio of the layers at rest is closely related to the existence of vortex-pair equilibria and their geometrical properties
Recommended from our members
Filamentation of Unstable Vortex Structures via Separatrix Crossing: A Quantitative Estimate of Onset Time
The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction
Recommended from our members
Filamentation of Unstable Vortex Structures via Separatrix Crossing: A Quantitative Estimate of Onset Time
The onset of filamentation for compact vortex structures in two-dimensional incompressible flows is elucidated. An estimate is presented for the filamentation time of an unstably perturbed Kirchhoff ellipse, obtained from a linear analysis of the geometry of the instantaneous corotating streamfunction
The Fermi-Pasta-Ulam recurrence and related phenomena for 1D shallow-water waves in a finite basin
In this work, different regimes of the Fermi-Pasta-Ulam (FPU) recurrence are
simulated numerically for fully nonlinear "one-dimensional" potential water
waves in a finite-depth flume between two vertical walls. In such systems, the
FPU recurrence is closely related to the dynamics of coherent structures
approximately corresponding to solitons of the integrable Boussinesq system. A
simplest periodic solution of the Boussinesq model, describing a single soliton
between the walls, is presented in an analytical form in terms of the elliptic
Jacobi functions. In the numerical experiments, it is observed that depending
on a number of solitons in the flume and their parameters, the FPU recurrence
can occur in a simple or complicated manner, or be practically absent. For
comparison, the nonlinear dynamics of potential water waves over nonuniform
beds is simulated, with initial states taken in the form of several pairs of
colliding solitons. With a mild-slope bed profile, a typical phenomenon in the
course of evolution is appearance of relatively high (rogue) waves, while for
random, relatively short-correlated bed profiles it is either appearance of
tall waves, or formation of sharp crests at moderate-height waves.Comment: revtex4, 10 pages, 33 figure
Discrete Multiscale Analysis: A Biatomic Lattice System
We discuss a discrete approach to the multiscale reductive perturbative
method and apply it to a biatomic chain with a nonlinear interaction between
the atoms. This system is important to describe the time evolution of localized
solitonic excitations. We require that also the reduced equation be discrete.
To do so coherently we need to discretize the time variable to be able to get
asymptotic discrete waves and carry out a discrete multiscale expansion around
them. Our resulting nonlinear equation will be a kind of discrete Nonlinear
Schr\"odinger equation. If we make its continuum limit, we obtain the standard
Nonlinear Schr\"odinger differential equation
q-Breathers and thermalization in acoustic chains with arbitrary nonlinearity index
Nonlinearity shapes lattice dynamics affecting vibrational spectrum,
transport and thermalization phenomena. Beside breathers and solitons one finds
the third fundamental class of nonlinear modes -- -breathers -- periodic
orbits in nonlinear lattices, exponentially localized in the reciprocal mode
space. To date, the studies of -breathers have been confined to the cubic
and quartic nonlinearity in the interaction potential. In this paper we study
the case of arbitrary nonlinearity index in an acoustic chain. We
uncover qualitative difference in the scaling of delocalization and stability
thresholds of -breathers with the system size: there exists a critical index
, below which both thresholds (in nonlinearity strength) tend to
zero, and diverge when above. We also demonstrate that this critical index
value is decisive for the presence or absense of thermalization. For a generic
interaction potential the mode space localized dynamics is determined only by
the three lowest order nonlinear terms in the power series expansion.Comment: 5 pages, 4 figure
Kinetic and Transport Equations for Localized Excitations in Sine-Gordon Model
We analyze the kinetic behavior of localized excitations - solitons,
breathers and phonons - in Sine-Gordon model. Collision integrals for all type
of localized excitation collision processes are constructed, and the kinetic
equations are derived. We analyze the kinetic behavior of localized excitations
- solitons, breathers and phonons - in Sine-Gordon model. Collision integrals
for all type of localized excitation collision processes are constructed, and
the kinetic equations are derived. We prove that the entropy production in the
system of localized excitations takes place only in the case of inhomogeneous
distribution of these excitations in real and phase spaces. We derive transport
equations for soliton and breather densities, temperatures and mean velocities
i.e. show that collisions of localized excitations lead to creation of
diffusion, thermoconductivity and intrinsic friction processes. The diffusion
coefficients for solitons and breathers, describing the diffusion processes in
real and phase spaces, are calculated. It is shown that diffusion processes in
real space are much faster than the diffusion processes in phase space.Comment: 23 pages, latex, no figure
Solitons on the edge of a two-dimensional electron system
We present a study of the excitations of the edge of a two-dimensional
electron droplet in a magnetic field in terms of a contour dynamics formalism.
We find that, beyond the usual linear approximation, the non-linear analysis
yields soliton solutions which correspond to uniformly rotating shapes. These
modes are found from a perturbative treatment of a non-linear eigenvalue
problem, and as solutions to a modified Korteweg-de Vries equation resulting
from a local induction approximation to the nonlocal contour dynamics. We
discuss applications to the edge modes in the quantum Hall effect.Comment: 4 pages, 2 eps figures (included); to appear in Phys. Rev. Letter
- …