On anomalous diffusion in a plasma in velocity space

The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in momentum space. The generalized Fokker-Planck equation for description of diffusion (in momentum space) of particles (ions, grains etc.) in a stochastic system of light particles (electrons, or electrons and ions, respectively) is applied to the evolution of the momentum particle distribution in a plasma. In a plasma the developed approach is also applicable to the diffusion of particles with an arbitrary mass relation, due to the small characteristic momentum transfer. The cases of an exponentially decreasing in momentum space (including the Boltzmann-like) kernel in the PT-function, as well as the more general kernels, which create the anomalous diffusion in velocity space due to the long tail in the PT-function, are considered. Effective friction and diffusion coefficients for plasma-like systems are found.Comment: 18 pages, no figure

The Okubo-Weiss Criteria in Two-Dimensional Hydrodynamic and Magnetohydrodynamic Flows

The Okubo [2]-Weiss [3] criterion is recast by using the 2D hydrodynamic Beltrami condition (Shivamoggi et al.[13]) that approximates the slow flow-variation ansatz imposed in its derivation. This turns out to provide an interesting interpretation of the Okubo-Weiss criterion very logically in terms of the topological properties of the underlying vorticity manifold. These developments are then extended to 2D quasi-geostrophic flows (via the potential divorticity framework), magnetohydrodynamic flows and electron magnetohydrodynamic flows (via the generalized magnetic flux framework) and the Okubo-Weiss criteria for these cases are considered.Comment: 13 page

Laboratory experiments on multipolar vortices in a rotating fluid

The instability properties of isolated monopolar vortices have been investigated experimentally and the corresponding multipolar quasisteady states have been compared with semianalytical vorticity-distributed solutions to the Euler equations in two dimensions. A novel experimental technique was introduced to generate unstable monopolar vortices whose nonlinear evolution resulted in the formation of multipolar vortices. Dye-visualization and particle imaging techniques revealed the existence of tripolar, quadrupolar, and pentapolar vortices. Also evidence was found of the onset of hexapolar and heptapolar vortices. The observed multipolar vortices were found to be unstable and generally broke up into multipolar vortices of lesser complexity. The characteristic flow properties of the quadrupolar vortex were in close agreement with the semianalytical model solutions. Higher-order multipolar vortices were observed to be susceptible to strong inertial oscillations. © 2010 American Institute of Physic

Observations of fronts in the North Sea

The persistent presence of a cold bottom layer and associated bottom fronts was observed in the stratified central North Sea during an observational program in 1981 and 1982. Moored instruments, capturing a snap-shot of such a front while it was advected past these moorings, revealed the simultaneous presence of a well-defined frontal jet with velocities up to 15 cm s−1. The Coriolis force acting on this jet appeared to be in geostrophic balance with the locally intense pressure gradient forces. Hydrographic surveys revealed the presence of both small-scale and large-scale baroclinic waves on this front, the latter reaching wavelengths of 5–10 internal Ross by radii. Some evidence for a weak secondary circulation in the cross-frontal plane was obtained from the observed deformation of isolines near the front

Diffusion in a Time-dependent External Field

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced in [1,2]. We consider the case of the quasi Fokker-Planck approximation, when the probability transition function for diffusion (PTD-function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A new type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.Comment: 18 pages, no figure

Joint inversion for global isotropic and radially anisotropic mantle structure including crustal thickness perturbations

We present a new global whole‐mantle model of isotropic and radially anisotropic S velocity structure (SGLOBE‐rani) based on ~43,000,000 surface wave and ~420,000 body wave travel time measurements, which is expanded in spherical harmonic basis functions up to degree 35. We incorporate crustal thickness perturbations as model parameters in the inversions to properly consider crustal effects and suppress the leakage of crustal structure into mantle structure. This is possible since we utilize short‐period group‐velocity data with a period range down to 16 s, which are strongly sensitive to the crust. The isotropic S velocity model shares common features with previous global S velocity models and shows excellent consistency with several high‐resolution upper mantle models. Our anisotropic model also agrees well with previous regional studies. Anomalous features in our anisotropic model are faster SV velocity anomalies along subduction zones at transition zone depths and faster SH velocity beneath slabs in the lower mantle. The derived crustal thickness perturbations also bring potentially important information about the crustal thickness beneath oceanic crusts, which has been difficult to constrain due to poor access compared with continental crusts.Key PointsWe used a massive and varied data set to constrain radially anisotropic mantle structureWe include crustal thickness perturbations as model parametersWe observe faster SV velocity along subduction slabs in the transition zonePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/112272/1/jgrb51168.pd