Non-conserved Quantity Research Articles

The eddy transport of nonconserved trace species derived from satellite data

The two‐dimensional transport of conserved tracers by planetary waves results from two processes: dispersion and organized nondispersive advection. For nonconserved quantities an additional transport mechanism is the chemical eddy effect. This paper is concerned with the latter, which depends on spatial variation in the production and loss of a trace species and can occur in the absence of dispersion. A simple and commonly used form of representing the eddy flux is as a transport matrix multiplied by the mean gradient. Such a matrix is often called a diffusion matrix, although with off‐diagonal components it can represent transport across, as well as parallel to, the mean gradient. The two‐dimensional transport matrix in this form can, with the assumptions of linearity, stationarity, and a simple form of production and loss, be derived from the eddy tracer continuity equation. We have computed the chemical eddy contribution to the components of the matrix from LIMS satellite observations, using specified photochemical damping time scales. The dominant (Kyy) component of the transport matrices for several winter months are given for ozone, nitric acid, and quasi‐geostrophic potential vorticity (PV). The parameterized transports for these three species are compared with the “exact” transports, computed directly from the eddy LIMS data. The results indicate that the chemical eddy effect can account for most of the observed ozone transport in early winter, decreasing to less than half in late winter. The agreement between the parameterized and observed nitric acid and PV fluxes is not as good. In the lower stratosphere the observed eddy fluxes (the “exact” fluxes) for ozone and nitric acid exceed the parameterized chemical eddy fluxes by a substantial margin. This may be because dispersion, which is not included in the parameterization, is the primary mechanism for eddy transport in that part of the atmosphere. Other reasons that might explain the discrepancies between the parameterized chemical eddy fluxes and the observed fluxes are the inability of a simple flux‐gradient relation to characterize the transport, the approximations made in the calculation of the transport matrix, the inaccuracies in the specified damping times, or the problems with the observed (“exact”) eddy fluxes, which can be sensitive to errors in the wave data.

Hydrodynamic time correlation functions for a Lennard-Jones fluid.

Four time correlation functions of a Lennard-Jones (LJ) fluid at a reduced density of ${n}^{\mathrm{*}}$=n${\ensuremath{\sigma}}_{\mathrm{LJ}{}^{3}=0.845}$ and a reduced temperature of ${T}^{\mathrm{*}}$=${k}_{\mathrm{B}\mathrm{T}/{\ensuremath{\varepsilon}}_{\mathrm{LJ}=1.71}}$ have been determined numerically using molecular dynamics. They were computed as a function of wave number k for reduced wave numbers 0\ensuremath{\le}k${\ensuremath{\sigma}}_{\mathrm{LJ}l15}$ and for reduced times 0\ensuremath{\le}t/${\ensuremath{\tau}}_{\ensuremath{\sigma}}$2.6, where ${\ensuremath{\tau}}_{\ensuremath{\sigma}}$ is an average collision time. From these four, all 25 correlation functions can be derived between three conserved and two nonconserved quantities: the number density, energy density, longitudinal velocity, momentum flux, and energy flux, respectively. They can be fitted consistently by five exponentials that correspond to the five eigenmodes of a 5\ifmmode\times\else\texttimes\fi{}5 k-dependent, but not t-dependent, matrix based on the above-mentioned five quantities. Three of these eigenmodes are extensions of the usual hydrodynamic modes and suffice to describe the density-density correlation function alone. A comparison with previous work on Lennard-Jones, noble-gas, and hard-sphere fluids is made.

Conservative trees have universal segment measure distributions

It is shown that “conservative” trees, which posses some measure that is conserved across branchpoints, generate a distribution of the measure over the segments that is approximately hyperbolic. When the trees become large, the shape of the distribution becomes independent of drastic changes in the asymmetry of the branching, in the measure distribution of the root segments, or in the valency of the branchpoints. In contrast to the invariant shape, the amplitude of the distribution does depend on the above parameters, but it can be computed numerically or, in many important cases, analytically. These results can be used to compute the distribution of related (but nonconserved) quantities of the trees, to solve the scaling problem of large trees, and to gain insight into the relations between local and global consequences of dendritic growth.

Anomalous transport coefficients in a turbulent plasma

A general self-consistent framework is developed for the calculation of transport coefficients in a collisionless, weakly turbulent plasma. These coefficients characterize the response to a perturbation away from a quasi-steady turbulent state, which is assumed to exist as a result of the stabilization of the linear instabilities. It is shown that a purely hydrodynamical description does not exist for plasmas: the macroscopic picture must include non-conserved quantities, which lead to the plasmadynamical (or ‘two-fluid’) picture of the system. The number of independent transport coefficients, necessary for the macroscopic characterization of the plasma, is correspondingly increased as compared with a two- component mixture of two ordinary fluids. The typical turbulent contributions to the transport coefficients are clearly exhibited.

Dynamic Long-Range Forces andZBranches at Phase Transitions

We show that the critical dynamics of dense pseudospin systems interacting via retarded long-range forces (e.g., acoustic phonons) gives rise to the appearance of a $Z$ branch in the central-peak dispersion which should be observable by light-scattering techniques. The evolution of an initially nonconserved quantity towards a hydrodynamic regime leads to liquidlike behavior of the solid for a range of wave vectors.