NONLINEAR PLASMA OSCILLATIONS WITH TRAPPED ELECTRONS

Using 1958–2002 NCEP/NCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex (PV) in the stratosphere in Northern Hemisphere (NH) winter. This is done by analyzing the Eliassen-Palm (E-P) flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime (WVR) than during the strong polar vortex regime (SVR). On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.

Propagation of stationary planetary waves to the thermosphere at different levels of solar activity

The propagation of nonlinear stationary transverse waves in plasmas is investigated by first solving a relativistic Vlasov equation for the electrons under the influence of a Lorentz force, due to a propagating 4-potential, rigorously and without linearization. The solution, which reduces to a given equilibrium electron velocity distribution function, is then substituted into the Maxwell equations, and a set of wave equations is obtained. While nonlinearity couples the transverse and longitudinal modes except for one special case, propagation of plane-polarized transverse waves in both cold and hot (Maxwellian) plasmas is studied in the quasineutrality approximation. The conditions for the existence of periodic solutions for the nonlinear transverse wave equations indicate that propagation is possible only when the wave velocity exceeds the velocity of light (for plasmas free from external magnetic field). Expressions for waveform and frequency in terms of elliptical integrals are derived. Unlike the case of longitudinal waves, the nonlinear effect on transverse waves is manifested primarily in the reduction of frequency rather than distortion in waveform. Several typical examples of waveform and dispersion characteristics (frequency vs phase velocity) are computed and plotted, ranging from cold to ultrarelativistically hot plasmas. The nonlinear effect is more pronounced at lower electron temperatures.

Sand wave formation by stationary waves

Quasi-stationary Rossby waves with a wavenumber 1 component (wave 1) and eastward-traveling waves with a wavenumber 2 component (wave 2), whose period lies in 10–20 days, have been frequently observed during the late winter and early spring in the stratosphere of the Southern Hemisphere. Temporal variations of these amplitudes are remarkably enhanced during this period.The interaction among wave 1, wave 2, and the zonal mean flow was simulated using a low-order truncated semispectral model. It was assumed that both the stationary wave 1 and eastward-traveling wave 2 are forced at the tropopause. When the wavenumbers from 1 to 3 or 4 were included in the model with use of a reasonable forcing amplitude and the observed monthly mean zonal wind, the following results were obtained. 1) The amplitude of wave 1 reaches a maximum value when the ridge of wave 2 overlaps that of wave 1. 2) The amplitude of wave 2 is negatively correlated with wave 1. 3) In many cases the large amplification of wave 1 occu...

Theory of nonlinear stationary longitudinal waves in relativistic plasmas is treated by solving a relativistic Boltzmann equation without the conventional approximation of linearization. It is proved here that in plasmas of physically reasonable electron velocity distributions, stationary waves of arbitrary amplitude can be propagated and obey a dispersion equation. If the velocity of propagation V is less than the velocity of light c, the amplitude of these waves will generally be limited; if the velocity of wave propagation is greater than c, however, there is no amplitude limitation. The nonlinearity in the Boltzmann equation causes a decrease of frequency of oscillation for a given wave velocity in addition to the distortion in waveform from pure sinusoidal waves. Detailed solutions for plasmas with Maxwellian electron velocity distribution and relativistic electron beams are given. In the former case, a dispersion equation including nonlinear effect is derived through a series expansion to an order higher than that used in the linearized theory. In the latter, a complete analytic solution in terms of elliptical integrals is given. In both cases dispersion characteristics for several parameters are computed and plotted. The agreement between these nonlinear dispersion equations in the limit of vanishing amplitudes and those of the linearized theory published in literature is indicated.

Abstract. We examine the effects of relaxing the assumption of quasi-charge neutrality on the propagation of stationary whistler waves. This necessitates that in the wave frame the equations of motion must be made fully relativistic and when this is done, the correct form of the relativistic dispersive effects is recovered. Our numerical solutions indicate that fully relativistic effects can prevent the formation of oscillitons by virtue of the weakening of dispersive effects required to counterbalance those of nonlinear steepening.

The suppression of stationary planetary waves by internal gravity waves in the mesosphere is treated using a quasi-geostrophic model on a midlatitude beta-plane. The drag forces due to internal gravity waves are parameterized based on the wave breaking assumption recently proposed by Lindzen. In the present model the vertical propagation of internal gravity waves is affected not only by mean zonal wind distribution but also by eastward and northward velocity perturbations associated with stationary planetary waves, viz., the total local velocity. Numerical mulls show that the drag force due to breaking internal gravity waves acts like a Rayleigh friction, and the amplitudes of stationary planetary waves in the mesosphere are much reduced by this effect. Equivalent Rayleigh friction coefficients are also presented.

Propagation of stationary random waves along substructural chains

A β plane model is formulated for the study of vertical propagation of stationary planetary waves in an atmosphere where the zonal wind, the basic state temperature field, and the Newtonian cooling coefficient are all functions of altitude. The differential equation governing a disturbance forced by a specified height field at 30 km and subject to a radiation boundary condition at great heights is solved numerically. Both the negative wind shear on the top side of the model westerly wind jet and the decrease of basic state temperature in the mesosphere are important for wave trapping of the Charney-Drazin type. Wave heat flux is the appropriate measure of wave transmission across any given level in an atmosphere where the zonal wind varies with altitude. For a weak westerly jet in which no trapping occurs the heat flux at 80 km is determined by dissipation over the path length between 30 and 80 km and is sensitive to changes in the relative position of the profiles of zonal wind and Newtonian cooling coefficient. For westerly wind jets with maximum speed of 60 m s−1 or more, characteristic of winter situations, the heat flux at 80 km is controlled by the degree of wave trapping and depends only slightly on dissipation over the path length.

Stationary random waves propagation in 3D viscoelastic stratified solid

It is important to clarify how the propagation of a longitudinal wave in a visco-elastic bar is affected by the lateral inertia. This paper purports to clarify the coupling effect of the viscous force and the lateral inertia force on the propagation of the wave, especially in the vicinity of the wave front. It is assumed that the visco-elastic material is represented by a Voigt model. The equation of motion of the bar, in which the effect of the lateral inertia is taken into consideration, is obtained with Hamilton's principle. The solutions of the equation are presented for two cases. One is the case of one end of the bar being impacted at a constant velocity and the other is the case of the stress or strain at the impacted end being kept constant.

Propagation of longitudinal viscoelastic stress waves in a fluid saturated Voigt porous medium

Propagation of Love waves in a transversely isotropic poroelastic layer bounded between two compressible viscous liquids is presented. The equations of motion in a transversely isotropic poroelastic solid are formulated in the framework of Biot’s theory. A closed-form solution for the propagation of Love waves is obtained in a transversely isotropic poroelastic layer. The complex frequency equation for phase velocity and attenuation of Love waves is derived for a transversely isotropic poroelastic layer when it is bounded between two viscous liquids and the results are compared with that of the poroelastic layer. The effect of viscous liquids on the propagation of Love waves is discussed. It is observed that the presence of viscous liquids decreases phase velocity in both transversely isotropic poroelastic layer and poroelastic layer. Results related to the case without viscous liquids have been compared with some of the earlier results and comparison shows good agreement.

Approximately 2 yr (2010–2011) of continuous seismic records from a subset of the Antarctic component of the Polar Earth Observing Network (POLENET-ANET) seismic network deployed in West Antarctica are used to compute the nine components of the correlation tensor between each pair of stations in the network. Rayleigh wave velocity information from the vertical and radial components was extracted in the form of group and phase velocity dispersion curves, whereas the transverse component provided complimentary Love wave velocity information. The multicomponent Rayleigh wave measurements (ZZ, RR, ZR, and RZ) were averaged and used to infer the measurement uncertainties. The Rayleigh and Love wave group and phase velocities were then regionalized in space using a 2D deterministic tomography. A transect that spans the West Antarctic rift system was extracted from the tomography at individual periods between 7 and 60 s for the four types of surface wave velocities (i.e., Rayleigh and Love phase and group velocities). A transdimensional Bayesian joint inversion algorithm was used to invert these four datasets for a 1D model of isotropic shear-wave velocity versus depth at each point along the transect. In this way, surface wave dispersion curves from multicomponent noise correlations were used to build a 2D isotropic shear-wave velocity model down to ∼55 km depth. In this model, the top of the large low-velocity zone beneath Marie Byrd Land was imaged (up to a 5% decrease in velocity at ∼50 km depth), which provides further evidence for a mantle hot spot beneath the crust that supports the high topography in this region. We also observed a large velocity contrast in the lower crust beneath Marie Byrd Land at a depth where previous long-period seismicity has been observed. This strong contrast occurs more shallow than in previous crustal models, which compared to our model identify a deeper Moho (∼5–10 km deeper) beneath Marie Byrd Land. This new model has implications for interpreting earthquake locations in this region and perhaps necessitates that we revisit past hypocenter estimation studies using updated velocity models for the region.