Wave Normal Surfaces Research Articles

Alfvén gravity waves in viscous solar plasma

We study the propagation and dissipation of Alfvén gravity waves in the solar corona, considering viscosity as a damping mechanism, and derive a general dispersion relation for Alfvén gravity waves under WKB and Boussinesq approximation. We find that in the presence of viscosity, the wave normal surfaces do not differ significantly from the results obtained in an ideal MHD. From dissipation point of view, we find that for the wave frequency less than the Brunt–Väisälä frequency (i.e., ω¯<1) there are two types of damping, one is strong damping when LD∼λ and the other is weak damping when LD≫λ. For the wave frequencies greater than the Brunt–Väisälä frequency (i.e., ω¯>1), however, we get only weak damped oscillations. Thus, Brunt–Väisälä frequency separates regimes of wave frequency in which damping is weak or strong.

Waves in the Hall-magnetohydrodynamics model

The three magnetohydrodynamic (MHD) waves are followed as they transition under the influence of an increasingly strong Hall current effect to the characteristic waves of the Hall-MHD model. Also followed are the wave normal surfaces and the ray surfaces (approximating wave fronts) of these waves. The changes in the nature of the waves are found to be considerable, and are described both analytically and numerically. Most notably, the incompressible MHD shear Alfvén wave becomes a compressible fluid-dynamical wave with negligible perturbation of the electromagnetic field, while the two MHD compressible waves become incompressible, the fast wave becoming mostly electromagnetic and the slow wave becoming mostly fluid-dynamical.

Valve Like Critical Levels for Internal Gravity Waves in Compressible Shear Flows

The propagation of internal gravity waves in isothermal compressible shear (both vertical and horizontal) flows ar investigated. In slowly-varying shear flows the local dispersion relation is used to study the wave-normal surfaces and the possible types of ray trajectory. Of the seven singular levels for the wave equation only two offer resistance to wave propagation and these two exhibit valve like behaviour. It is observed that though the effect of compressibility does not increase the number of critical levels it modifies the position of the critical levels and the attenuation of waves at the critical levels. In a slowly varying medium it is observed that only these two critical levels are present and strictly behave like valves. In a full wave treatment it is demonstrated that compressibility decreases the amount of attenuation of each wave ils critical level.

Linear and nonlinear modes in nonrelativistic electron-positron plasmas.

A comprehensive two-fluid model is developed for collective modes in a nonrelativistic electron-positron plasma. Longitudinal and transverse electrostatic and electromagnetic modes, both in the presence and absence of a magnetic field, are studied. Wave properties are discussed in terms of dispersion relations, wave normal surfaces, and cylindrical mirror analyzer clemmow-Mullaly-Allis diagrams. The results are extended to include the two-stream instability and ion acoustic solitary waves. For the two-stream instability, a similar result is found as in the electron-ion plasma. For ion acoustic solitary waves, only subsonic solutions are found to exist. Furthermore, their width is proportional to their amplitude, unlike the electron-ion plasma case, where the speed is proportional to the amplitude.

Stationary MHD waves modified by hall current coupling

The extension of the MHD equations to include Hall current effects couples the Alfvén and magnetoacoustic modes and introduces dispersion into the already anisotropic nature of the wave properties. We examine the structure of the system of stationary waves generated by the inductive interaction between a conducting body and a magnetized plasma in relative motion. The geometry of the wave normal surfaces in the frame of the body are particularly useful in constructing the wavecrests associated with the far field disturbance. In the special limit of a cold compressible flow we investigate the topology of these surfaces and the wavecrests surfaces.

Internal waves in a horizontally inhomogeneous flow

The effect of horizontally inhomogeneous flows on internal wave propagation in a stratified ocean with a constant Brunt-Väisälä frequency is analysed. Dispersion characteristics of internal waves in a moving fluid and kinematics of wave packets in smoothly inhomogeneous flows are considered using wave-normal surfaces. It is shown that internal-wave blocking and short-wave transformation may occur in longitudinally inhomogeneous flows. For parallel flows internal-wave trapping is possible in the vicinity of the limiting layer where the wave frequency in the locally comoving frame of reference coincides with the Brunt-Väisälä frequency. Internal-wave trapping also takes place in jet-type flows in the vicinity of the flow-velocity maximum. WKB solutions of the equation describing internal-wave propagation in a parallel horizontally inhomogeneous flow in the linear approximation are obtained. Singular points of this equation and the related effect of internal-wave amplification (overreflection) under the action of the flow are investigated. The spectrum and the growth rate of internal-wave localized modes in a jet-type flow are obtained.

On the propagation, reflexion, transmission and stability of atmospheric Rossby-gravity waves on a beta-plane in the presence of latitudinally sheared zonal flows

The propagation properties of Rossby-gravity waves in an isothermal atmosphere on a beta-plane are investigated in the presence of a latitudinally sheared zonal now. The perturbation equation is found to possess seven regular singularities provided the fluid is non -Boussinesq, and only five for Boussinesq fluids. In slowly varying shear a local dispersion relation is derived and used to study the wave normal surfaces and ray trajectories. The cross sections of the wave normal surfaces in horizontal planes possess three critical latitudes occurring where the intrinsic frequency w takes the values 0, + N ,where N is the Brunt—Väisällä frequency. The former is the usual Ross by wave critical latitude (R.w.c.l.) and the latter are essentially gravity wave critical latitudes (g.w.c.l.). Waves can propagate only on one side of a R.w.c.l. while propagation is possible on both sides of a g.w.c.l. provided the vertical wavenumber, m , there is real and non-zero. Also for real values of m and provided the atmosphere is non -Boussinesq the g.w.c.l. exhibits valve-like behaviour. Such valve behaviour is shown to be responsible for aiding high frequency waves (i.e. gravity waves) to penetrate jet-like wind streams and may facilitate the transfer of energy and momentum across latitudes. The full wave treatment shows that the system possesses a wave-invariant which has a simple physical interpretation only when m is real in which case it represents the conservation of the total northward wave energy flux. The invariant is used, together with the legitimate solutions near the critical latitudes, to study the influence of each of the critical latitudes on the intensity of the wave. It is found that the R.w.c.l. can be associated with energy absorption or emission, depending on certain specified conditions, but the g.w.c.l. is always associated with energy absorption although the amount of energy absorbed depends crucially on whether m is real or imaginary. The reflexion, transmission and stability of atmospheric waves by a finite shear, thickness L , are also studied, by using a full wave treatment in the presence of general flow profiles. For smoothly varying shear flows the use of the wave-invariant yields a relation between the reflexion and transmission coefficients. It is then deduced that in the absence of critical latitudes within the shear over-reflexion (i.e. the amplitude of the reflected wave exceeds that of the incident one) is possible only for real values of m in which case planetary waves incident on the shear are transmitted as gravity waves on the far side of the shear. Such over-reflecting régimes are, however, due to the presence of natural modes of the system. Moreover, it is found possible to isolate certain situations in which the R.w.c.l. within the shear enhances over-reflexion. The situation when the shear is linear and thin is studied analytically. Explicit expressions for the reflexion and transmission coefficients are obtained. It is then shown that over-reflexion is present in a stable shear in which case the energy is extracted from the mean flow primarily at the R.w.c.l. The influence of a general flow on the R.w.c.l. is also studied in a special case to show that the reflectivity and stability properties of the thin shear are strongly dependent on the type of shear present. Comparison of these results with those obtained for the corresponding vortex sheet show wide disagreement. A general criterion for determining whether a vortex sheet will adequately represent the corresponding thin shear layer is offered in the final section.

On the propagation of hydromagnetic- inertial-gravity waves in magnetic-velocity shear

Abstract The propagation properties of hydromagnetic-inertial-gravity waves in a Boussinesq fluid are studied for two representative models. One model is characterised by horizontal rotation, magnetic field and flow, the magnetic field and flow being perpendicular and vertically sheared. In the other model both magnetic field and rotation are vertical and uniform but the flow is horizontal and latitudinally sheared. In a slowly varying shear, when the WKBJ approximation is applicable, the wave normal surfaces for different values of magnetic field and flow are used to construct the various types of ray trajectories. In a full wave treatment, in which variations in the basic state are taken into account, it is found that the total wave energy flux (or the wave action flux), , in the direction of the shear is constant except at critical layers (i.e. singularities predicted by the WKBJ treatment), where it jumps from one constant value to another. The invariance of  is used to show that MAC-waves can be ov...

Waves in the solar atmosphere. IV - Magneto-gravity and acoustic-gravity modes

We consider the properties of waves in a stratified, conducting atmosphere under the influence of an applied magnetic field. Wave normal surfaces are exhibited for acoustic-gravity and magneto-gravity waves, and the propagation of these modes is compared. Subject headings: atmospheres, solar hydromagnetics solar atmospheric motions

Interaction of Hydromagnetic Waves with Hydromagnetic Shocks

The problem of the interaction of small-amplitude plane hydromagnetic waves with plane, oblique hydromagnetic shocks is treated. When the perturbations of the flow field on either side of the shock are expanded in terms of incident and diverging eigenwaves, the linearized de Hoffmann-Teller relations across the shock yield a system of equations for the amplitudes of the diverging waves and the motion of the perturbed shock. The shock motion and the amplitudes of the diverging waves as a function of the amplitude and direction of any given incident wave are found using this system of seven linear, inhomogeneous equations, along with Snell's laws. Snell's laws are interpreted graphically by making use of the geometry of the hydromagnetic wave normal surfaces in a moving medium. By considering some special cases it is shown that hydromagnetic waves are amplified on passage through a fast shock. The turbulent character of the region between the bow shock of the earth and the magnetopause may be due in part to the amplification of turbulent waves in the solar wind on passing through the bow shock.

Dispersion Relation in Compressible Plasma

The Maxwell‐Euler equations are reformulated through linear operator and generalized transform techniques into an equivalent matrix integral equation. The dispersion relation is obtained from the kernel of this integral equation for a homogeneous, anistropic, and compressible electron‐fluid plasma. Some illuminating graphs showing the propagation constants as functions of the normalized plasma frequency are developed analytically to study the dispersion relation. These kinds of graphs are usually plotted from the limited amount of numerical data available in the literature (e.g., Ginzburg, 1961). Clemmow‐Mullaly‐Allis type of diagram for the compressible plasma is sketched from these graphs. Actually, dispersion curves are obtained which are inversely related to the wave normal surfaces calculated by Allis, Buchsbaum and Bers (1963). A proper terminology for the three types of waves involved in an electron plasma is also introduced.

Čerenkov Radiation Spectra for a Cold Magnetoactive Plasma

The macroscopic theories of Eidman and Allis concerning the radiation from an electron moving in a cold and homogeneous magnetoactive plasma and the topology of wave normal surfaces respectively are combined to yield a rather simple picture of a generalized Cherenkov radiation spectrum. (N.W.R.)